Veröffentlichungen "Grüne, Lars"

2024

Schiller, Julian D. ; Grüne, Lars ; Müller, Matthias A.:
Optimal state estimation : Turnpike analysis and performance results.
Bayreuth ; Hannover , 2024 . - 8 S.
DOI: https://doi.org/10.48550/arXiv.2409.14873

Sperl, Mario ; Mysliwitz, Jonas ; Grüne, Lars:
Approximation of Separable Control Lyapunov Functions with Neural Networks.
Bayreuth , 2024 . - 11 S.
DOI: https://doi.org/10.15495/EPub_UBT_00007857

Bold, Lea ; Grüne, Lars ; Schaller, Manuel ; Worthmann, Karl:
Data-driven MPC with stability guarantees using extended dynamic mode decomposition.
In: IEEE Transactions on Automatic Control. Bd. Online First (Juli 2024) . - S. 1-8.
ISSN 1558-2523
DOI: https://doi.org/10.1109/TAC.2024.3431169

Schießl, Jonas ; Ou, Ruchuan ; Faulwasser, Timm ; Baumann, Michael Heinrich ; Grüne, Lars:
Near-optimal performance of stochastic economic MPC.
Bayreuth , 2024 . - 7 S.
DOI: https://doi.org/10.48550/arXiv.2403.15159

Angeli, David ; Grüne, Lars:
Dissipativity in infinite horizon optimal control and dynamic programming.
In: Applied Mathematics and Optimization. Bd. 89 (2024) . - 42.
ISSN 1432-0606
DOI: https://doi.org/10.1007/s00245-024-10103-y

Pioch, Kilian ; Kriecherbauer, Thomas ; Margaliot, Michael ; Grüne, Lars:
Model order reduction for the TASEP Master equation.
In: IFAC-PapersOnLine. Bd. 58 (2024) Heft 17 . - S. 109-114.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2024.10.122

Katz, Rami ; Kriecherbauer, Thomas ; Grüne, Lars ; Margaliot, Michael:
On the gain of entrainment in a class of weakly contractive bilinear control systems.
In: SIAM Journal on Control and Optimization. Bd. 62 (2024) Heft 5 . - S. 2723-2749.
ISSN 1095-7138
DOI: https://doi.org/10.1137/23M1585714

Braun, Philipp ; Faulwasser, Timm ; Grüne, Lars ; Kellett, Christopher M. ; Semmler, Willi ; Weller, Steven R.:
On the social cost of carbon and discounting in the DICE model.
In: AIMS Environmental Science. Bd. 11 (2024) Heft 3 . - S. 471-495.
ISSN 2372-0352
DOI: https://doi.org/10.3934/environsci.2024024

2023

Schießl, Jonas ; Ou, Ruchuan ; Faulwasser, Timm ; Baumann, Michael Heinrich ; Grüne, Lars:
Pathwise turnpike and dissipativity results for discrete-time stochastic linear-quadratic optimal control problems.
In: 2023 62nd IEEE Conference on Decision and Control (CDC). - Singapore, Singapore , 2023 . - S. 2790-2795
ISBN 979-8-3503-0124-3
DOI: https://doi.org/10.1109/CDC49753.2023.10384081

Sperl, Mario ; Saluzzi, Luca ; Grüne, Lars ; Kalise, Dante:
Separable approximations of optimal value functions under a decaying sensitivity assumption.
In: 62nd IEEE Conference on Decision and Control (CDC) 2023. - Singapore, Singapore , 2023 . - S. 259-264
DOI: https://doi.org/10.1109/CDC49753.2023.10383497

Ou, Ruchuan ; Schießl, Jonas ; Baumann, Michael Heinrich ; Grüne, Lars ; Faulwasser, Timm:
A Polynomial Chaos Approach to Stochastic LQ Optimal Control: Error Bounds and Infinite-Horizon Results.
Dortmund ; Bayreuth , 2023
DOI: https://doi.org/10.48550/arXiv.2311.17596

Schießl, Jonas ; Ou, Ruchuan ; Faulwasser, Timm ; Baumann, Michael Heinrich ; Grüne, Lars:
Turnpike and dissipativity in generalized discrete-time stochastic linear-quadratic optimal control.
Bayreuth , 2023
DOI: https://doi.org/10.48550/arXiv.2309.05422

Ernst, Andreas ; Grüne, Lars ; Rieger, Janosch:
A linear programming approach to approximating the infinite time reachable set of strictly stable linear control systems.
In: Journal of Global Optimization. Bd. 86 (2023) . - S. 521-543.
ISSN 1573-2916
DOI: https://doi.org/10.1007/s10898-022-01261-w

Baumann, Michael Heinrich ; Baumann, Michaela ; Grüne, Lars ; Herz, Bernhard:
Market Structure and Instability Artifacts in Heterogeneous Agent Models: Lessons from Implicit Discretizations of Stiff Equations.
In: Computational Economics. Bd. 62 (2023) . - S. 855-890.
ISSN 1572-9974
DOI: https://doi.org/10.1007/s10614-022-10285-z

Braun, Philipp ; Grüne, Lars ; Kellett, Christopher ; Worthmann, Karl:
Model Predictive Control and Distributed Optimization in Smart Grid Applications.
In: Fathi, Michel ; Zio, Enrico ; Pardalos, Panos M. (Hrsg.): Handbook of Smart Energy Systems. - Cham : Springer , 2023 . - 25 S.
ISBN 978-3-030-72322-4
DOI: https://doi.org/10.1007/978-3-030-72322-4_163-1

Eichfelder, Gabriele ; Grüne, Lars ; Krügel, Lisa ; Schießl, Jonas:
Relaxed dissipativity assumptions and a simplified algorithm for multiobjective MPC.
In: Computational Optimization and Applications. Bd. 86 (2023) . - S. 1081-1116.
ISSN 0926-6003
DOI: https://doi.org/10.1007/s10589-022-00398-4

Köhler, Johannes ; Zeilinger, Melanie ; Grüne, Lars:
Stability and performance analysis of NMPC : Detectable stage costs and general terminal costs.
In: IEEE Transactions on Automatic Control. Bd. 68 (2023) Heft 10 . - S. 6114-6129.
ISSN 1558-2523
DOI: https://doi.org/10.1109/TAC.2023.3235244

Grüne, Lars ; Sperl, Mario:
Examples for separable control Lyapunov functions and their neural network approximation.
In: IFAC-PapersOnLine. Bd. 56 (2023) Heft 1 . - S. 19-24.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2023.02.004

Krügel, Lisa ; Faulwasser, Timm ; Grüne, Lars:
Local Turnpike Properties in Finite Horizon Optimal Control.
In: 62nd IEEE Conference on Decision and Control (CDC) 2023. - Singapore , 2023 . - S. 5273-5278
DOI: https://doi.org/10.1109/CDC49753.2023.10383850

Ofir, Ron ; Kriecherbauer, Thomas ; Grüne, Lars ; Margaliot, Michael:
On the gain of entrainment in the n-dimensional ribosome flow model.
In: Interface : Journal of the Royal Society. Bd. 20 (2023) Heft 199 . - 20220763.
ISSN 1742-5662
DOI: https://doi.org/10.1098/rsif.2022.0763

Schießl, Jonas ; Baumann, Michael Heinrich ; Faulwasser, Timm ; Grüne, Lars:
On the relationship between stochastic turnpike and dissipativity notions.
Bayreuth , 2023
DOI: https://doi.org/10.48550/arXiv.2311.07281

Köhler, Matthias ; Krügel, Lisa ; Grüne, Lars ; Müller, Matthias A. ; Allgöwer, Frank:
Transient Performance of MPC for Tracking.
In: IEEE Control Systems Letters. Bd. 7 (2023) . - S. 2545-2550.
ISSN 2475-1456
DOI: https://doi.org/10.1109/LCSYS.2023.3287798

2022

25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022.
Hrsg.: Baumann, Michael Heinrich ; Grüne, Lars ; Jacob, Birgit ; Worthmann, Karl
IFAC-PapersOnLine. Bd. 55 (2022) Heft 30 . - 516 S.
ISSN 2405-8963

Grüne, Lars:
Dissipativity and optimal control : Examining the Turnpike Phenomenon.
In: IEEE Control Systems Magazine. Bd. 42 (2022) Heft 2 . - S. 74-87.
ISSN 1066-033X
DOI: https://doi.org/10.1109/MCS.2021.3139724

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Efficient Model Predictive Control for parabolic PDEs with goal oriented error estimation.
In: SIAM Journal on Scientific Computing. Bd. 44 (2022) Heft 1 . - A471-A500.
ISSN 1095-7197
DOI: https://doi.org/10.1137/20M1356324

Grüne, Lars ; Meurer, Thomas:
Finite-dimensional output stabilization for a class of linear distributed parameter systems : A small-gain approach.
In: Systems & Control Letters. Bd. 164 (2022) . - 105237.
ISSN 1872-7956
DOI: https://doi.org/10.1016/j.sysconle.2022.105237

Faulwasser, Timm ; Grüne, Lars ; Humaloja, Jukka-Pekka ; Schaller, Manuel:
The interval turnpike property for adjoints.
In: Pure and Applied Functional Analysis. Bd. 7 (2022) Heft 4 . - S. 1187-1207.
ISSN 2189-3756

Grüne, Lars ; Krügel, Lisa ; Müller, Matthias A.:
Multiobjective strict dissipativity via a weighted sum approach.
In: Systems & Control Letters. Bd. 170 (2022) . - 105396.
ISSN 1872-7956
DOI: https://doi.org/10.1016/j.sysconle.2022.105396

Andrej, Julian ; Grüne, Lars ; Mechelli, Luca ; Meurer, Thomas ; Pirkelmann, Simon ; Volkwein, Stefan:
Parallelized POD-based Suboptimal Economic Model Predictive Control of a State-Constrained Boussinesq approximation.
In: Computers & Mathematics with Applications. Bd. 116 (2022) . - S. 71-81.
ISSN 0898-1221
DOI: https://doi.org/10.1016/j.camwa.2021.09.004

Grüne, Lars ; Philipp, Friedrich ; Schaller, Manuel:
Strict dissipativity for generalized linear-quadratic problems in infinite dimensions.
In: IFAC-PapersOnLine. Bd. 55 (2022) Heft 30 . - S. 311-316.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2022.11.071

Faulwasser, Timm ; Grüne, Lars:
Turnpike Properties in Optimal Control : An Overview of Discrete-Time and Continuous-Time Results.
In: Trélat, Emmanuel ; Zuazua, Enrique (Hrsg.): Handbook of Numerical Analysis : Numerical Control. Part A. - Amsterdam : North-Holland , 2022 . - S. 367-400 . - (Handbook of Numerical Analysis ; 23 )
DOI: https://doi.org/10.1016/bs.hna.2021.12.011

Extended Abstracts presented at the 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022 : held 12-16 September 2022 in Bayreuth, Germany.
Hrsg.: Baumann, Michael Heinrich ; Grüne, Lars ; Jacob, Birgit ; Worthmann, Karl . 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022
Bayreuth , 2022 . - 815 S.

DOI: https://doi.org/10.15495/EPub_UBT_00006809

2021

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs.
In: ESAIM : Control, Optimisation and Calculus of Variations. Bd. 27 (2021) . - 56.
ISSN 1262-3377
DOI: https://doi.org/10.1051/cocv/2021030

Wu, Chengshuai ; Grüne, Lars ; Kriecherbauer, Thomas ; Margaliot, Michael:
Behavior of totally positive differential systems near a periodic solution.
In: Proceedings of the 2021 IEEE Conference on Decision and Control (CDC). - Austin, Texas, USA , 2021 . - S. 3160-3165
DOI: https://doi.org/10.1109/CDC45484.2021.9683061

Grüne, Lars:
Computing Lyapunov functions using deep neural networks.
In: Journal of Computational Dynamics. Bd. 8 (2021) Heft 2 . - S. 131-152.
ISSN 2158-2491
DOI: https://doi.org/10.3934/jcd.2021006

Grüne, Lars ; Muff, David ; Schaller, Manuel:
Conditions for strict dissipativity of infinite-dimensional generalized linear-quadratic problems.
In: IFAC-PapersOnLine. Bd. 54 (2021) Heft 19 . - S. 302-306.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2021.11.094

Baumann, Michael Heinrich ; Grüne, Lars:
Does the effort of Monte Carlo pay off? : A case study on stochastic MPC.
In: IFAC-PapersOnLine. Bd. 54 (2021) Heft 6 . - S. 70-75.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2021.08.526

Braun, Philipp ; Grüne, Lars ; Kellett, Christopher M.:
(In-)Stability of Differential Inclusions : Notions, Equivalences, and Lyapunov-like Characterizations.
Cham : Springer , 2021 . - IX, 116 S. - (Springer Briefs in Mathematics )
ISBN 978-3-030-76316-9

DOI: https://doi.org/10.1007/978-3-030-76317-6

Faulwasser, Timm ; Grüne, Lars ; Humaloja, Jukka-Pekka ; Schaller, Manuel:
Inferring the adjoint turnpike property from the primal turnpike property.
In: Proceedings of the 2021 IEEE Conference on Decision and Control (CDC). - Austin, Texas, USA , 2021 . - S. 2578-2583
DOI: https://doi.org/10.1109/CDC45484.2021.9683079

Grüne, Lars ; Krügel, Lisa:
Local turnpike analysis using local dissipativity for discrete time discounted optimal control.
In: Applied Mathematics and Optimization. Bd. 84 (2021) Heft Suppl. 2 . - S. 1585-1606.
ISSN 1432-0606
DOI: https://doi.org/10.1007/s00245-021-09805-4

Hahn, Markus ; Grüne, Lars ; Plank, Christian ; Katzer, Felix ; Rüther, Tom ; Jahn, Leonard ; Danzer, Michael A.:
Model predictive fast charging control by means of a real-time discrete electrochemical model.
In: Journal of Energy Storage. Bd. 42 (2021) . - 103056.
ISSN 2352-152X
DOI: https://doi.org/10.1016/j.est.2021.103056

Grüne, Lars ; Guglielmi, Roberto:
On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems.
In: Mathematical Control and Related Fields. Bd. 11 (2021) Heft 1 . - S. 169-188.
ISSN 2156-8472
DOI: https://doi.org/10.3934/mcrf.2020032

Grüne, Lars:
Overcoming the curse of dimensionality for approximating Lyapunov functions with deep neural networks under a small-gain condition.
In: IFAC-PapersOnLine. Bd. 54 (2021) Heft 9 . - S. 317-322.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2021.06.152

Grüne, Lars ; Mechelli, Luca ; Pirkelmann, Simon ; Volkwein, Stefan:
Performance estimates for economic model predictive control and their application in proper orthogonal decomposition-based implementations.
In: Mathematical Control and Related Fields. Bd. 11 (2021) Heft 3 . - S. 579-599.
ISSN 2156-8472
DOI: https://doi.org/10.3934/mcrf.2021013

Grüne, Lars ; Kriecherbauer, Thomas ; Margaliot, Michael:
Random attraction in the TASEP model.
In: SIAM Journal on Applied Dynamical Systems. Bd. 20 (2021) Heft 1 . - S. 65-93.
ISSN 1536-0040
DOI: https://doi.org/10.1137/20M131446X

Rez.:

AMS MatSciNet

Ou, Ruchuan ; Baumann, Michael Heinrich ; Grüne, Lars ; Faulwasser, Timm:
A Simulation Study on Turnpikes in Stochastic LQ Optimal Control.
In: IFAC-PapersOnLine. Bd. 54 (2021) Heft 3 . - S. 516-521.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2021.08.294

Fleig, Arthur ; Grüne, Lars:
Strict dissipativity analysis for classes of optimal control problems involving probability density functions.
In: Mathematical Control and Related Fields. Bd. 11 (2021) Heft 4 . - S. 935-964.
ISSN 2156-8472
DOI: https://doi.org/10.3934/mcrf.2020053

Grüne, Lars ; Müller, Matthias A. ; Kellett, Christopher M. ; Weller, Steven R.:
Strict dissipativity for discrete time discounted optimal control problems.
In: Mathematical Control and Related Fields. Bd. 11 (2021) Heft 4 . - S. 771-796.
ISSN 2156-8472
DOI: https://doi.org/10.3934/mcrf.2020046

Yegorov, Ivan ; Dower, Peter M. ; Grüne, Lars:
Synthesis of control Lyapunov functions and stabilizing feedback strategies using exit‐time optimal control. Part I: Theory.
In: Optimal Control Applications and Methods. Bd. 42 (2021) Heft 5 . - S. 1385-1409.
ISSN 1099-1514
DOI: https://doi.org/10.1002/oca.2732

Yegorov, Ivan ; Dower, Peter M. ; Grüne, Lars:
Synthesis of control Lyapunov functions and stabilizing feedback strategies using exit‐time optimal control. Part II: Numerical approach.
In: Optimal Control Applications and Methods. Bd. 42 (2021) Heft 5 . - S. 1410-1440.
ISSN 1099-1514
DOI: https://doi.org/10.1002/oca.2733

Grüne, Lars ; Morris, Kirsten Anna:
Mini-Workshop : Analysis of Data-driven Optimal Control.
In: Oberwolfach Reports. Bd. 18 (2021) Heft 2 . - S. 1209-1257.
ISSN 1660-8941
DOI: https://doi.org/10.4171/OWR/2021/23

2020

Baumann, Michael Heinrich ; Baumann, Michaela ; Grüne, Lars ; Herz, Bernhard:
Improving Heterogeneous Agent Models by Avoiding Explicit Discretizations of Stiff Equations.
2020
Veranstaltung: 8th UECE Conference on Economic and Financial Adjustments , 27. November 2020 , Online / Lisbon, Portugal.
(Veranstaltungsbeitrag: Kongress/Konferenz/Symposium/Tagung , Vortrag )

Baumann, Michael Heinrich ; Baumann, Michaela ; Grüne, Lars ; Herz, Bernhard:
Improving Heterogeneous Agent Models by Avoiding Explicit Discretizations of Stiff Equations.
2020
Veranstaltung: FAST (Finance & Stochastic) Research Seminar, University of Sussex , 11. November 2020 , Online / Brighton, Sussex, UK.
(Veranstaltungsbeitrag: Vortragsreihe , Vortrag )

Baumann, Michael Heinrich ; Baumann, Michaela ; Grüne, Lars ; Herz, Bernhard:
Improving Heterogeneous Agent Models by Avoiding Explicit Discretizations of Stiff Equations.
2020
Veranstaltung: GENED Mini Workshop on Agent Based Modelling and New Economic Dynamics , 5. Oktober 2020 , Online.
(Veranstaltungsbeitrag: Workshop , Vortrag )

Baumann, Michael Heinrich ; Baumann, Michaela ; Grüne, Lars ; Herz, Bernhard:
Improving Heterogeneous Agent Models by Avoiding Explicit Discretizations of Stiff Equations.
Bayreuth , 2020 . - 38 S.
DOI: https://doi.org/10.15495/EPub_UBT_00004718

Fischer, Florian ; Fleig, Arthur ; Klar, Markus ; Grüne, Lars ; Müller, Jörg:
An Optimal Control Model of Mouse Pointing Using the LQR.
Bayreuth , 2020

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Exponential sensitivity analysis for Model Predictive Control of PDEs.
Department of Mathematics, University of Bayreuth
Bayreuth , 2020 . - 4 S.

Grüne, Lars:
Why does strict dissipativity help in model predictive control?
Department of Mathematics, University of Bayreuth
Bayreuth , 2020 . - 4 S.

Noroozi, Navid ; Geiselhart, Roman ; Grüne, Lars ; Wirth, Fabian:
Control of discrete-time nonlinear systems via finite-step control Lyapunov functions.
In: Systems & Control Letters. Bd. 138 (2020) . - 104631.
ISSN 1872-7956
DOI: https://doi.org/10.1016/j.sysconle.2020.104631

Grüne, Lars ; Pirkelmann, Simon:
Economic Model Predictive Control for Time-Varying System : Performance and Stability Results.
In: Optimal Control Applications and Methods. Bd. 41 (2020) Heft 1 . - S. 42-64.
ISSN 1099-1514
DOI: https://doi.org/10.1002/oca.2492

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations.
In: Journal of Differential Equations. Bd. 268 (2020) Heft 12 . - S. 7311-7341.
ISSN 1090-2732
DOI: https://doi.org/10.1016/j.jde.2019.11.064

Grüne, Lars ; Junge, Oliver:
From Bellman to Dijkstra : Set oriented construction of globally optimal controllers.
In: Junge, Oliver ; Schütze, Oliver ; Froyland, Gary ; Ober-Blöbaum, Sina ; Padberg-Gehle, Kathrin (Hrsg.): Advances in dynamics, optimization and computation : a volume dedicated to Michael Dellnitz on the occasion of his 60th birthday. - Cham : Springer , 2020 . - S. 265-294 . - (Studies in Systems, Decision and Control ; 304 )
ISBN 978-3-030-51263-7
DOI: https://doi.org/10.1007/978-3-030-51264-4_11

Coron, Jean-Michel ; Grüne, Lars ; Worthmann, Karl:
Model predictive control, cost controllability, and homogeneity.
In: SIAM Journal on Control and Optimization. Bd. 58 (2020) Heft 5 . - S. 2979-2996.
ISSN 1095-7138
DOI: https://doi.org/10.1137/19M1265995

Banholzer, Stefan ; Fabrini, Giulia ; Grüne, Lars ; Volkwein, Stefan:
Multiobjective model predictive control of a parabolic advection-diffusion-reaction equation.
In: Mathematics. Bd. 8 (2020) Heft 5 . - 777.
ISSN 2227-7390
DOI: https://doi.org/10.3390/math8050777

Grüne, Lars:
Numerical methods for nonlinear optimal control problems, 2nd edition.
In: Samad, Tariq ; Baillieul, John (Hrsg.): Encyclopedia of Systems and Control. - London : Springer , 2020
ISBN 978-1-447-15057-2
DOI: https://doi.org/10.1007/978-1-4471-5102-9_208-3

Borzì, Alfio ; Grüne, Lars:
Towards a solution of mean-field control problems using model predictive control.
In: IFAC-PapersOnLine. Bd. 53 (2020) Heft 2 . - S. 4973-4978.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2020.12.1086

Braun, Philipp ; Grüne, Lars ; Kellett, Christopher M. ; Weller, Steven R. ; Worthmann, Karl:
Towards price-based predictive control of a small scale electricity network.
In: International Journal of Control. Bd. 93 (2020) Heft 1 . - S. 40-61.
ISSN 0020-7179
DOI: https://doi.org/10.1080/00207179.2017.1339329

2019

Tanwani, Aneel ; Chatterjee, Debasish ; Grüne, Lars:
Performance bounds for stochastic receding horizon control with randomly sampled measurements.
In: Proceedings of the 2019 IEEE Conference on Decision and Control (CDC). - Nice, France , 2019 . - S. 2330-2335
DOI: https://doi.org/10.1109/CDC40024.2019.9029947

Baumann, Michael Heinrich ; Baumann, Michaela ; Grüne, Lars ; Herz, Bernhard:
On Modeling Heterogeneous Agents Avoiding Stiff Equations.
2019
Veranstaltung: 43rd Annual Meeting of the AMASES Association for Mathematics Applied to Social and Economic Sciences , September 9-11, 2019 , Perugia, Italy.
(Veranstaltungsbeitrag: Kongress/Konferenz/Symposium/Tagung , Vortrag )

Baumann, Michael Heinrich ; Baumann, Michaela ; Grüne, Lars ; Herz, Bernhard:
Analyzing Heterogeneous Agents Models: Avoiding the Explicit Discretization of Stiff Equations.
2019
Veranstaltung: Graduiertenseminar der VWL-Lehrstühle der Universität Bayreuth , 11./12.07.2019 , Bayreuth.
(Veranstaltungsbeitrag: Sonstige Veranstaltungsart, Vortrag )

Baumann, Michael Heinrich ; Baumann, Michaela ; Grüne, Lars ; Herz, Bernhard:
Analyzing Heterogeneous Agents Models: Avoiding the Explicit Discretization of Stiff Equations.
2019
Veranstaltung: Second Behavioral Macroeconomics Workshop: Heterogeneity and Expectations in Macroeconomics and Finance , June 13-15, 2019 , Otto-Friedrich-Universität Bamberg.
(Veranstaltungsbeitrag: Workshop , Vortrag )

Baumann, Michael Heinrich ; Baumann, Michaela ; Grüne, Lars ; Herz, Bernhard:
Analyzing Heterogeneous Agents Models Avoiding the Explicit Discretization of Stiff Equations (Enlarged Abstract).
Universität Bayreuth
Bayreuth , 2019 . - 8 S.
DOI: https://doi.org/10.15495/EPub_UBT_00004307

Pirkelmann, Simon ; Angeli, David ; Grüne, Lars:
Approximate computation of storage functions for discrete-time systems using sum-of-squares techniques.
In: IFAC-PapersOnLine. Bd. 52 (2019) Heft 16 . - S. 508-513.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2019.12.012

Kellett, Christopher M. ; Weller, Steven R. ; Faulwasser, Timm ; Grüne, Lars ; Semmler, Willi:
Feedback, dynamics, and optimal control in climate economics.
In: Annual Reviews in Control. Bd. 47 (2019) . - S. 7-20.
ISSN 1367-5788
DOI: https://doi.org/10.1016/j.arcontrol.2019.04.003

Hans, Christian A. ; Braun, Philipp ; Raisch, Jörg ; Grüne, Lars ; Reincke-Collon, Carsten:
Hierarchical distributed model predictive control of interconnected microgrids.
In: IEEE Transactions on Sustainable Energy. Bd. 10 (2019) Heft 1 . - S. 407-416.
ISSN 1949-3029
DOI: https://doi.org/10.1109/TSTE.2018.2802922

Grüne, Lars ; Stieler, Marleen:
Multiobjective Model Predictive Control for Stabilizing Cost Criteria.
In: Discrete and Continuous Dynamical Systems. Series B. Bd. 24 (2019) Heft 8 . - S. 3905-3928.
ISSN 1531-3492
DOI: https://doi.org/10.3934/dcdsb.2018336

Baier, Robert ; Braun, Philipp ; Grüne, Lars ; Kellett, Christopher M.:
Numerical Calculation of Nonsmooth Control Lyapunov Functions via Piecewise Affine Approximation.
In: IFAC-PapersOnLine. Bd. 52 (2019) Heft 16 . - S. 370-375.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2019.11.808

Grüne, Lars ; Pirkelmann, Simon:
Numerical Verification of Turnpike and Continuity Properties for Time-Varying PDEs.
In: IFAC-PapersOnLine. Bd. 52 (2019) Heft 2 . - S. 7-12.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2019.08.002

Fleig, Arthur ; Grüne, Lars:
On Dissipativity of the Fokker-Planck Equation for the Ornstein-Uhlenbeck Process.
In: IFAC-PapersOnLine. Bd. 52 (2019) Heft 2 . - S. 13-18.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2019.08.003

Höger, Matthias ; Grüne, Lars:
On the relation between detectability and strict dissipativity for nonlinear discrete time systems.
In: IEEE Control Systems Letters. Bd. 3 (2019) Heft 2 . - S. 458-462.
ISSN 2475-1456
DOI: https://doi.org/10.1109/LCSYS.2019.2899241

Baumann, Michael Heinrich ; Grüne, Lars:
Positive Expected Feedback Trading Gain for all Essentially Linearly Representable Prices.
In: 2019 12th Asian Control Conference (ASCC). - Piscataway, NJ : IEEE , 2019 . - S. 150-155
ISBN 978-1-7281-0263-4

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Sensitivity Analysis of Optimal Control for a Class of Parabolic PDEs Motivated by Model Predictive Control.
In: SIAM Journal on Control and Optimization. Bd. 57 (2019) Heft 4 . - S. 2753-2774.
ISSN 1095-7138
DOI: https://doi.org/10.1137/18M1223083

2018

Yegorov, Ivan ; Dower, Peter ; Grüne, Lars:
A characteristics based curse-of-dimensionality-free approach for approximating control Lyapunov functions and feedback stabilization.
In: Proceedings of the 23rd International Symposium on Mathematical Theory of Networks and Systems. - Hong Kong , 2018 . - S. 342-349

Grüne, Lars ; Dower, Peter:
Hamiltonian based a posteriori error estimation for Hamilton-Jacobi-Bellman equations.
In: Proceedings of the 23rd International Symposium on Mathematical Theory of Networks and Systems. - Hong Kong , 2018 . - S. 372-374

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Sensitivity analysis of optimal control motivated by model predictive control.
In: Proceedings of the 23rd International Symposium on Mathematical Theory of Networks and Systems. - Hong Kong , 2018 . - S. 93-96

Stieler, Marleen ; Baumann, Michael Heinrich ; Grüne, Lars:
Noncooperative Model Predictive Control.
2018
Veranstaltung: 89th GAMM Annual Meeting 2018 , 19. - 23. März 2018 , München.
(Veranstaltungsbeitrag: Kongress/Konferenz/Symposium/Tagung , Vortrag )

Stieler, Marleen ; Baumann, Michael Heinrich ; Grüne, Lars:
Nichtkooperative linear-quadratische Spiele, ihre Beziehung zu Riccati-artigen Gleichungen und ein Lösungsansatz mittels Modellprädiktiver Regelung.
2018
Veranstaltung: Forschungszentrum Modellierung und Simulation (MODUS) , 24.01.2018 , Bayreuth.
(Veranstaltungsbeitrag: Vortragsreihe , Vortrag )

Braun, Philipp ; Grüne, Lars ; Kellett, Christopher M.:
Complete Instability of Differential Inclusions using Lyapunov Methods.
In: 2018 IEEE Conference on Decision and Control (CDC). Tagungsband. - Miami Beach, Florida , 2018 . - S. 718-724
ISBN 978-1-5386-1395-5
DOI: https://doi.org/10.1109/CDC.2018.8618663

Grüne, Lars:
Dynamic programming, optimal control and model predictive control.
In: Raković, Saša V. ; Levine, William S. (Hrsg.): Handbook of Model Predictive Control. - Basel : Birkhäuser , 2018 . - S. 29-52
ISBN 978-3-319-77489-3
DOI: https://doi.org/10.1007/978-3-319-77489-3_2

Faulwasser, Timm ; Grüne, Lars ; Müller, Matthias A.:
Economic Nonlinear Model Predictive Control.
In: Foundations and Trends® in Systems and Control. Bd. 5 (2018) Heft 1 . - S. 1-98.
ISSN 2325-6826
DOI: https://doi.org/10.1561/2600000014

Margaliot, Michael ; Grüne, Lars ; Kriecherbauer, Thomas:
Entrainment in the Master Equation.
In: Royal Society Open Science. Bd. 5 (2018) Heft 4 . - 172157.
ISSN 2054-5703
DOI: https://doi.org/10.1098/rsos.172157

Braun, Philipp ; Faulwasser, Timm ; Grüne, Lars ; Kellett, Christopher M. ; Weller, Steven R. ; Worthmann, Karl:
Hierarchical distributed ADMM for predictive control with applications in power networks.
In: IFAC Journal of Systems and Control. Bd. 3 (2018) . - S. 10-22.
ISSN 2468-6018
DOI: https://doi.org/10.1016/j.ifacsc.2018.01.001

Fleig, Arthur ; Grüne, Lars:
L²-Tracking of Gaussian Distributions via Model Predictive Control for the Fokker-Planck Equation.
In: Vietnam Journal of Mathematics. Bd. 46 (2018) . - S. 915-948.
ISSN 2305-2228
DOI: https://doi.org/10.1007/s10013-018-0309-8

Noroozi, Navid ; Geiselhart, Roman ; Grüne, Lars ; Rüffer, Björn ; Wirth, Fabian:
Non-conservative discrete-time ISS small-gain conditions for closed sets.
In: IEEE Transactions on Automatic Control. Bd. 63 (2018) Heft 5 . - S. 1231-1242.
ISSN 1558-2523
DOI: https://doi.org/10.1109/TAC.2017.2735194

Stieler, Marleen ; Baumann, Michael Heinrich ; Grüne, Lars:
Noncooperative Model Predictive Control for Affine-Quadratic Games.
In: Proceedings in Applied Mathematics and Mechanics. Bd. 18 (2018) Heft 1 . - e201800036.
ISSN 1617-7061
DOI: https://doi.org/10.1002/pamm.201800036

Baier, Robert ; Braun, Philipp ; Grüne, Lars ; Kellett, Christopher M.:
Numerical construction of nonsmooth control Lyapunov functions.
In: Giselsson, Pontus ; Rantzer, Anders (Hrsg.): Large-Scale and Distributed Optimization. - Cham : Springer , 2018 . - S. 343-373 . - (Lecture Notes in Mathematics ; 2227 )
ISBN 978-3-319-97477-4
DOI: https://doi.org/10.1007/978-3-319-97478-1_12

Rez.:

AMS MathSciNet Zentralblatt

Numerical Methods for Optimal Control Problems.
Hrsg.: Falcone, Maurizio ; Ferretti, Roberto ; Grüne, Lars ; McEneaney, William M.
Cham : Springer , 2018 . - X, 268 S. - (Springer INdAM Series ; 29 )
ISBN 978-3-030-01959-4

DOI: https://doi.org/10.1007/978-3-030-01959-4

Gaitsgory, Vladimir ; Grüne, Lars ; Höger, Matthias ; Kellett, Christopher M. ; Weller, Steven R.:
Stabilization of strictly dissipative discrete time systems with discounted optimal control.
In: Automatica. Bd. 93 (2018) . - S. 311-320.
ISSN 1873-2836
DOI: https://doi.org/10.1016/j.automatica.2018.03.076

Grüne, Lars ; Pirkelmann, Simon ; Stieler, Marleen:
Strict dissipativity implies turnpike behavior for time-varying discrete time optimal control problems.
In: Feichtinger, Gustav ; Kovacevic, Raimund M. ; Tragler, Gernot (Hrsg.): Control Systems and Mathematical Methods in Economics: Essays in Honor of Vladimir M. Veliov. - Cham : Springer , 2018 . - S. 195-218 . - (Lecture Notes in Economics and Mathematical Systems ; 687 )
ISBN 978-3-319-75169-6
DOI: https://doi.org/10.1007/978-3-319-75169-6_10

Grüne, Lars ; Guglielmi, Roberto:
Turnpike properties and strict dissipativity for discrete time linear quadratic optimal control problems.
In: SIAM Journal on Control and Optimization. Bd. 56 (2018) Heft 2 . - S. 1282-1302.
ISSN 1095-7138
DOI: https://doi.org/10.1137/17M112350X

Braun, Philipp ; Grüne, Lars:
Verteilte Optimierung : Anwendungen in der Modellprädiktiven Regelung.
In: Automatisierungstechnik. Bd. 66 (2018) Heft 11 . - S. 939-949.
ISSN 2196-677X
DOI: https://doi.org/10.1515/auto-2018-0009

2017

Grüne, Lars ; Stieler, Marleen:
Performance Guarantees for Multiobjective Model Predictive Control.
In: Proceedings of the 2017 IEEE 56th Annual Conference on Decision and Control (CDC). - Melbourne, Australia , 2017 . - S. 5545-5550
ISBN 978-1-5090-2873-3
DOI: https://doi.org/10.1109/CDC.2017.8264482

Baumann, Michael Heinrich ; Grüne, Lars ; Herz, Bernhard:
Effects of Control-based Trading : Between the Poles of Economics&Finance and Mathematics&Engineering.
2017
Veranstaltung: Interdisciplinary Symposium - Track "interdisciplinarity in economics" , July 5-7, 2017 , Corté, Università di Corsica, France.
(Veranstaltungsbeitrag: Kongress/Konferenz/Symposium/Tagung , Vortrag )

Baumann, Michael Heinrich ; Grüne, Lars:
Simultaneously long short trading in discrete and continuous time - AudioSlides.
: Elsevier AudioSlides , 2017 . - 37 slides, 04:59 min

Grüne, Lars ; Pirkelmann, Simon:
Closed-loop performance analysis for economic model predictive control of time-varying systems.
In: Proceedings of the 56th IEEE Annual Conference on Decision and Control (CDC 2017), Melbourne, Australia. - Melbourne , 2017 . - S. 5563-5569
ISBN 978-1-5090-2873-3
DOI: https://doi.org/10.1109/CDC.2017.8264485

Grüne, Lars ; Le, Thuy Thi Thien:
A double-sided Dynamic Programming approach to the minimum time problem and its numerical approximation.
In: Applied Numerical Mathematics. Bd. 121 (2017) . - S. 68-81.
ISSN 1873-5460
DOI: https://doi.org/10.1016/j.apnum.2017.06.008

Braun, Philipp ; Grüne, Lars ; Kellett, Christopher M.:
Feedback Design Using Nonsmooth Control Lyapunov Functions: A Numerical Case Study for the Nonholonomic Integrator.
In: Proceedings of the 56th IEEE Annual Conference on Decision and Control (CDC 2017), Melbourne, Australia. - Melbourne , 2017 . - S. 4890-4895
ISBN 978-1-5090-2873-3
DOI: https://doi.org/10.1109/CDC.2017.8264382

Grüne, Lars ; Pannek, Jürgen:
Nonlinear Model Predictive Control : Theory and Algorithms. 2nd Edition.
Cham : Springer , 2017 . - 456 S. - (Communications and Control Engineering )
ISBN 978-3-319-46024-6

Rez.:

Zentralblatt Mathematik Mathematical Reviews

DOI: https://doi.org/10.1007/978-3-319-46024-6

Botner, Meir ; Zarai, Yoram ; Margaliot, Michael ; Grüne, Lars:
On approximating contractive systems.
In: IEEE Transactions on Automatic Control. Bd. 62 (2017) Heft 12 . - S. 6451-6457.
ISSN 1558-2523
DOI: https://doi.org/10.1109/TAC.2017.2651649

Müller, Matthias A. ; Grüne, Lars:
On the relation between dissipativity and discounted dissipativity.
In: Proceedings of the 56th IEEE Annual Conference on Decision and Control (CDC 2017), Melbourne, Australia. - Melbourne , 2017 . - S. 5570-5575
ISBN 978-1-5090-2873-3
DOI: https://doi.org/10.1109/CDC.2017.8264486

Grüne, Lars ; Kellett, Christopher M. ; Weller, Steven R.:
On the relation between turnpike properties for finite and infinite horizon optimal control problems.
In: Journal of Optimization Theory and Applications. Bd. 173 (2017) Heft 3 . - S. 727-745.
ISSN 0022-3239
DOI: https://doi.org/10.1007/s10957-017-1103-6

Zanon, Mario ; Grüne, Lars ; Diehl, Moritz:
Periodic optimal control, dissipativity and MPC.
In: IEEE Transactions on Automatic Control. Bd. 62 (2017) Heft 6 . - S. 2943-2949.
ISSN 1558-2523
DOI: https://doi.org/10.1109/TAC.2016.2601881

Baumann, Michael Heinrich ; Grüne, Lars:
Simultaneously long short trading in discrete and continuous time.
In: Systems & Control Letters. Bd. 99 (2017) . - S. 85-89.
ISSN 1872-7956
DOI: https://doi.org/10.1016/j.sysconle.2016.11.011

2016

Baumann, Michael Heinrich ; Grüne, Lars:
Positive Expected Feedback Trading Gain for all Essentially Linearly Representable Prices.
2016
Veranstaltung: The XVII Workshop on Quantitative Finance - Pisa 2016 , 28.-29.01.2016 , Pisa.
(Veranstaltungsbeitrag: Workshop , Vortrag )

Grüne, Lars:
Approximation properties of receding horizon optimal control.
In: Jahresbericht der Deutschen Mathematiker-Vereinigung. Bd. 118 (2016) Heft 1 . - S. 3-37.
ISSN 0012-0456
DOI: https://doi.org/10.1365/s13291-016-0134-5

Li, Huijuan ; Grüne, Lars:
Computation of Local ISS Lyapunov Functions for Discrete-time Systems Via Linear Programming.
In: Journal of Mathematical Analysis and Applications. Bd. 438 (2016) Heft 2 . - S. 701-719.
ISSN 1096-0813
DOI: https://doi.org/10.1016/j.jmaa.2016.01.045

Braun, Philipp ; Grüne, Lars ; Kellett, Christopher M. ; Weller, Steven R. ; Worthmann, Karl:
A distributed optimization algorithm for the predictive control of smart grids.
In: IEEE Transactions on Automatic Control. Bd. 61 (2016) Heft 12 . - S. 3898-3911.
ISSN 1558-2523
DOI: https://doi.org/10.1109/TAC.2016.2525808

Müller, Matthias A. ; Grüne, Lars:
Economic model predictive control without terminal constraints for optimal periodic behavior.
In: Automatica. Bd. 70 (2016) . - S. 128-139.
ISSN 1873-2836
DOI: https://doi.org/10.1016/j.automatica.2016.03.024

Fleig, Arthur ; Grüne, Lars:
Estimates on the Minimal Stabilizing Horizon Length in Model Predictive Control for the Fokker-Planck Equation.
In: IFAC-PapersOnLine. Bd. 49 (2016) Heft 8 . - S. 260-265.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2016.07.451

Grüne, Lars ; Junge, Oliver:
Gewöhnliche Differentialgleichungen : eine Einführung aus der Perspektive der dynamischen Systeme. 2. Auflage.
Heidelberg : Springer , 2016 . - 249 S.
ISBN 978-3-658-10240-1

Rez.:

Zentralblatt Mathematik

DOI: https://doi.org/10.1007/978-3-658-10241-8

Braun, Philipp ; Faulwasser, Timm ; Grüne, Lars ; Kellett, Christopher M. ; Weller, Steven R. ; Worthmann, Karl:
Maximal Islanding Time For Microgrids via Distributed Predictive Control.
In: University of Minnesota (Hrsg.): 22nd International Symposium on Mathematical Theory of Networks and Systems : July 12-15, 2016 (MTNS 2016, Proceedings). - Minneapolis, Minnesota , 2016 . - S. 652-659
ISBN 978-1-5323-1385-5

Fleig, Arthur ; Grüne, Lars:
Model Predictive Control for the Fokker-Planck equation : analysis and structural insight.
In: University of Minnesota (Hrsg.): 22nd International Symposium on Mathematical Theory of Networks and Systems : July 12-15, 2016 (MTNS 2016, Proceedings). - Minneapolis, Minnesota , 2016 . - S. 689-690
ISBN 978-1-5323-1385-5

Braun, Philipp ; Grüne, Lars ; Kellett, Christopher M. ; Weller, Steven R. ; Worthmann, Karl:
Model predictive control of residential energy systems using energy storage and controllable loads.
In: Russo, Giovanni ; Capasso, Vincenzo ; Nicosia, Giuseppe ; Romano, Vittorio (Hrsg.): Progress in Industrial Mathematics at ECMI 2014. - Heidelberg : Springer , 2016 . - S. 617-623 . - (Mathematics in Industry ; 22 )
ISBN 978-3-319-23413-7
DOI: https://doi.org/10.1007/978-3-319-23413-7_85

Grüne, Lars ; Kellett, Christopher M. ; Weller, Steven R.:
On a discounted notion of strict dissipativity.
In: IFAC-PapersOnLine. Bd. 49 (2016) Heft 18 . - S. 247-252.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2016.10.171

Grüne, Lars ; Müller, Matthias A.:
On the relation between strict dissipativity and turnpike properties.
In: Systems & Control Letters. Bd. 90 (2016) . - S. 45-53.
ISSN 1872-7956
DOI: https://doi.org/10.1016/j.sysconle.2016.01.003

2015

Braun, Philipp ; Grüne, Lars ; Kellett, Christopher M. ; Weller, Steven R. ; Worthmann, Karl:
A real-time pricing scheme for residential energy systems using a market maker.
In: The Institution of Engineers Australia (Hrsg.): Proceedings of 2015 Australian Control Conference (AUCC). - Barton, Australia , 2015 . - S. 259-262
ISBN 978-1-4673-9552-6

Li, Huijuan ; Baier, Robert ; Grüne, Lars ; Hafstein, Sigurdur Freyr ; Wirth, Fabian:
Computation of local ISS Lyapunov functions with low gains via linear programming.
In: Discrete and Continuous Dynamical Systems. Series B. Bd. 20 (2015) Heft 8 . - S. 2477-2495.
ISSN 1531-3492
DOI: https://doi.org/10.3934/dcdsb.2015.20.2477

Rez.:

AMS MathSciNet Zentralblatt

Worthmann, Karl ; Kellett, Christopher M. ; Braun, Philipp ; Grüne, Lars ; Weller, Steven R.:
Distributed and decentralized control of residential energy systems incorporating battery storage.
In: IEEE Transactions on Smart Grid. Bd. 6 (2015) Heft 4 . - S. 1914-1923.
ISSN 1949-3053
DOI: https://doi.org/10.1109/TSG.2015.2392081

Müller, Matthias A. ; Grüne, Lars:
Economic model predictive control without terminal constraints : optimal periodic operation.
In: Proceedings of the 54th IEEE Conference on Decision and Control. - Piscataway, NJ : IEEE , 2015 . - S. 4946-4951
DOI: https://doi.org/10.1109/CDC.2015.7402992

Sigurani, Manuela ; Stöcker, Christian ; Grüne, Lars ; Lunze, Jan:
Experimental evaluation of two complementary decentralized event-based control methods.
In: Control Engineering Practice. Bd. 35 (2015) . - S. 22-34.
ISSN 0967-0661
DOI: https://doi.org/10.1016/j.conengprac.2014.10.002

Grüne, Lars ; Sigurani, Manuela:
Numerical event-based ISS controller design via a dynamic game approach.
In: Journal of Computational Dynamics. Bd. 2 (2015) Heft 1 . - S. 65-81.
ISSN 2158-2491
DOI: https://doi.org/10.3934/jcd.2015.2.65

Grüne, Lars ; Panin, Anastasia:
On non-averaged performance of economic MPC with terminal conditions.
In: Proceedings of the 54th IEEE Conference on Decision and Control (CDC 2015). - Piscataway, NJ : IEEE , 2015 . - S. 4332-4337
ISBN 978-1-4799-7884-7
DOI: https://doi.org/10.1109/CDC.2015.7402895

Müller, Matthias A. ; Grüne, Lars ; Allgöwer, Frank:
On the role of dissipativity in economic model predictive control.
In: IFAC-PapersOnLine. Bd. 48 (2015) Heft 23 . - S. 110-116.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2015.11.269

Grüne, Lars:
Open problem : Strict Dissipativity and the Turnpike Property.
In: Oberwolfach Reports. Bd. 12 (2015) Heft 1 . - S. 651-652.
ISSN 1660-8941
DOI: https://doi.org/10.4171/OWR/2015/12

Braun, Philipp ; Grüne, Lars ; Kellett, Christopher M. ; Weller, Steven R. ; Worthmann, Karl:
Predictive control of a smart grid : a distributed optimization algorithm with centralized performance properties.
In: Proceedings of the 54th IEEE Conference on Decision and Control (CDC 2015). - Piscataway, NJ : IEEE , 2015 . - S. 5593-5598
DOI: https://doi.org/10.1109/CDC.2015.7403096

Grüne, Lars ; Palma, Vryan Gil:
Robustness of performance and stability for multistep and updated multistep MPC schemes.
In: Discrete and Continuous Dynamical Systems. Bd. 35 (2015) Heft 9 . - S. 4385-4414.
ISSN 1553-5231
DOI: https://doi.org/10.3934/dcds.2015.35.4385

Gaitsgory, Vladimir ; Grüne, Lars ; Thatcher, Neil:
Stabilization with discounted optimal control.
In: Systems & Control Letters. Bd. 82 (2015) . - S. 91-98.
ISSN 1872-7956
DOI: https://doi.org/10.1016/j.sysconle.2015.05.010

Worthmann, Karl ; Reble, Marcus ; Grüne, Lars ; Allgöwer, Frank:
Unconstrained nonlinear MPC : performance estimates for sampled-data systems with zero order hold.
In: Proceedingss of the 54th IEEE Conference on Decision and Control (CDC 2015). - Piscataway, NJ : IEEE , 2015 . - S. 4971-4976
DOI: https://doi.org/10.1109/CDC.2015.7402996

Grüne, Lars ; Semmler, Willi ; Stieler, Marleen:
Using nonlinear model predictive control for dynamic decision problems in economics.
In: Journal of Economic Dynamics and Control. Bd. 60 (2015) . - S. 112-133.
ISSN 1879-1743
DOI: https://doi.org/10.1016/j.jedc.2015.08.010

Bokanowski, Olivier ; Falcone, Maurizio ; Ferretti, Roberto ; Grüne, Lars ; Kalise, Dante ; Zidani, Hasnaa:
Value iteration convergence of ε-monotone schemes for stationary Hamilton-Jacobi equations.
In: Discrete and Continuous Dynamical Systems. Bd. 35 (2015) Heft 9 . - S. 4041-4070.
ISSN 1553-5231
DOI: https://doi.org/10.3934/dcds.2015.35.4041

Grüne, Lars ; Zidani, Hasnaa:
Zubov's equation for state-constrained perturbed nonlinear systems.
In: Mathematical Control and Related Fields. Bd. 5 (2015) Heft 1 . - S. 55-71.
ISSN 2156-8472
DOI: https://doi.org/10.3934/mcrf.2015.5.55

Grüne, Lars ; Picarelli, Athena:
Zubov's method for controlled diffusions with state constraints.
In: Nonlinear Differential Equations and Applications NoDEA. Bd. 22 (2015) Heft 6 . - S. 1765-1799.
ISSN 1021-9722
DOI: https://doi.org/10.1007/s00030-015-0343-0

2014

Worthmann, Karl ; Kellett, Christopher M. ; Grüne, Lars ; Weller, Steven R.:
Distributed control of residential energy systems using a market maker.
In: Boje,Edward (Hrsg.): Proceedings of the 19th IFAC World Congress : IFAC-PapersOnLine. - Cape Town, South Africa , 2014 . - S. 11641-11646
ISBN 978-3-902823-62-5
DOI: https://doi.org/10.3182/20140824-6-ZA-1003.01785

Grüne, Lars ; Stieler, Marleen:
Asymptotic stability and transient optimality of economic MPC without terminal conditions.
In: Journal of Process Control. Bd. 24 (2014) Heft 8 . - S. 1187-1196.
ISSN 0959-1524
DOI: https://doi.org/10.1016/j.jprocont.2014.05.003

Li, Huijuan ; Baier, Robert ; Grüne, Lars ; Hafstein, Sigurdur Freyr ; Wirth, Fabian:
Computation of local ISS Lyapunov functions via linear programming.
In: MTNS 2014 : MTNS 2014 : Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems. - Groningen : University of Groningen Press , 2014 . - S. 1189-1195
ISBN 978-90-367-6321-9

Grüne, Lars ; Sigurani, Manuela:
Construction of event-based ISS controllers on coarse quantizations.
In: 2014 IEEE 53rd Annual Conference on Decision and Control (CDC 2014). - Piscataway, NJ : IEEE , 2014 . - S. 836-841
ISBN 978-1-4799-7746-8
DOI: https://doi.org/10.1109/CDC.2014.7039485

Grüne, Lars ; Allgöwer, Frank ; Findeisen, Rolf ; Fischer, Jörg ; Groß, Dominic ; Hanebeck, Uwe D. ; Kern, Benjamin ; Müller, Matthias A. ; Pannek, Jürgen ; Reble, Marcus ; Stursberg, Olaf ; Varutti, Paolo ; Worthmann, Karl:
Distributed and networked model predictive control.
In: Lunze, Jan (Hrsg.): Control theory of digitally networked dynamic systems. - Cham : Springer , 2014 . - S. 111-167
ISBN 978-3-319-01130-1
DOI: https://doi.org/10.1007/978-3-319-01131-8_4

Rez.:

Zentralblatt

Greiner, Alfred ; Grüne, Lars ; Semmler, Willi:
Economic growth and the transition from non-renewable to renewable energy.
In: Environment and Development Economics. Bd. 19 (2014) Heft 4 . - S. 417-439.
ISSN 1355-770X
DOI: https://doi.org/10.1017/S1355770X13000491

Grüne, Lars ; Hirche, Sandra ; Junge, Oliver ; Koltai, Peter ; Lehmann, Daniel ; Lunze, Jan ; Molin, Adam ; Sailer, Rudolf ; Sigurani, Manuela ; Stöcker, Christian ; Wirth, Fabian:
Event-based control.
In: Lunze, Jan (ed.): Control theory of digitally networked dynamic systems. - Cham : Springer , 2014 . - S. 169-261
ISBN 978-3-319-01130-1
DOI: https://doi.org/10.1007/978-3-319-01131-8_5

Rez.:

Zentralblatt

Damm, Tobias ; Grüne, Lars ; Stieler, Marleen ; Worthmann, Karl:
An exponential turnpike theorem for dissipative discrete time optimal control problems.
In: SIAM Journal on Control and Optimization. Bd. 52 (2014) Heft 3 . - S. 1935-1957.
ISSN 1095-7138
DOI: https://doi.org/10.1137/120888934

Rez.:

AMS MathSciNet Zentralblatt

Lunze, Jan ; Grüne, Lars:
Introduction to networked control systems.
In: Lunze, Jan (Hrsg.): Control theory of digitally networked dynamic systems. - Cham : Springer , 2014 . - S. 1-30
ISBN 978-3-319-01130-1
DOI: https://doi.org/10.1007/978-3-319-01131-8_1

Rez.:

Zentralblatt

Grüne, Lars ; Kellett, Christopher M.:
ISS-Lyapunov functions for discontinuous discrete-time systems.
In: IEEE Transactions on Automatic Control. Bd. 59 (2014) Heft 11 . - S. 3098-3103.
ISSN 1558-2523
DOI: https://doi.org/10.1109/TAC.2014.2321667

Grüne, Lars ; Sigurani, Manuela:
A Lyapunov based nonlinear small-gain theorem for discontinuous discrete-time large-scale systems.
In: MTNS 2014 : Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems. - Groningen : University of Groningen , 2014 . - S. 1031-1037
ISBN 978-90-367-6321-9

Grüne, Lars ; Stieler, Marleen:
A Lyapunov function for economic MPC without terminal conditions.
In: Proceedings of the IEEE 53rd Annual Conference on Decision and Control Held in Los Angeles, California, 2014. - Los Angeles, CA : IEEE , 2014 . - S. 2740-2745
ISBN 978-1-4799-7746-8
DOI: https://doi.org/10.1109/CDC.2014.7039809

Grüne, Lars:
Nominal model predictive control.
In: Samad, Tariq ; Baillieul, John (Hrsg.): Encyclopedia of Systems and Control. - London : Springer , 2014
ISBN 978-1-447-15057-2
DOI: https://doi.org/10.1007/978-1-4471-5102-9_1-2

Grüne, Lars:
Numerical methods for nonlinear optimal control problems.
In: Samad, Tariq ; Baillieul, John (Hrsg.): Encyclopedia of Systems and Control. - London : Springer , 2014
ISBN 978-1-447-15057-2
DOI: https://doi.org/10.1007/978-1-4471-5102-9_208-2

Grüne, Lars ; Palma, Vryan Gil:
On the benefit of re-optimization in optimal control under perturbations.
In: MTNS 2014 : Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems. - Groningen : University of Groningen , 2014 . - S. 439-446
ISBN 978-90-367-6321-9

Grüne, Lars ; Zanon, Mario:
Periodic optimal control, dissipativity and MPC.
In: MTNS 2014 : Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems. - Groningen : University of Groningen , 2014 . - S. 1804-1807
ISBN 978-90-367-6321-9

Worthmann, Karl ; Reble, Marcus ; Grüne, Lars ; Allgöwer, Frank:
The role of sampling for stability and performance in unconstrained nonlinear model predictive control.
In: SIAM Journal on Control and Optimization. Bd. 52 (2014) Heft 1 . - S. 581-605.
ISSN 1095-7138
DOI: https://doi.org/10.1137/12086652X

Fleig, Arthur ; Grüne, Lars ; Guglielmi, Roberto:
Some results on Model Predictive Control for the Fokker-Planck equation.
In: MTNS 2014 : 21st International Symposium on Mathematical Theory of Networks and Systems, July 7-11, 2014, Groningen, The Netherlands ; Proceedings. - Groningen , 2014 . - S. 1203-1206
ISBN 978-90-367-6321-9

Boccia, Andrea ; Grüne, Lars ; Worthmann, Karl:
Stability and feasibility of state constrained MPC without stabilizing terminal constraints.
In: Systems & Control Letters. Bd. 72 (2014) . - S. 14-21.
ISSN 1872-7956
DOI: https://doi.org/10.1016/j.sysconle.2014.08.002

Rez.:

AMS MathSciNet Zentralblatt

Boccia, Andrea ; Grüne, Lars ; Worthmann, Karl:
Stability and feasibility of state-constrained linear MPC without stabilizing terminal constraints.
In: MTNS 2014 : Proceedings on the 21st International Symposium on Mathematical Theory of Networks and Systems, July 7-11, 2014, University of Groningen. - Groningen , 2014 . - S. 453-460
ISBN 978-90-367-6321-9

Grüne, Lars ; Kellett, Christopher M.:
Strong implication-form ISS-Lyapunov functions for discontinuous discrete-time systems.
In: MTNS 2014 : Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems. - Groningen : University of Groningen , 2014 . - S. 1023-1030
ISBN 978-90-367-6321-9

2013

Grüne, Lars ; Sigurani, Manuela:
Numerical ISS controller design via a dynamic game approach.
In: 2013 IEEE 52nd Annual Conference on Decision and Control (CDC 2013). - Piscataway, NJ : IEEE , 2013 . - S. 1732-1737
ISBN 978-1-4673-5714-2
DOI: https://doi.org/10.1109/CDC.2013.6760132

Altmüller, Nils ; Grüne, Lars:
A comparative stability analysis of Neumann and Dirichlet boundary MPC for the heat equation.
In: IFAC Proceedings Volumes. Bd. 46 (2013) Heft 26 . - S. 161-166.
ISSN 1474-6670
DOI: https://doi.org/10.3182/20130925-3-FR-4043.00048

Grüne, Lars:
Economic receding horizon control without terminal constraints.
In: Automatica. Bd. 49 (2013) Heft 3 . - S. 725-734.
ISSN 1873-2836
DOI: https://doi.org/10.1016/j.automatica.2012.12.003

Grüne, Lars ; Karafyllis, Iasson:
Lyapunov function based step size control for numerical ODE solvers with application to optimization algorithms.
In: Hüper, Knut ; Trumpf, Jochen (Hrsg.): Mathematical System Theory : Festschrift in Honor of Uwe Helmke on the Occasion of his 60th Birthday. - S.l. : CreateSpace Independent Publishing Platform , 2013 . - S. 183-210

2012

Grüne, Lars ; Pannek, Jürgen ; Seehafer, Martin ; Worthmann, Karl:
Analysis of unconstrained nonlinear MPC schemes with time varying control horizon.
In: 51st IEEE Conference on Decision and Control : Final Program and Book of Abstracts. - Piscataway, NJ : IEEE , 2012 . - S. 2605-2610
ISBN 978-1-4673-2065-8
DOI: https://doi.org/10.1109/CDC.2012.6426581

Grüne, Lars ; Jahn, Thomas U.:
Computing reachable sets via barrier methods on SIMD architectures.
In: Eberhardsteiner, Josef ; Böhm, Helmut J. ; Rammerstorfer, Franz G. (eds.): Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) Held at the University of Vienna, Austria, September 10-14, 2012. - Vienna : Vienna University of Technology , 2012 . - S. 2076-2095
ISBN 9783950248197

Altmüller, Nils ; Grüne, Lars:
Distributed and boundary model predictive control for the heat equation.
In: GAMM-Mitteilungen. Bd. 35 (2012) Heft 2 . - S. 131-145.
ISSN 1522-2608
DOI: https://doi.org/10.1002/gamm.201210010

Grüne, Lars ; Worthmann, Karl:
A Distributed NMPC Scheme without Stabilizing Terminal Constraints.
In: Johansson, Rolf ; Rantzer, Anders (Hrsg.): Distributed Decision Making and Control. - London : Springer , 2012 . - S. 261-287 . - (Lecture Notes in Control and Information Sciences ; 417 )
ISBN 978-1-4471-2264-7
DOI: https://doi.org/10.1007/978-1-4471-2265-4_12

Grüne, Lars:
Economic MPC and the role of exponential turnpike properties.
In: Oberwolfach Reports. Bd. 9 (2012) Heft 1 . - S. 678-681.
ISSN 1660-8941
DOI: https://doi.org/10.4171/OWR/2012/12

Grüne, Lars:
Economic MPC without terminal constraints.
In: Proceedings on the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012). - Melbourne, Australia : Think Business Events , 2012 . - 4 S.
ISBN 978-0-646-58062-3

Grüne, Lars ; Pannek, Jürgen ; Worthmann, Karl:
Ensuring stability in networked systems with nonlinear MPC for continuous time systems.
In: 51st IEEE Conference on Decision and Control : Final Program and Book of Abstracts. - Piscataway, NJ : IEEE , 2012 . - S. 14-19
ISBN 978-1-4673-2065-8
DOI: https://doi.org/10.1109/CDC.2012.6426278

Baier, Robert ; Grüne, Lars ; Freyr Hafstein, Sigurđur:
Linear programming based Lyapunov function computation for differential inclusions.
In: Discrete and Continuous Dynamical Systems. Series B. Bd. 17 (2012) Heft 1 . - S. 33-56.
ISSN 1531-3492
DOI: https://doi.org/10.3934/dcdsb.2012.17.33

Rez.:

Mathematical Review Zentralblatt

Grüne, Lars:
NMPC without terminal constraints.
In: IFAC Proceedings Volumes. Bd. 45 (2012) Heft 17 . - S. 1-13.
ISSN 1474-6670
DOI: https://doi.org/10.3182/20120823-5-NL-3013.00030

Hänel, Maria ; Kuhn, Stefan ; Henrich, Dominik ; Grüne, Lars ; Pannek, Jürgen:
Optimal camera placement to measure distances regarding static and dynamic obstacles.
In: International Journal of Sensor Networks. Bd. 12 (2012) Heft 1 . - S. 25-36.
ISSN 1748-1287
DOI: https://doi.org/10.1504/IJSNET.2012.047713

Palma, Vryan Gil ; Grüne, Lars:
Stability, performance and robustness of sensitivity-based multistep feedback NMPC.
In: MTNS 2012 : Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems. - Melbourne , 2012
ISBN 978-0-646-58062-3

2011

Grüne, Lars ; Serea, Oana Silvia:
Differential Games and Zubov's Method.
In: SIAM Journal on Control and Optimization. Bd. 49 (2011) Heft 6 . - S. 2349-2377.
ISSN 1095-7138
DOI: https://doi.org/10.1137/100787829

Karafyllis, Iasson ; Grüne, Lars:
Feedback stabilization methods for the numerical solution of ordinary differential equations.
In: Discrete and Continuous Dynamical Systems. Series B. Bd. 16 (2011) Heft 1 . - S. 283-317.
ISSN 1531-3492
DOI: https://doi.org/10.3934/dcdsb.2011.16.283

Aoyama, Hideaki ; Grüne, Lars ; Semmler, Willi ; Fujiwara, Yoshi ; Souma, Wataru:
Fluctuation of Firm Size in the Long-Run and Bimodal Distribution.
In: Advances in Operations Research. Bd. 2011 (2011) . - 269239.
ISSN 1687-9147
DOI: https://doi.org/10.1155/2011/269239

Grüne, Lars ; Pannek, Jürgen:
Nonlinear Model Predictive Control : Theory and Algorithms.
London : Springer , 2011 . - XII, 360 S. - (Communications and Control Engineering )
ISBN 978-0-85729-500-2

DOI: https://doi.org/10.1007/978-0-85729-501-9

Grüne, Lars:
Optimal invariance via receding horizon control.
In: 50th IEEE Conference on Decision and Control and European Control Conference. - Piscataway, NJ : IEEE , 2011 . - S. 2668-2673
ISBN 978-1-61284-800-6
DOI: https://doi.org/10.1109/CDC.2011.6160242

Findeisen, Rolf ; Grüne, Lars ; Pannek, Jürgen ; Varutti, Paolo:
Robustness of Prediction Based Delay Compensation for Nonlinear Systems.
In: IFAC Proceedings Volumes. Bd. 44 (2011) Heft 1 . - S. 203-208.
ISSN 1474-6670
DOI: https://doi.org/10.3182/20110828-6-IT-1002.03090

Grüne, Lars ; Worthmann, Karl:
Sampled-data redesign for nonlinear multi-input systems.
In: Ancona, Fabio ; Bressan, Alberto ; Cannarsa, Piermarco ; Clarke, Francis ; Wolenski, Peter R. (Hrsg.): Geometric Control And Nonsmooth Analysis : in honor of the 73rd birthday of H. Hermes and the 71st birthday of R. T. Rockafellar. - New Jersey, NJ : World Scientific , 2011 . - S. 206-227 . - (Series on Advances in Mathematics for Applied Sciences ; 76 )
ISBN 978-981-277-606-8
DOI: https://doi.org/10.1142/9789812776075_0011

2010

Grüne, Lars ; Pannek, Jürgen:
Analysis of unconstrained NMPC schemes with incomplete optimization.
In: IFAC Proceedings Volumes. Bd. 43 (2010) Heft 14 . - S. 238-243.
ISSN 1474-6670
DOI: https://doi.org/10.3182/20100901-3-IT-2016.00124

Grüne, Lars ; Pannek, Jürgen ; Seehafer, Martin ; Worthmann, Karl:
Analysis of Unconstrained Nonlinear MPC Schemes with Time Varying Control Horizon.
In: SIAM Journal on Control and Optimization. Bd. 48 (2010) Heft 8 . - S. 4938-4962.
ISSN 1095-7138
DOI: https://doi.org/10.1137/090758696

Baier, Robert ; Grüne, Lars ; Hafstein, Sigurdur Freyr:
Computing Lyapunov functions for strongly asymptotically stable differential inclusions.
In: IFAC Proceedings Volumes. Bd. 43 (2010) Heft 14 . - S. 1098-1103.
ISSN 1474-6670
DOI: https://doi.org/10.3182/20100901-3-IT-2016.00132

Grüne, Lars ; Müller, Florian:
Global optimal control of quantized systems.
In: Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010. - Budapest , 2010 . - S. 1231-1237
ISBN 978-963-311-370-7

Greiner, Alfred ; Grüne, Lars ; Semmler, Willi:
Growth and Climate Change : Threshold and Multiple Equilibria.
In: Crespo Cuaresma, Jesús ; Palokangas, Tapio ; Tarasyev, Alexander (Hrsg.): Dynamic Systems, Economic Growth, and the Environment. - Berlin : Springer , 2010 . - S. 63-78 . - (Dynamic Modeling and Econometrics in Economics and Finance ; 12 )
ISBN 978-3-642-02132-9
DOI: https://doi.org/10.1007/978-3-642-02132-9_4

Altmüller, Nils ; Grüne, Lars ; Worthmann, Karl:
Instantaneous Control of the linear wave equation.
In: Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010. - Budapest , 2010 . - S. 1895-1899
ISBN 978-963-311-370-7

Grüne, Lars ; von Lossow, Marcus ; Pannek, Jürgen ; Worthmann, Karl:
MPC : implications of a growth condition on exponentially controllable systems.
In: IFAC Proceedings Volumes. Bd. 43 (2010) Heft 14 . - S. 385-390.
ISSN 1474-6670
DOI: https://doi.org/10.3182/20100901-3-IT-2016.00225

Grüne, Lars ; von Lossow, Marcus ; Worthmann, Karl:
NMPC Suboptimality Estimates for Sampled–Data Continuous Systems.
In: Diehl, Moritz ; Glineur, Francois ; Jarlebring, Elias ; Michiels, Wim (Hrsg.): Recent Advances in Optimization and its Applications in Engineering. - Berlin : Springer , 2010 . - S. 329-338
ISBN 978-3-642-12597-3
DOI: https://doi.org/10.1007/978-3-642-12598-0_29

Altmüller, Nils ; Grüne, Lars ; Worthmann, Karl:
Performance of NMPC Schemes without Stabilizing Terminal Constraints.
In: Diehl, Moritz ; Glineur, Francois ; Jarlebring, Elias ; Michiels, Wim (Hrsg.): Recent Advances in Optimization and its Applications in Engineering. - Berlin : Springer , 2010 . - S. 289-298
ISBN 978-3-642-12597-3
DOI: https://doi.org/10.1007/978-3-642-12598-0_25

Grüne, Lars ; Sager, Sebastian ; Allgöwer, Frank ; Bock, Hans Georg ; Diehl, Moritz:
Predictive Planning and Systematic Action : On the Control of Technical Processes.
In: Grötschel, Martin ; Lucas, Klaus ; Mehrmann, Volker (Hrsg.): Production Factor Mathematics. - Berlin : Springer , 2010 . - S. 9-37
ISBN 978-3-642-11247-8
DOI: https://doi.org/10.1007/978-3-642-11248-5_2

Altmüller, Nils ; Grüne, Lars ; Worthmann, Karl:
Receding horizon optimal control for the wave equation.
In: 49th IEEE Conference on Decision and Control (CDC). - Piscataway, NJ : IEEE , 2010 . - S. 3427-3432
ISBN 978-1-4244-7745-6
DOI: https://doi.org/10.1109/CDC.2010.5717272

Grüne, Lars ; Müller, Florian ; Jerg, Stefan ; Junge, Oliver ; Post, Marcus ; Lehmann, Daniel ; Lunze, Jan:
Two Complementary Approaches to Event-based Control : Zwei komplementäre Zugänge zur ereignisbasierten Regelung.
In: Automatisierungstechnik. Bd. 58 (2010) Heft 4 . - S. 173-182.
ISSN 2196-677X
DOI: https://doi.org/10.1524/auto.2010.0832

Grüne, Lars:
Worst case vs. average performance estimates for unconstrained NMPC schemes.
In: Proceedings in Applied Mathematics and Mechanics. Bd. 10 (2010) Heft 1 . - S. 607-608.
ISSN 1617-7061
DOI: https://doi.org/10.1002/pamm.201010296

2009

Grüne, Lars ; Müller, Florian:
An algorithm for event-based optimal feedback control.
In: Proceedings of the 48th IEEE Conference on Decision and Control. - Piscataway, NJ : IEEE , 2009 . - S. 5311-5316
ISBN 9781424438716

Grüne, Lars:
Analysis and Design of Unconstrained Nonlinear MPC Schemes for Finite and Infinite Dimensional Systems.
In: SIAM Journal on Control and Optimization. Bd. 48 (2009) Heft 2 . - S. 1206-1228.
ISSN 1095-7138
DOI: https://doi.org/10.1137/070707853

Grüne, Lars ; Nešić, Dragan ; Worthmann, Karl:
Digital redesign of nonlinear multi-input systems.
In: Oberwolfach Reports. Bd. 6 (2009) Heft 1 . - S. 619-622.
ISSN 1660-8941

Camilli, Fabio ; Grüne, Lars ; Wirth, Fabian:
Domains of attraction of interconnected systems : A Zubov method approach.
In: Proceedings of the European Control Conference (ECC). - Piscataway, NJ : IEEE , 2009 . - S. 91-96
ISBN 978-3-9524173-9-3
DOI: https://doi.org/10.23919/ECC.2009.7074385

Semmler, Willi ; Grüne, Lars ; Öhrlein, Caroline:
Dynamic Consumption and Portfolio Decisions with Time Varying Asset Returns.
In: The Journal of Wealth Management. Bd. 12 (2009) Heft 2 . - S. 21-47.
ISSN 2374-1368
DOI: https://doi.org/10.3905/jwm.2009.12.2.021

Karafyllis, Iasson ; Grüne, Lars:
Feedback Stabilization Methods for the Numerical Solution of Systems of Ordinary Differential Equations.
In: Numerical analysis and applied mathematics : International Conference on Numerical Analysis and Applied Mathematics 2009. - Melville, NY : American Inst. of Physics , 2009 . - S. 152-155 . - (AIP Conference Proceedings ; 1168 )
ISBN 978-0-7354-0709-1
DOI: https://doi.org/10.1063/1.3241391

Grüne, Lars:
Gewöhnliche Differentialgleichungen : Eine Einführung aus der Perspektive der dynamischen Systeme.
Wiesbaden : Vieweg + Teubner , 2009 . - XI, 243 S.
ISBN 978-3-8348-0381-8

DOI: https://doi.org/10.1007/978-3-8348-9261-4

Grüne, Lars ; Pannek, Jürgen ; Worthmann, Karl:
A networked unconstrained nonlinear MPC scheme.
In: Proceedings of the European Control Conference (ECC). - Piscataway, NJ : IEEE , 2009 . - S. 371-376
ISBN 978-3-9524173-9-3
DOI: https://doi.org/10.23919/ECC.2009.7074430

Grüne, Lars ; Pannek, Jürgen:
Practical NMPC suboptimality estimates along trajectories.
In: Systems & Control Letters. Bd. 58 (2009) Heft 3 . - S. 161-168.
ISSN 1872-7956
DOI: https://doi.org/10.1016/j.sysconle.2008.10.012

Grüne, Lars ; Pannek, Jürgen ; Worthmann, Karl:
A prediction based control scheme for networked systems with delays and packet dropouts.
In: Proceedings of the 48th IEEE Conference on Decision and Control. - Piscataway, NJ : IEEE , 2009 . - S. 537-542
ISBN 9781424438716

Grüne, Lars ; Junge, Oliver:
Set Oriented Construction of Globally Optimal Controllers : Mengenorientierte Konstruktion global optimaler Regler.
In: Automatisierungstechnik. Bd. 57 (2009) Heft 6 . - S. 287-295.
ISSN 2196-677X
DOI: https://doi.org/10.1524/auto.2009.0777

Grüne, Lars ; Sager, Sebastian ; Allgöwer, Frank ; Bock, Hans Georg ; Diehl, Moritz:
Vorausschauend Planen, Gezielt Handeln : Über die Regelung und Steuerung technischer Prozesse.
In: Gröschel, Martin ; Lucas, Klaus ; Mehrmann, Volker (Hrsg.): Produktionsfaktor Mathematik. - Berlin : Springer , 2009 . - S. 27-62
ISBN 978-3-540-89434-6
DOI: https://doi.org/10.1007/978-3-540-89435-3_2

2008

Grüne, Lars ; Worthmann, Karl:
Nonlinear sampled-data redesign : analytical formulas and their practical implementation.
In: Mathematical Theory of Networks and Systems (MTNS2008) : Proceedings of the 18th International Symposium Blacksburg, Virginia, USA. - Blacksburg, VA, USA , 2008 . - CD-ROM, Paper 084.pdf, 6 S.

Grüne, Lars ; Müller, Florian:
Set oriented optimal control using past information.
In: Mathematical Theory of Networks and Systems (MTNS2008) : Proceedings of the 18th International Symposium Blacksburg, Virginia, USA. - Blacksburg, VA, USA , 2008 . - CD-Rom, Paper 125.pdf, 6 S.

Grüne, Lars ; Pannek, Jürgen:
Trajectory based suboptimality estimates for receding horizon controllers.
In: Mathematical Theory of Networks and Systems (MTNS2008) : Proceedings of the 18th International Symposium Blacksburg, Virginia, USA. - Blacksburg, VA, USA , 2008 . - CD-ROM, Paper 023.pdf, 6 S.

Grüne, Lars ; Semmler, Willi:
Asset pricing with loss aversion.
In: Journal of Economic Dynamics and Control. Bd. 32 (2008) Heft 10 . - S. 3253-3274.
ISSN 1879-1743
DOI: https://doi.org/10.1016/j.jedc.2008.01.002

Grüne, Lars ; Worthmann, Karl ; Nešić, Dragan:
Continuous-time controller redesign for digital implementation : A trajectory based approach.
In: Automatica. Bd. 44 (2008) Heft 1 . - S. 225-232.
ISSN 1873-2836
DOI: https://doi.org/10.1016/j.automatica.2007.05.003

Camilli, Fabio ; Grüne, Lars ; Wirth, Fabian:
Control Lyapunov Functions and Zubov's Method.
In: SIAM Journal on Control and Optimization. Bd. 47 (2008) Heft 1 . - S. 301-326.
ISSN 1095-7138
DOI: https://doi.org/10.1137/06065129X

Grüne, Lars ; Junge, Oliver:
Global Optimal Control of Perturbed Systems.
In: Journal of Optimization Theory and Applications. Bd. 136 (2008) Heft 3 . - S. 411-429.
ISSN 0022-3239
DOI: https://doi.org/10.1007/s10957-007-9312-z

Grüne, Lars:
Input-to-state stability, numerical dynamics and sampled-data control.
In: GAMM-Mitteilungen. Bd. 31 (2008) Heft 1 . - S. 94-114.
ISSN 1522-2608
DOI: https://doi.org/10.1002/gamm.200890005

Grüne, Lars ; Rantzer, Anders:
On the Infinite Horizon Performance of Receding Horizon Controllers.
In: IEEE Transactions on Automatic Control. Bd. 53 (2008) Heft 9 . - S. 2100-2111.
ISSN 1558-2523
DOI: https://doi.org/10.1109/TAC.2008.927799

Grüne, Lars:
Optimization Based Stabilization of Nonlinear Control Systems.
In: Lirkov, Ivan D. ; Margenov, Svetozar ; Waśniewski, Jerzy (Hrsg.): Large-Scale Scientific Computing : 6th International Conference, LSSC 2007, Sozopol, Bulgaria, June 5-9, 2007 ; revised papers. - Berlin : Springer , 2008 . - S. 52-65 . - (Lecture Notes in Computer Science ; 4818 )
ISBN 978-3-540-78825-6
DOI: https://doi.org/10.1007/978-3-540-78827-0_5

Grüne, Lars ; Pannek, Jürgen ; Worthmann, Karl ; Nešić, Dragan:
Redesign Techniques for Nonlinear Sampled-data Systems : (Entwurfstechniken für nichtlineare Abtastsysteme).
In: Automatisierungstechnik. Bd. 56 (2008) Heft 1 . - S. 38-48.
ISSN 2196-677X
DOI: https://doi.org/10.1524/auto.2008.0684

2007

Grüne, Lars ; Junge, Oliver:
Approximately optimal nonlinear stabilization with preservation of the Lyapunov function property.
In: 46th IEEE Conference on Decision and Control. - Piscataway, NJ : IEEE , 2007 . - S. 702-707
ISBN 1-4244-1497-0
DOI: https://doi.org/10.1109/CDC.2007.4434428

Grüne, Lars ; Semmler, Willi:
Asset pricing with dynamic programming.
In: Computational Economics. Bd. 29 (2007) . - S. 233-265.
ISSN 1572-9974
DOI: https://doi.org/10.1007/s10614-006-9063-1

Becker, Stephanie ; Grüne, Lars ; Semmler, Willi:
Comparing accuracy of second-order approximation and dynamic programming.
In: Computational Economics. Bd. 30 (2007) . - S. 65-91.
ISSN 1572-9974
DOI: https://doi.org/10.1007/s10614-007-9087-1

Grüne, Lars:
Computing minimal optimization horizons for stabilizing unconstrained MPC schemes.
In: Proceedings in Applied Mathematics and Mechanics. Bd. 7 (2007) Heft 1 . - S. 4130007-4130008.
ISSN 1617-7061
DOI: https://doi.org/10.1002/pamm.200700203

Grüne, Lars:
Computing stability and performance bounds for unconstrained NMPC schemes.
In: 46th IEEE Conference on Decision and Control. - Piscataway, NJ : IEEE , 2007 . - S. 1263-1268
ISBN 1-4244-1497-0
DOI: https://doi.org/10.1109/CDC.2007.4434156

Grüne, Lars ; Junge, Oliver:
An efficient algorithm for perturbed shortest path problems.
In: Proceedings in Applied Mathematics and Mechanics. Bd. 7 (2007) Heft 1 . - S. 1025003-1025004.
ISSN 1617-7061
DOI: https://doi.org/10.1002/pamm.200700714

Grüne, Lars ; Semmler, Willi ; Bernard, Lucas:
Firm value, diversified capital assets, and credit risk: towards a theory of default correlation.
In: The Journal of Credit Risk. Bd. 3 (2007) Heft 4 . - S. 81-109.
ISSN 1755-9723
DOI: https://doi.org/10.21314/JCR.2007.053

Grüne, Lars ; Kloeden, Peter E. ; Siegmund, Stefan ; Wirth, Fabian:
Lyapunov's second method for nonautonomous differential equations.
In: Discrete and Continuous Dynamical Systems. Bd. 18 (2007) Heft 2-3 . - S. 375-403.
ISSN 1553-5231
DOI: https://doi.org/10.3934/dcds.2007.18.375

Grüne, Lars ; Nešić, Dragan ; Pannek, Jürgen:
Model predictive control for nonlinear sampled-data systems.
In: Findeisen, Rolf ; Allgöwer, Frank ; Biegler, Lorenz T. (Hrsg.): Assessment and Future Directions of Nonlinear Model Predictive Control. - Berlin : Springer , 2007 . - S. 105-113 . - (Lecture Notes in Control and Information Sciences ; 358 )
ISBN 978-3-540-72698-2
DOI: https://doi.org/10.1007/978-3-540-72699-9_8

2006

Bauer, Florian ; Grüne, Lars ; Semmler, Willi:
Adaptive spline interpolation for Hamilton–Jacobi–Bellman equations.
In: Applied Numerical Mathematics. Bd. 56 (2006) Heft 9 . - S. 1196-1210.
ISSN 1873-5460
DOI: https://doi.org/10.1016/j.apnum.2006.03.011

Grüne, Lars ; Nešić, Dragan ; Worthmann, Karl:
High order approximations by sampled-data feedback.
In: MTNS 2006 : Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems. - Kyoto, Japan : Kyoto Univ. , 2006 . - S. 1780-1787

Grüne, Lars ; Kloeden, Peter E.:
Higher order numerical approximation of switching systems.
In: Systems & Control Letters. Bd. 55 (2006) Heft 9 . - S. 746-754.
ISSN 1872-7956
DOI: https://doi.org/10.1016/j.sysconle.2006.03.002

Grüne, Lars ; Saint-Pierre, Patrick:
An invariance kernel representation of ISDS Lyapunov functions.
In: Systems & Control Letters. Bd. 55 (2006) Heft 9 . - S. 736-745.
ISSN 1872-7956
DOI: https://doi.org/10.1016/j.sysconle.2006.02.003

Grüne, Lars ; Junge, Oliver:
Optimal stabilization of hybrid systems using a set oriented approach.
In: MTNS 2006 : Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems. - Kyoto, Japan : Kyoto Univ. , 2006 . - S. 2089-2093

Nešić, Dragan ; Grüne, Lars:
A receding horizon control approach to sampled-data implementation of continuous-time controllers.
In: Systems & Control Letters. Bd. 55 (2006) Heft 8 . - S. 660-672.
ISSN 1872-7956
DOI: https://doi.org/10.1016/j.sysconle.2005.09.013

Camilli, Fabio ; Cesaroni, Annalisa ; Grüne, Lars ; Wirth, Fabian:
Stabilization of controlled diffusions and Zubov's method.
In: Stochastics and Dynamics. Bd. 6 (2006) Heft 3 . - S. 373-394.
ISSN 0219-4937
DOI: https://doi.org/10.1142/S0219493706001803

Grüne, Lars ; Ratzer, A.:
Suboptimality estimates for receding horizon controllers.
In: MTNS 2006 : Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems. - Kyoto, Japan : Kyoto Univ. , 2006 . - S. 120-127

2005

Camilli, Fabio ; Grüne, Lars ; Wirth, Fabian:
Calculating the domain of attraction : Zubov's method and extensions.
In: Proceedings of the Stability and Control Processes Conference (SCP 2005), dedicated to the 75th birthday anniversary of V. I. Zubov. - St. Petersburg , 2005 . - S. 27-36

Grüne, Lars ; Junge, Oliver:
Constructing Robust Feedback Laws by Set Oriented Numerical Methods.
In: Proceedings in Applied Mathematics and Mechanics. Bd. 5 (2005) Heft 1 . - S. 157-160.
ISSN 1617-7061
DOI: https://doi.org/10.1002/pamm.200510059

Grüne, Lars ; Semmler, Willi ; Sieveking, Malte:
Creditworthiness and thresholds in a credit market model with multiple equilibria.
In: Economic Theory. Bd. 25 (2005) Heft 2 . - S. 287-315.
ISSN 1432-0479
DOI: https://doi.org/10.1007/s00199-003-0442-8

Grüne, Lars ; Semmler, Willi:
Default Risk, Asset Pricing, and Debt Control.
In: Journal of Financial Econometrics. Bd. 3 (2005) Heft 1 . - S. 79-106.
ISSN 1479-8417
DOI: https://doi.org/10.1093/jjfinec/nbi006

Nešić, Dragan ; Grüne, Lars:
Lyapunov-based continuous-time nonlinear controller redesign for sampled-data implementation.
In: Automatica. Bd. 41 (2005) Heft 7 . - S. 1143-1156.
ISSN 1873-2836
DOI: https://doi.org/10.1016/j.automatica.2005.03.001

Grüne, Lars ; Nešić, Dragan ; Pannek, Jürgen:
Model predictive sampled-data redesign for nonlinear systems.
In: Proceedings of the 44th IEEE Conference on Decision and Control. - Piscatawny, NJ : IEEE , 2005 . - S. 36-41
ISBN 0-7803-9567-0
DOI: https://doi.org/10.1109/CDC.2005.1582127

Grüne, Lars ; Nešić, Dragan:
Nonlinear sampled-data controller redesign via Lyapunov functions.
In: Horáček, Petr (Hrsg.): Preprints of the 16th World Congress of the International Federation of Automatic Control : July 3 - 8, 2005, Prague, Czech Republic. - s.l. : IFAC , 2005 . - DVD-ROM, Paper No. Fr-A17-TO/5

Grüne, Lars ; Nešić, Dragan ; Pannek, Jürgen:
Redesign techniques for nonlinear sampled-data control.
In: Oberwolfach Reports. Bd. 2 (2005) Heft 1 . - S. 584-586.
ISSN 1660-8941

Grüne, Lars ; Junge, Oliver:
A set oriented approach to optimal feedback stabilization.
In: Systems & Control Letters. Bd. 54 (2005) Heft 2 . - S. 169-180.
ISSN 1872-7956
DOI: https://doi.org/10.1016/j.sysconle.2004.08.005

Grüne, Lars ; Saint-Pierre, Patrick:
A set valued characterization of ISDS Lyapunov functions.
In: Proceedings of the 44th IEEE Conference on Decision and Control. - Piscatawny, NJ : IEEE , 2005 . - S. 4718-4723
ISBN 0-7803-9567-0
DOI: https://doi.org/10.1109/CDC.2005.1582127

Grüne, Lars ; Kato, Mika ; Semmler, Willi:
Solving ecological management problems using dynamic programming.
In: Journal of Economic Behavior & Organization. Bd. 57 (2005) Heft 4 . - S. 448-473.
ISSN 1879-1751
DOI: https://doi.org/10.1016/j.jebo.2005.04.002

Camilli, Fabio ; Grüne, Lars ; Wirth, Fabian:
Zubov's method for stochastic control systems.
In: IFAC Proceedings Volumes. Bd. 38 (2005) Heft 1 . - S. 259-264.
ISSN 1474-6670
DOI: https://doi.org/10.3182/20050703-6-CZ-1902.00443

2004

Camilli, Fabio ; Grüne, Lars ; Wirth, Fabian:
Characterizing controllability probabilities of stochastic control systems via Zubov's method.
In: de Moor, B. ; Motmans, Bart ; Willems, J. ; van Dooren, Paul ; Blondel, Vincent (Hrsg.): Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS2004). - Leuven : KU Leuven - ESAT , 2004 . - CD-ROM, WA3, Paper No. 65

Camilli, Fabio ; Grüne, Lars ; Wirth, Fabian:
Construction of Lyapunov functions on the domain of asymptotic nullcontrollability : Numerics.
In: IFAC Proceedings Volumes. Bd. 37 (2004) Heft 13 . - S. 715-720.
ISSN 1474-6670
DOI: https://doi.org/10.1016/S1474-6670(17)31309-5

Camilli, Fabio ; Grüne, Lars ; Wirth, Fabian:
Construction of Lyapunov functions on the domain of asymptotic nullcontrollability : Theory.
In: IFAC Proceedings Volumes. Bd. 37 (2004) Heft 13 . - S. 709-714.
ISSN 1474-6670
DOI: https://doi.org/10.1016/S1474-6670(17)31308-3

Grüne, Lars:
Error estimation and adaptive discretization for the discrete stochastic Hamilton-Jacobi-Bellman equation.
In: Numerische Mathematik. Bd. 99 (2004) Heft 1 . - S. 85-112.
ISSN 0029-599X
DOI: https://doi.org/10.1007/s00211-004-0555-4

Grüne, Lars:
Quantitative aspects of the input-to-state stability property.
In: Queiroz, Marcio S. de ; Malisoff, Michael ; Wolenski, Peter (Hrsg.): Optimal control, stabilization and nonsmooth analysis. - Berlin : Springer , 2004 . - S. 215-230 . - (Lecture Notes in Control and Information Sciences ; 301 )
ISBN 3-540-21330-9

Grüne, Lars:
Robust asymptotic controllability under time-varying perturbations.
In: Stochastics and Dynamics. Bd. 4 (2004) Heft 3 . - S. 297-316.
ISSN 0219-4937
DOI: https://doi.org/10.1142/S0219493704001085

Grüne, Lars ; Semmler, Willi:
Using dynamic programming with adaptive grid scheme for optimal control problems in economics.
In: Journal of Economic Dynamics and Control. Bd. 28 (2004) Heft 12 . - S. 2427-2456.
ISSN 1879-1743
DOI: https://doi.org/10.1016/j.jedc.2003.11.002

2003

Grüne, Lars:
Attraction Rates, Robustness, and Discretization of Attractors.
In: SIAM Journal on Numerical Analysis. Bd. 41 (2003) Heft 6 . - S. 2096-2113.
ISSN 1095-7170
DOI: https://doi.org/10.1137/S003614290139411X

Camilli, Fabio ; Grüne, Lars:
Characterizing attraction probabilities via the stochastic Zubov equation.
In: Discrete and Continuous Dynamical Systems. Series B. Bd. 3 (2003) Heft 3 . - S. 457-468.
ISSN 1531-3492
DOI: https://doi.org/10.3934/dcdsb.2003.3.457

Grüne, Lars ; Kloeden, Peter E.:
Numerical Schemes of Higher Order for a Class of Nonlinear Control Systems.
In: Dimov, Ivan ; Lirkov, Ivan ; Margenov, Svetozar ; Zlatev, Zahari (Hrsg.): Numerical Methods and Applications : 5th International Conference, NMA 2002 Borovets, Bulgaria, August 20–24, 2002 ; Revised Papers. - Berlin : Springer , 2003 . - S. 213-220 . - (Lecture Notes in Computer Science ; 2542 )
ISBN 978-3-540-00608-4
DOI: https://doi.org/10.1007/3-540-36487-0_23

Grüne, Lars ; Nešić, Dragan:
Optimization-Based Stabilization of Sampled-Data Nonlinear Systems via Their Approximate Discrete-Time Models.
In: SIAM Journal on Control and Optimization. Bd. 42 (2003) Heft 1 . - S. 98-122.
ISSN 1095-7138
DOI: https://doi.org/10.1137/S036301290240258X

2002

Grüne, Lars:
Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization.
Berlin : Springer , 2002 . - 235 S. - (Lecture Notes in Mathematics ; 1783 )
ISBN 978-3-540-43391-0

Rez.:

Zentralblatt Mathematik Mathematical Reviews

DOI: https://doi.org/10.1007/b83677

Dynamics, Bifurcations and Control.
Hrsg.: Colonius, Fritz ; Grüne, Lars
Berlin : Springer , 2002 . - 301 S. - (Lecture Notes in Control and Information Sciences ; 273 )
ISBN 978-3-540-42890-9

Rez.:

Zentralblatt Mathematik

DOI: https://doi.org/10.1007/3-540-45606-6

Grüne, Lars:
Gain preserving Lyapunov functions for perturbed and controlled systems.
In: Proceedings of the 41st IEEE Conference on Decision and Control. Volume 1. - Piscataway, NJ : IEEE , 2002 . - S. 707-712
ISBN 0-7803-7516-5
DOI: https://doi.org/10.1109/CDC.2002.1184587

Camilli, Fabio ; Grüne, Lars ; Wirth, Fabian:
A generalization of Zubov's method to perturbed systems.
In: Proceedings of the 41st IEEE Conference on Decision and Control. Volume 3. - Piscataway, NJ : IEEE , 2002 . - S. 3518-3523
ISBN 0-7803-7516-5
DOI: https://doi.org/10.1109/CDC.2002.1184420

Grüne, Lars:
Input-to-state dynamical stability and its Lyapunov function characterization.
In: IEEE Transactions on Automatic Control. Bd. 47 (2002) Heft 9 . - S. 1499-1504.
ISSN 1558-2523
DOI: https://doi.org/10.1109/TAC.2002.802761

Cyganowski, Sasha ; Grüne, Lars ; Kloeden, Peter E.:
MAPLE for Jump-Diffusion Stochastic Differential Equations in Finance.
In: Nielsen, Søren S. (Hrsg.): Programming Languages and Systems in Computational Economics and Finance. - Boston : Kluwer Academic Publ. , 2002 . - S. 441-460 . - (Advances in Computational Economics ; 18 )
ISBN 1-4020-7139-6

Grüne, Lars:
Quantitative aspects of the input-to-state stability property.
In: Gilliam, David S. ; Rosenthal, Joachim (Hrsg.): Proceedings of the Fifteenth International Symposium on Mathematical Theory of Networks and Systems, MTNS 2002 : University of Notre Dame, South Bend, Indiana, USA, August 12 - 16, 2002. - South Bend, Indiana , 2002 . - Article TUA4-4 [Elektronische Ressource]

Grüne, Lars ; Nešić, Dragan:
Stabilization of sampled-data nonlinear systems via their approximate models : an optimization based approach.
In: Proceedings of the 41st IEEE Conference on Decision and Control. Volume 1. - Piscataway, NJ : IEEE , 2002 . - S. 1934-1939
ISBN 0-7803-7516-5
DOI: https://doi.org/10.1109/CDC.2002.1184810

Grüne, Lars:
Subdivision techniques for the computation of domains of attraction and reachable sets.
In: Kuržanskij, Aleksandr B. ; Fradkov, A. L. (Hrsg.): Nonlinear control systems 2001 : (NOLCOS 2001); a proceedings volume from the 5th IFAC Symposium St. Petersburg, Russia, 4 - 6 July 2001. Volume 2. - Oxford : Pergamon , 2002 . - S. 762-767
ISBN 0-08-043560-2

2001

Grüne, Lars:
Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations.
In: Falcone, Maurizio ; Makridakis, Charalampos (Hrsg.): Numerical Methods for Viscosity Solutions and Applications. - Singapore : World Scientific , 2001 . - S. 153-172 . - (Series on Advances in Mathematics for Applied Sciences ; 59 )
ISBN 981-02-4717-6

Grüne, Lars:
Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization.
Frankfurt/Main , 2001
( Habilitation, 2001 , Goethe-Universität Frankfurt am Main)

Grüne, Lars ; Kloeden, Peter E.:
Discretization, inflation and perturbation of attractors.
In: Fiedler, Bernold (Hrsg.): Ergodic theory, analysis and efficient simulation of dynamical systems. - Berlin : Springer , 2001 . - S. 399-416
ISBN 978-3-642-56589-2
DOI: https://doi.org/10.1007/978-3-642-56589-2_17

Camilli, Fabio ; Grüne, Lars ; Wirth, Fabian:
A Generalization of Zubov's Method to Perturbed Systems.
In: SIAM Journal on Control and Optimization. Bd. 40 (2001) Heft 2 . - S. 496-515.
ISSN 1095-7138
DOI: https://doi.org/10.1137/S036301299936316X

Grüne, Lars ; Kloeden, Peter E.:
Higher order numerical schemes for affinely controlled nonlinear systems.
In: Numerische Mathematik. Bd. 89 (2001) . - S. 669-690.
ISSN 0029-599X
DOI: https://doi.org/10.1007/s002110000279

Grüne, Lars:
Homogeneous control Lyapunov functions for homogeneous control systems.
In: el Jai, Abdelhaq (Hrsg.): Mathematical Theory of Networks and Systems. - Zielona Gora : Techn. Univ. Press , 2001

Cyganowski, Sasha ; Grüne, Lars ; Kloeden, Peter:
MAPLE for Stochastic Differential Equations.
In: Blowey, James F. ; Coleman, John P. ; Craig, Alan W. (Hrsg.): Theory and Numerics of Differential Equations : Durham 2000. - Berlin : Springer , 2001 . - S. 127-177
ISBN 978-3-662-04354-7
DOI: https://doi.org/10.1007/978-3-662-04354-7_3

Grüne, Lars ; Kloeden, Peter E.:
Pathwise Approximation of Random Ordinary Differential Equations.
In: BIT Numerical Mathematics. Bd. 41 (2001) Heft 4 . - S. 711-721.
ISSN 0006-3835
DOI: https://doi.org/10.1023/A:1021995918864

Grüne, Lars:
Persistence of attractors for one-step discretization of ordinary differential equations.
In: IMA Journal of Numerical Analysis. Bd. 21 (2001) Heft 3 . - S. 751-767.
ISSN 1464-3642
DOI: https://doi.org/10.1093/imanum/21.3.751

Camilli, Fabio ; Grüne, Lars ; Wirth, Fabian:
A regularization of Zubov's equation for robust domains of attraction.
In: Isidori, Alberto ; Lamnabhi-Lagarrigue, Françoise ; Respondek, Witold (Hrsg.): Nonlinear control in the Year 2000. Volume 1. - Berlin : Springer , 2001 . - S. 277-290 . - (Lecture Notes in Control and Information Sciences ; 258 )
ISBN 978-1-85233-363-8
DOI: https://doi.org/10.1007/BFb0110220

Grüne, Lars ; Camilli, Fabio ; Wirth, Fabian:
Zubov's method for perturbed differential equations.
In: el Jai, Abdelhaq (Hrsg.): Mathematical Theory of Networks and Systems. - Zielona Gora : Techn. Univ. Press , 2001

2000

Grüne, Lars:
Attractors under perturbation and discretization.
In: Proceedings of the 39th IEEE Conference on Decision and Control. Volume 3. - Piscataway, NJ : IEEE , 2000 . - S. 2118-2122
ISBN 0-7803-6638-7
DOI: https://doi.org/10.1109/CDC.2000.914107

Grüne, Lars:
Computation of the Lyapunov Spectrum (Appendix D).
In: Colonius, Fritz ; Kliemann, Wolfgang (Hrsg.): The Dynamics of Control. - Boston ; Basel : Birkhäuser , 2000 . - S. 569-596
ISBN 978-3-7643-3683-7

Grüne, Lars ; Wirth, Fabian:
Computing control Lyapunov functions via a Zubov type algorithm.
In: Proceedings of the 39th IEEE Conference on Decision and Control. Volume 3. - Piscataway, NJ : IEEE , 2000 . - S. 2129-2134
ISBN 0-7803-6638-7
DOI: https://doi.org/10.1109/CDC.2000.914109

Grüne, Lars:
Convergence Rates of Perturbed Attracting Sets with Vanishing Perturbation.
In: Journal of Mathematical Analysis and Applications. Bd. 244 (2000) Heft 2 . - S. 369-392.
ISSN 1096-0813
DOI: https://doi.org/10.1006/jmaa.2000.6707

Grüne, Lars:
Homogeneous state feedback stabilization of homogeneous systems.
In: Proceedings of the 39th IEEE Conference on Decision and Control. Volume 4. - Piscataway, NJ : IEEE , 2000 . - S. 3409-3414
ISBN 0-7803-6638-7
DOI: https://doi.org/10.1109/CDC.2000.912230

Grüne, Lars:
Homogeneous State Feedback Stabilization of Homogenous Systems.
In: SIAM Journal on Control and Optimization. Bd. 38 (2000) Heft 4 . - S. 1288-1308.
ISSN 1095-7138
DOI: https://doi.org/10.1137/S0363012998349303

Falcone, Maurizio ; Grüne, Lars ; Wirth, Fabian:
A maximum time approach to the computation of robust domains of attraction.
In: Fiedler, Bernold ; Gröger, Konrad ; Sprekels, Jürgen (Hrsg.): International Conference on Differential Equations : Berlin, Germany, 1 - 7 August 1999. Volume 1. - Singapore : World Scientific , 2000 . - S. 844-849
ISBN 9810243596

Camilli, Fabio ; Grüne, Lars:
Numerical Approximation of the Maximal Solutions for a Class of Degenerate Hamilton-Jacobi Equations.
In: SIAM Journal Numerical Analysis. Bd. 38 (2000) Heft 5 . - S. 1540-1560.
ISSN 1095-7170
DOI: https://doi.org/10.1137/S003614299834798X

Grüne, Lars ; Sontag, E. ; Wirth, Fabian:
On equivalence of exponential and asymptotic stability under changes of variables.
In: Fiedler, Bernold ; Gröger, Konrad ; Sprekels, Jürgen (Hrsg.): International Conference on Differential Equations. Volume 2. - Singapore : World Scientific , 2000 . - S. 850-852
ISBN 981-02-4989-6

Grüne, Lars ; Wirth, Fabian:
On the rate of convergence of infinite horizon discounted optimal value functions.
In: Nonlinear Analysis : Real World Applications. Bd. 1 (2000) Heft 4 . - S. 499-515.
ISSN 1468-1218
DOI: https://doi.org/10.1016/S0362-546X(99)00288-6

Grüne, Lars:
A uniform exponential spectrum for linear flows on vector bundles.
In: Journal of Dynamics and Differential Equations. Bd. 12 (2000) Heft 2 . - S. 435-448.
ISSN 1572-9222
DOI: https://doi.org/10.1023/A:1009024610394

1999

Grüne, Lars ; Sontag, Eduardo D. ; Wirth, Fabian:
Asymptotic stability equals exponential stability, and ISS equals finite energy gain - if you twist your eyes.
In: Systems & Control Letters. Bd. 38 (1999) Heft 2 . - S. 127-134.
ISSN 1872-7956
DOI: https://doi.org/10.1016/S0167-6911(99)00053-5

Grüne, Lars ; Wirth, Fabian:
Feedback stabilization of discrete-time homogeneous semi-linear systems.
In: Systems & Control Letters. Bd. 37 (1999) Heft 1 . - S. 19-30.
ISSN 1872-7956
DOI: https://doi.org/10.1016/S0167-6911(98)00110-8

Grüne, Lars:
Input-to-state stability of exponentially stabilized semilinear control systems with inhomogeneous perturbations.
In: Systems & Control Letters. Bd. 38 (1999) Heft 1 . - S. 27-35.
ISSN 1872-7956
DOI: https://doi.org/10.1016/S0167-6911(99)00044-4

Grüne, Lars ; Metscher, Martin ; Ohlberger, Mario:
On Numerical Algorithm and Interactive Visualization for Optimal Control Problems.
In: Computing and Visualization in Science. Bd. 1 (1999) Heft 4 . - S. 221-229.
ISSN 1433-0369
DOI: https://doi.org/10.1007/s007910050020

Grüne, Lars ; Sontag, Eduardo D. ; Wirth, Fabian:
On the equivalence between asymptotic and exponential stability, and between ISS and finite H-infinity gain.
In: Proceedings of the 38th IEEE Conference on Decision and Control. Volume 2. - Piscataway, NJ : IEEE , 1999 . - S. 1220-1225
ISBN 0-7803-5250-5

Grüne, Lars:
Stabilization by sampled and discrete feedback with positive sampling rate.
In: Aeyels, Dirk ; Lamnabhi-Lagarrigue, Françoise ; Schaft, Arjan van der (Hrsg.): Stability and Stabilization of Nonlinear Systems. - Berlin : Springer , 1999 . - S. 165-182 . - (Lecture Notes in Control and Information Sciences ; 246 )
ISBN 978-1-84628-577-6
DOI: https://doi.org/10.1007/1-84628-577-1_9

1998

Grüne, Lars:
Asymptotic Controllability and Exponential Stabilization of Nonlinear Control Systems at Singular Points.
In: SIAM Journal on Control and Optimization. Bd. 36 (1998) Heft 5 . - S. 1485-1503.
ISSN 1095-7138
DOI: https://doi.org/10.1137/S0363012997315919

Camilli, Fabio ; Grüne, Lars:
Maximal solutions for a class of singular Hamilton-Jacobi equations.
In: Beghi, Alessandro (Hrsg.): Mathematical theory of networks and systems : Proceedings of the MTNS 98 Symposium held in Padova, Italy, July 1998. - Padova : Il Poligrafo , 1998 . - S. 447-450
ISBN 88-7115-117-8

Grüne, Lars:
Numerical stabilization at singular points.
In: Beghi, Alessandro (Hrsg.): Mathematical theory of networks and systems : Proceedings of the MTNS 98 Symposium held in Padova, Italy, July 1998. - Padova : Il Poligrafo , 1998 . - S. 633-636
ISBN 88-7115-117-8

Grüne, Lars:
On input-to-state stabilizability of semilinear control systems.
In: Beghi, Alessandro (Hrsg.): Mathematical theory of networks and systems : Proceedings of the MTNS 98 Symposium held in Padova, Italy, July 1998. - Padova : Il Poligrafo , 1998 . - S. 181-184
ISBN 88-7115-117-8

Grüne, Lars ; Wirth, Fabian:
On linear convergence of discounted optimal control problems with vanishing discount rate.
In: Beghi, Alessandro (Hrsg.): Mathematical theory of networks and systems : Proceedings of the MTNS 98 Symposium held in Padova, Italy, July 1998. - Padova : Il Poligrafo , 1998 . - S. 185-188
ISBN 88-7115-117-8

Grüne, Lars:
On the Relation between Discounted and Average Optimal Value Functions.
In: Journal of Differential Equations. Bd. 148 (1998) Heft 1 . - S. 65-99.
ISSN 1090-2732
DOI: https://doi.org/10.1006/jdeq.1998.3451

Grüne, Lars ; Wirth, Fabian:
Stabilization of discrete-time bilinear systems.
In: ZAMM : Journal of Applied Mathematics and Mechanics = Zeitschrift für angewandte Mathematik und Mechanik. Bd. 78 (1998) Heft S 3 . - S. fmii925-fmi926.
ISSN 1521-4001
DOI: https://doi.org/10.1002/zamm.19980781535

1997

Grüne, Lars:
An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation.
In: Numerische Mathematik. Bd. 75 (1997) Heft 3 . - S. 319-337.
ISSN 0029-599X
DOI: https://doi.org/10.1007/s002110050241

Grüne, Lars:
Discrete Feedback Stabilization of Nonlinear Control Systems at a Singular Point.
In: Belgian Interuniversity Attraction Pole N° 2 (Hrsg.): European Control Conference : ECC 97. - Piscataway, NJ : IEEE , 1997 . - S. 3200-3203
ISBN 978-3-9524269-0-6

Grüne, Lars:
A spectral condition for asymptotic controllability and stabilization at singular points.
In: Proceedings of the 36th IEEE Conference on Decision and Control. Volume 5. - Piscataway, NJ : IEEE , 1997 . - S. 4431-4435
ISBN 0-7803-4187-2
DOI: https://doi.org/10.1109/CDC.1997.649648

1996

Grüne, Lars:
Discrete feedback stabilization of semilinear control systems.
In: ESAIM : Control, Optimisation and Calculus of Variations. Bd. 1 (1996) . - S. 207-224.
ISSN 1262-3377
DOI: https://doi.org/10.1051/cocv:1996106

Grüne, Lars:
Numerical Stabilization of Bilinear Control Systems.
In: SIAM Journal on Control and Optimization. Bd. 34 (1996) Heft 6 . - S. 2024-2050.
ISSN 1095-7138
DOI: https://doi.org/10.1137/S0363012994272290

Grüne, Lars:
Numerische Berechnung des Lyapunov-Spektrums bilinearer Kontrollsysteme.
Berlin : Logos-Verl. , 1996 . - II, 131 S.
ISBN 3-931216-29-2
( Dissertation, 1996 , Universität Augsburg, Mathematisch-Naturwissenschaftliche Fakultät)

1994

Grüne, Lars:
Numerische optimale Steuerung und Stabilisierung.
Augsburg , 1994
(Diplomarbeit, 1994 , Universität Augsburg, Mathematisch-Naturwissenschaftliche Fakultät, Institut für Mathematik)