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Does the effort of Monte Carlo pay off? : A case study on stochastic MPC

Title data

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

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Abstract in another language

Stochastic Model Predictive Control (MPC) has established itself as a simple method to approximate stochastically disturbed optimal control problems, yet it comes with significant computational effort. In particular, taking into account all information of stochastic disturbances—if at all possible—can be expensive. However, due to the continuous re-optimization, MPC schemes also have a certain inherent robustness. Hence, we ask the question, which part of the perturbation is absorbed by the MPC-inherent robustness, and which needs to be explicitly taken into account in the optimization.

In this paper, we compare several stochastic MPC algorithms taking into account a growing amount of the stochastic information: starting with deterministic schemes of certainty equivalence type, we use the noise’s distribution’s quantiles and finally we take, potentially, all stochastic information into account when performing Monte Carlo simulations in the MPC scheme. We carry out a numerical case study for the inverted pendulum, in which we observe that for short prediction horizons Monte Carlo does not pay off while for large prediction horizon it has slight advantages. Further, we discuss possible explanations for this behavior.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Model Predictive Control; Stochastic Control Problem; Scenario Approach; Quantile Function; Case Study
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Research Institutions
Research Institutions > Research Centres
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 14 Sep 2021 09:22
Last Modified: 14 Sep 2021 09:22
URI: https://eref.uni-bayreuth.de/id/eprint/67028