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Model predictive control, cost controllability, and homogeneity

Title data

Coron, Jean-Michel ; Grüne, Lars ; Worthmann, Karl:
Model predictive control, cost controllability, and homogeneity.
In: SIAM Journal on Control and Optimization. Vol. 58 (October 2020) Issue 5 . - pp. 2979-2996.
ISSN 0363-0129
DOI: https://doi.org/10.1137/19M1265995

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We are concerned with the design of Model Predictive Control (MPC) schemes such that asymptotic stability of the resulting closed loop is guaranteed even if the linearization at the desired set point fails to be stabilizable. Therefore, we propose to construct the stage cost based on the homogeneous approximation and rigorously show that applying MPC yields an asymp-totically stable closed-loop behavior if the homogeneous approximation is asymptotically null controllable. To this end, we verify cost controllability - a condition relating the current state, the stage cost, and the growth of the value function w.r.t. time - for this class of systems in order to provide stability and performance guarantees for the proposed MPC scheme without stabilizing terminal costs or constraints.

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Item Type: Article in a journal
Refereed: Yes
Keywords: cost controllability; homogeneity; homogeneous approximation; model predictive control; stability guarantee
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
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 02 Nov 2020 07:45
Last Modified: 02 Nov 2020 07:45
URI: https://eref.uni-bayreuth.de/id/eprint/58960

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