Probabilistically Input-to-State Stable Stochastic Model Predictive Control

Employing model predictive control to systems with unbounded, stochastic disturbances poses the challenge of guaranteeing safety, i.e., repeated feasibility and stability of the closed-loop system. Especially, there are no strict repeated feasibility guarantees for standard stochastic MPC formulatio...

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Bibliographic Details
Published in:arXiv.org 2024-10
Main Authors: Pfefferkorn, Maik, Findeisen, Rolf
Format: Article
Language:English
Subjects:
Closed loops
Feasibility studies
Feedback control
Predictive control
Stability analysis
Stochastic models
Online Access:Get full text
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Summary:Employing model predictive control to systems with unbounded, stochastic disturbances poses the challenge of guaranteeing safety, i.e., repeated feasibility and stability of the closed-loop system. Especially, there are no strict repeated feasibility guarantees for standard stochastic MPC formulations. Thus, traditional stability proofs are not straightforwardly applicable. We exploit the concept of input-to-state stability in probability and outline how it can be used to provide stability guarantees, circumventing the requirement for strict repeated feasibility guarantees. Loss of feasibility is captured by a back-up controller, which is explicitly taken into account in the stability analysis. We illustrate our findings using a numeric example.
ISSN:2331-8422