Probabilistically Input-to-State Stable Stochastic Model Predictive Control

Maik Pfefferkorn; Rolf Findeisen

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arXiv · 2410.08186

Probabilistically Input-to-State Stable Stochastic Model Predictive Control

Maik Pfefferkorn·Rolf Findeisen

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Abstract

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.

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BibTeX RIS

Maik Pfefferkorn, Rolf Findeisen. 2024-10-10. Probabilistically Input-to-State Stable Stochastic Model Predictive Control. https://arxiv.org/abs/2410.08186

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