Probabilistically Input-to-State Stable Stochastic Model Predictive Control
<|reference_start|>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 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.<|reference_end|>
@article{pfefferkorn2024probabilistically,
    title={Probabilistically Input-to-State Stable Stochastic Model Predictive
  Control},
    author={Maik Pfefferkorn, Rolf Findeisen},
    journal={arXiv preprint arXiv:2410.08186},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.08186},
    primaryClass={eess.SY cs.SY}
}