Predictive control for nonlinear stochastic systems: Closed-loop guarantees with unbounded noise
<|reference_start|>Predictive control for nonlinear stochastic systems: Closed-loop guarantees with unbounded noise: We present a stochastic predictive control framework for nonlinear systems subject to unbounded process noise with closed-loop guarantees. First, we first provide a conceptual shrinking-horizon framework that utilizes general probabilistic reachable sets and minimizes the expected cost. Then, we provide a tractable receding-horizon formulation that uses a nominal state and a simple constraint tightening. Both formulations ensure recursive feasibility, satisfaction of chance constraints, and bounds on the expected cost for the resulting closed-loop system. We provide a constructive design for probabilistic reachable sets of nonlinear systems using stochastic contraction metrics. We demonstrate the practicality of the proposed method through a simulation of a chain of mass-spring-dampers with nonlinear Coulomb friction. Overall, this paper provides a framework for computationally tractable stochastic predictive control approaches with closed-loop guaranteed for nonlinear systems with unbounded noise.<|reference_end|>
@article{köhler2024predictive,
    title={Predictive control for nonlinear stochastic systems: Closed-loop
  guarantees with unbounded noise},
    author={Johannes K"ohler, Melanie N. Zeilinger},
    journal={arXiv preprint arXiv:2407.13257},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.13257},
    primaryClass={eess.SY cs.SY math.OC}
}