Probabilistically Input-to-State Stable Stochastic Model Predictive Control

TL;DR

This paper introduces a stochastic model predictive control approach that guarantees probabilistic stability without requiring strict repeated feasibility, using input-to-state stability in probability and backup strategies.

Contribution

It develops a novel stability analysis framework for stochastic MPC leveraging input-to-state stability in probability, addressing feasibility challenges.

Findings

Provides probabilistic stability guarantees for stochastic MPC

Incorporates backup controller to handle feasibility loss

Demonstrates effectiveness through a numerical example

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.