Provably-Stable Stochastic MPC for a Class of Nonlinear Contractive Systems

Abstract

We present a model predictive control framework for a class of nonlinear systems affected by additive stochastic disturbances with (possibly) unbounded support. We consider hard input constraints and chance state constraints and we employ the unscented transform method to propagate the disturbances over the nonlinear dynamics in a computationally efficient manner. The main contribution of our work is the establishment of sufficient conditions for stability and recursive feasibility of the closed-loop system, based on the design of a terminal cost and a terminal set. We focus here on a special class of nonlinear systems that exhibit contractive properties in the dynamics. By assuming this property, we propose a novel approach to efficiently compute the terminal conditions without the need of performing any linearization of the dynamics. Finally, we provide an illustrative example to corroborate our theoretical findings.