Randomized Nonlinear MPC for Uncertain Control-Affine Systems with Bounded Closed-Loop Constraint Violations

Abstract

In this paper we consider uncertain nonlinear control-affine systems with probabilistic constraints. In particular, we investigate Stochastic Model Predictive Control (SMPC) strategies for nonlinear systems subject to chance constraints. The resulting non-convex chance constrained Finite Horizon Optimal Control Problems are computationally intractable in general and hence must be approximated. We propose an approximation scheme which is based on randomization and stems from recent theoretical developments on random non-convex programs. Since numerical solvers for non-convex optimization problems can typically only reach local optima, our method is designed to provide probabilistic guarantees for any local optimum inside a set of chosen complexity. Moreover, the proposed method comes with bounds on the (time) average closed-loop constraint violation when SMPC is applied in a receding horizon fashion. Our numerical example shows that the number of constraints of the proposed random non-convex program can be up to ten times smaller than those required by existing methods.