On convex problems in chance-constrained stochastic model predictive control

TL;DR

This paper explores convex reformulations of chance-constrained stochastic model predictive control problems for linear systems, enabling more tractable optimization of control policies under probabilistic constraints.

Contribution

It demonstrates that, with appropriate control policy parametrization, many chance-constrained problems are convex or can be approximated convexly, improving solution tractability.

Findings

Many chance-constrained problems are convex or approximately convex.

Convex reformulations facilitate more efficient control policy optimization.

The approach applies to linear stochastic systems with probabilistic constraints.

Abstract

We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then reformulated in terms of probabilistic constraints. It is shown that, for a suitable parametrization of the control policy, a wide class of the resulting optimization problems are convex, or admit reasonable convex approximations.