Convex Chance Constrained Model Predictive Control

TL;DR

This paper introduces a novel approach for solving chance constrained model predictive control problems for polynomial systems with disturbances, using measure and moment theory to ensure probabilistic constraints are met with convergence guarantees.

Contribution

It develops a sequence of finite semidefinite programs that approximate the optimal control solution, providing a convergent method for probabilistic control of polynomial systems.

Findings

Convergent semidefinite programming approach for chance constrained control

Numerical examples demonstrate computational effectiveness

Control laws achieve low risk of constraint violation

Abstract

We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost function subject to probabilistic constraints, over a finite horizon. The control laws provided have a predefined (low) risk of not reaching the desired target set. Building on the theory of measures and moments, a sequence of finite semidefinite programmings are provided, whose solution is shown to converge to the optimal solution of the original problem. Numerical examples are presented to illustrate the computational performance of the proposed approach.