Nonlinear Model Predictive Control with Explicit Backoffs for Stochastic Systems under Arbitrary Uncertainty

Abstract

The majority of work on chance constrained model predictive control (MPC) for stochastic systems adopts the concept of implicit constraint backoffs for handling state chance constraints. However, implicit backoffs cannot be computed analytically in nonlinear MPC (NMPC), so that they must be approximated and, as a result, chance constraints are not guaranteed by the closed-loop system. This paper proposes a strategy for explicit computation of constraint backoffs that allows tightly guaranteeing chance constraints in NMPC for stochastic systems with arbitrary uncertainty distributions. The proposed method relies on uncertainty propagation through closed-loop system dynamics. Thus, this paper also investigates the use of stochastic surrogate models for constructing the distribution of closed-loop quantities of interest such as state constraint functions or any general performance objectives. To this end, an extension of polynomial chaos that can handle arbitrary probability measures is proposed for a class of disturbance models representing plant-model mismatch. The proposed methods are illustrated on a benchmark continuously-stirred tank reactor problem.