Tube-Based Stochastic Nonlinear Model Predictive Control: A Comparative Study on Constraint Tightening

Abstract

This paper presents a comparative study between two constraint-tightening approaches for tube-based stochastic nonlinear model predictive control (SNMPC) with and without terminal constraints. A simple constraint-tightening method based on the exponential decay rate of a delta-Lyapunov function is extended to the stochastic setting. This method uses the notion of incremental stabilizability to alleviate the need for offline, but involved computation of terminal constraints. The proposed method is compared to a SNMPC formulation that employs terminal constraints and Lipschitz constant-based constraint tightening. A comparative analysis is presented on a benchmark continuous stirred-tank reactor problem. Practical approximations for computing terminal sets are discussed in the context of this comparison.