Maximal Admissible Disturbance Constraint Set for Tube-Based Model Predictive Control

Abstract

Tube-based model predictive control (TMPC) is an outstanding control technique in robust control realms. However, the existing works are generally based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> known admissible sets of disturbances, i.e., disturbance constraint sets, the sizes of which are by default small enough such that the region of attraction is non-empty. If the size of the disturbance constraint set specified is too large, or even oversized in some particular direction, TMPC may not be capable of handling it and lose the feasibility of the optimization problem. Otherwise, a small disturbance constraint set may be inadequate to cover all realizations of the actual disturbances. This implies that an improper selection of the disturbance constraint set may lead to the invalidity of TMPC. To address this issue, this technical note proposes an optimization-based algorithm to determine the maximal admissible disturbance constraint set for classical TMPC [1], which evaluates the robustness of TMPC. The proposed algorithm is also applicable to other TMPC methods for linear systems with a slight modification.