Maximal robust feasible sets for constrained linear systems controlled by piecewise affine feedback laws

Abstract

For time-invariant linear systems subject to linear constraints, Model Predictive Control techniques provide piecewise affine feedback control laws within a polyhedral set of initial states called the feasible set. In the presence of model mismatch, when the controller designed using the nominal model is applied to the real plant, the feasible set may lose its invariance property, and this means violation of constraints. Moreover, since the controller is designed only over the feasible set, there is the technical problem that the control action is undefined if the state moves outside of the feasible set. In this paper we propose a tool to analyze how uncertainty in the real plant will affect the piecewise affine control law computed using the nominal model. Given the linear system describing the plant and the piecewise affine control law, the algorithm presented considers a polytopic model uncertainty defined by the user and constructs the maximal robust feasible set, i.e. the largest subset of the feasible set which is guaranteed to be feasible for any model in the family of models described by the polytopic uncertainty.