Invariant Sets for Constrained Nonlinear Discrete-time Systems with Application to Feasibility in Model Predictive Control

An understanding of invariant set theory is essential in the design of controllers for constrained systems, since state and control constraints can be satisfied if and only if the initial state belongs to a positively invariant set for the closed-loop system. The paper briefly reviews some concepts in invariant set theory and shows that the various sets can be computed using a single recursive algorithm. The ideas presented in the first part of the paper are applied to the fundamental design goal of guaranteeing feasibility in predictive control. New necessary and sufficient conditions based on the control horizon, prediction horizon and terminal constraint set are given in order to guarantee that the predictive control problem will be feasible for all time, given any feasible initial state.