An input‐to‐state stable model predictive control framework for Lipschitz nonlinear parameter varying systems

Abstract

SummaryThis article develops a state‐feedback model predictive control (MPC) framework for nonlinear parameter varying (NLPV) systems with explicit Lipschitz nonlinearities along the input trajectory. Considering a guess for the evolution of the scheduling parameters along the prediction horizon, the proposed optimization procedure for the MPC design includes a terminal stage cost, a contracting terminal region constraint and nominal predictions scheduled with respect to this guess. The terminal region is taken so that it is monotonically decreasing to a pre‐determined set, which guarantees recursive feasibility of the algorithm with respect to a bound on the admissible uncertainties (introduced from the scheduling parameter guess). The terminal set is a scheduled robust control invariant set for Lipschitz nonlinear systems, computed through some proposed LMIs. The inclusion of the terminal ingredient also serves to demonstrate input‐to‐state quadratic stability. This article ends with a successful numerical simulation example of the technique applied to the control of a semiactive automotive suspension system equipped with electro‐rheological dampers. Comparisons are given with respect to open‐loop behavior and to a robust LQR controller.