Computation of terminal costs and sets for discrete–time nonlinear MPC

Abstract

The terminal cost and terminal set method for guaranteeing stability of nonlinear model predictive control (MPC) closed–loop systems is theoretically appealing but often impractical. This is due to the difficulty of computing invariant sets and control Lyapunov functions for general nonlinear systems. In this paper we propose a novel method for computing time–varying terminal costs and sets by means of first order or second order Taylor approximations of the nonlinear system dynamics. The method first solves a set of linear matrix inequalities to compute the terminal ingredients for the approximated dynamics. Then, a small scale global nonlinear optimization problem is solved to check the validity of the terminal ingredients for the nonlinear dynamics. The proposed method also allows for time–varying linear or nonlinear terminal control laws. The developed method can result in significant enlargements of the domain of attraction of the nonlinear MPC closed–loop system, as demonstrated by a benchmark academic example.