Stabilizing Model Predictive Control of Nonlinear Continuous Time Systems

Abstract

This paper surveys some of the main design strategies of nonlinear MPC (Model Predictive Control). The system under control, the performance index to be minimized and the state and control constraints to be fulfilled are defined in the continuous time. The considered algorithms are analyzed and compared in terms of stability, performance and implementation issues. In particular, it is shown that the solution of the optimization problem underlying the MPC formulation calls for (a) a suitable parametrization of the control variable, (b) the use of a suitable discretization of time, that is of a “sampled” control law and, (c) the numerical integration of the system over the considered prediction horizon. In turn, these implementation aspects are such that many theoretical results concerning stability have to be critically evaluated. In order to cope with these problems, two different methods guaranteeing stability are presented. One of them is used to global stabilize a pendulum