Robust explicit model predictive control for linear systems via interpolation techniques

Abstract

This paper presents a novel interpolation-based model predictive control (IMPC) for constrained linear systems with bounded disturbances. The idea of so-called 'pre-stabilizing' MPC is extended by making interpolation among several 'pre-stabilizing' MPC controllers, through which the domain of attraction can be magnificently enlarged. Compared with the standard 'prestabilizing' MPC, the proposed approach has the advantage of combining the merits of having a large domain of attraction and a good behavior. Furthermore, such an IMPC problem can be solved off-line by multi-parametric programming. The optimal solution is given in an explicitly piecewise affine form. A simple algorithm for the implementation of the explicit MPC control laws is also proposed. Copyright © 2009 John Wiley & Sons, Ltd.