Robust model predictive control for constrained linear systems based on contractive set and multi-parameter linear programming

Abstract

A new robust model predictive control (MPC) approach is proposed for constrained linear systems in this paper. It adopts a contractive state set as terminal set in MPC problem and employs a novel function of the state with respect to this terminal set as the stage cost of the objective function. When the controlled systems are subject to linear constraints, explicit MPC law can be obtained as a piecewise affine linear state feedback control law via multi-parameter linear programming method. The presented MPC, along with linear variable-structure control law associated with the terminal set, is essentially a dual mode control scheme to stabilize the constrained uncertain linear system. Compared to the existing MPC methods, the proposed approach have both better real-time applicability and more general robust stability guarantee.