Improved MPC design based on saturating control laws

This paper is concerned with the design of stabilizing MPC controllers for constrained linear systems. This is achieved by obtaining a suitable terminal cost and terminal constraint using a saturating control law as local controller. The system controlled by the saturating control law is modeled by a polytopic differential inclusion. Based on this, it is shown how to determine a Lyapunov function and a polyhedral invariant set which can be used as terminal cost and constraint. The obtained invariant set is potentially larger than the maximal invariant set for the unsaturated linear controller, O∞. Furthermore, considering these elements, a dual-mode MPC is proposed. This controller guarantees the enlargement of the domain of attraction or, equivalently, the reduction of the prediction horizon for a given set of stabilizable initial states. If the local control law is the saturating LQR controller, then the proposed dual-mode MPC controller maintains the local optimality of the standard MPC. An illustrative example is given.