An Efficient MPC Algorithm based on a Priori Zone Control

This paper presents an efficient MPC algorithm for uncertain time-varying systems with input constraints. The proposed algorithm adopts the method of increasing free control horizon in the dual mode (i.e., a free control mode in the first finite horizon and a state-feedback mode in the following infinite horizon) paradigm so as to enlarge the set of stabilizable initial states. In the method, however, since the number of LMIs growing exponentially with the free control horizon makes the corresponding optimization problems intractable even for small horizon, it is impracticable to blindly increase the free control horizon. The objective of this paper is to relax the restriction on increase of the free control horizon, incurred on computational burdens in the method. By choosing a combination of hyper-boxes including a possible region of the initial states and then by designing a priori zone controller for each hyper-box so as to send any initial states in the hyper-box into the invariant ellipsoidal target set, the algorithm can dramatically reduce the on-line computational burden for enlarging the set of stabilizable initial states