An improved constrained robust model predictive control algorithm for linear systems with polytopic uncertainty

A constrained robust model predictive control algorithm for linear systems with polytopic uncertainty is presented in this paper. At each sample time the algorithm aims at minimizing an infinite horizon worst-case quadratic cost function. Compared with existed techniques, the proposed algorithm uses a sequence of slack inequalities to construct a tighter upper bound of robust cost function. A control structure with two linear state feedback controllers feeding the system alternatively is introduced to reduce the conservativeness and make the optimization problem tractable. The on-line optimization problem can be formulated as a convex optimization problem subject to a number of LMI constraints. A simulation example illustrates the effectiveness of proposed algorithm.