Improved off-line formulation of robust model predictive control for a discrete time incertain system

An improved off-line robust model predictive control (MPC) is presented for a discrete time uncertain dynamic system with input constraints, where the uncertainties that satisfy the so-called norm-bound conditions exist in state matrices and input matrices. The new approach synthesizes the advantage of on-line MPC and off-line MPC. First, off-line, generate a sequence of asymptotically stable invariant ellipsoids one inside another near the origin, and a sequence of explicit control laws corresponded with these invariant ellipsoids. Second, on-line, judge whether the current state is in these ellipsoids. If in, apply off-line the control law corresponded. If out, apply the on-line robust MPC with N-step free control moves. The main advantage of this new approach with respect to other well-known technique is the guaranteed robust stability, the guaranteed performance, and the reduced computation. This makes robust MPC a very attractive control methodology for application to large scale systems and fast processes. The performance of the controller is demonstrated by an example.