An efficient offline implementation for output feedback min-max MPC

Previous works have presented the output feedback min-max model predictive control (MPC) for the discrete-time system with both polytopic uncertainty and bounded persistent disturbance, where the controller parameters are optimized at each sampling instant. This paper proposes the corresponding offline approach in order to reduce the online computational burden. Such offline MPC, when the state is measurable and there is no disturbance, has been constructed in the work of Wan and Kothare (An efficient off-line formulation of robust model predictive control using linear matrix inequalities. Automatica. 2003;39(5):837-846). Since this paper considers the case when the true state is unknown, the ellipsoidal regions of attraction (applying only to the estimated state) lose their asymptotic invariance property, and the estimation error set (EES) has a major effect on the control performance. This paper refreshes EES invoking the one-step reachable set and guarantees that the signals being penalized in the performance cost function to converge to a neighborhood of the equilibrium point. Two examples are given to illustrate the effectiveness of the approach.