A scheduling minmax predictive control algorithm for LPV systems subject to bounded rate parameters

Abstract

A novel optimal receding horizon control strategy for input saturated linear time-varying (LTV) discrete-time systems with polytopic model uncertainties when the actual realization of the uncertain parameter is known and when bounded rate uncertain parameter variations are present, is proposed. The approach is based, on the updating at each step, in a binary tree fashion, of the closed convex hulls of all k-steps state trajectories originating from x at time 0 under a quadratically scheduling stabilizing state feedback. The solution is computed by solving an upper-bound on the "worst-case" infinite horizon quadratic cost under the constraint of steering the future state evolutions emanating from the current state into a feasible and positive invariant set. whose "size" depends on the rate variation of the uncertain parameter. Feasibility and closed loop stability of this strategy are here proved.