Off-line robust constrained MPC with parameter-dependent feedback law

A polytopic invariant terminal set with an arbitrary predefine number of vertices is proposed for the linear time-varying system with polytopic uncertainty, which could significantly enlarge the terminal set. However the high computation load of polytopic set limits the application of online robust model predictive control with polytopic terminal set. Based on a sequence of feedback control laws corresponding a sequence of asymptotically stable invariant polytopes constructed off-line one within another, an off-line robust model predictive control online finds the smallest polytopic set containing the current state and implements the parameter-dependent feedback law, which is parameter-dependent on the location of the current state between the adjacent polytopic invariant sets