Quasi-min-max MPC algorithm for constraint LPV system based on time-varying one-step invariant set

This paper considers a quasi-min-max model predictive control (MPC) problem for constrained linear parameter varying (LPV) systems with polytopic description. A method based on invariant set is proposed to reduce the computational complexity of designing the stable controller. The proposed method constructs the one-step invariant set comprises an interpolation between several pre-computed invariant sets at each time instant. Then control law is obtained by solving a constrained QP problem, and ensures constraint satisfaction and asymptotic stability of the closed-loop system if the SDP problem is feasible. Compared with the robust MPC approach based on single invariant set implementations, this proposed approach has the advantage of combining the merits of having a large domain of attraction and good asymptotic behavior. The performances of the approach are presented via an example.