LMI-based robust mixed-integer model predictive control for hybrid systems

This paper proposes a linear matrix inequality (LMI) approach to mixed-integer model predictive control (MPC) of uncertain hybrid systems with binary and real valued control inputs. The stability condition of the hybrid system is obtained by using the Lyapunov function and then a sufficient state feedback control law is achieved so that guarantees the closed-loop stability and also minimises an infinite horizon performance index. The primal optimisation problem is convex, therefore, a convex relaxation is investigated by introducing the Lagrange dual function. The real and binary control inputs are obtained by solving the dual of the dual problem in the framework of LMIs. The performance and effectiveness of the proposed MPC approach and the duality gap of the convex relaxation are studied through simulation results of a hybrid system with mixed real and binary inputs.