Safety MPC of constrained switched systems with control barrier function

This paper studies model predictive control (MPC) with control barrier function to solve the stability and safety problems of switched systems subject to input and state constraints. Considering that the system state is unmeasurable and disturbed, an observer-based MPC $ H_\infty $ H∞ method is adopted to estimate the system state and suppress disturbances. A cost function is designed to optimise the state and control input of switched systems by minimising its upper bound, and the optimisation problem is further transformed into a feasibility problem. Moreover, a control barrier function is introduced to constrain the controller gains, which ensures that the initial state of switched systems converges to the steady state without entering the specified unsafe region. Furthermore, a set of matrix inequality conditions is given to express the input and state constraints. Then, the Lyapunov function and average dwell time (ADT) approach are used to obtain sufficient conditions for the asymptotic stability of switched systems. Finally, two simulation examples are given to verify the effectiveness of the proposed method.