A minimax sliding mode control design on finite horizon for linear evolution equations with switching modes

In this paper we consider a family of linear evolution equations in infinite dimensions (Hilbert spaces) with initial state, input and output bounded uncertainty, and allow the possibility of switching between the given systems. The achievable measurement/actuator location will be fixed over certain time intervals. Based on uncertain output measurements, we use a minimax sliding mode control approach to design a switching controller which steers a state to a finite-dimensional hyperplane in finite time. We show that the switching controller provides an optimal solution to a particular optimal minimax sliding mode control problem with switching modes and state/measurement/input disturbances. The proposed approach is summarized in an algorithm and it is illustrated through a numerical study on a family of delay evolution equations with switching modes and bounded disturbances.