Novel Discrete Optimal Sliding Mode Control

In this paper, the discrete optimal control is made to have the robust property of sliding mode controller. A augmented system with a virtual state is constructed for this objective and noble sliding surface is constructed based on this system. The sliding surface is the same as the optimal control trajectory in the original system. The states follow the optimal trajectory even if there exist uncertainties. The reaching phase problem of sliding mode control is desappear in this method.