Discrete Sliding Mode Control Using Neural Network

Abstract

In this paper, a discrete sliding mode is treated. Recentry, the sliding mode control attracts attention, because the sliding mode control is robust to the uncertainties of systems. Contrary to the continuous case, however, discrete sliding mode control has the faults which the states are chattering around switching surface and can not ride on the switching surface and so on. Therefore, the stability of system can not be guaranteed. In this paper, the control law on the basis of a discrete Lyapunov function is proposed. As a method eliminating the chattering, the equivalent control which make the stetes of systems stay on the switching surface is employed. This equivalent control is estimated by using neural network which has the capacity to learn arbitrary nonlinearity. Then, the estimated equivalent is introduced in the control law above mentioned and the new controller changes from the reaching control to the equivalent control smoothly. By using this control, for the systems with uncertainties the states of systems aproach the switching surface asymptoticaly and stay on it. This validity of this scheme is made sure by simulation.