Robust adaptive sliding mode control design for uncertain stochastic systems with time-varying delay

Based on a least square wavelet kernel support vector machine (LS-SVM) and a hybrid wavelet kernel least square SVM, two adaptive integral sliding mode control schemes are presented for uncertain stochastic systems with time-varying delay. Adaptive parameter is chosen based on estimation of uncertain function and Swarm Optimization algorithm. First, an integral sliding surface is constructed. Using the linear matrix inequalities, a sufficient condition for the existence of sliding surface is then derived. This condition guarantees the global stochastic stability of stochastic dynamics in the specified switching surface. Next, LS-SVM is used to establish an adaptive controller. Also, an on-line learning rule for the weight vector and bias term are derived. Simulation results show that the proposed controllers can achieve a satisfactory performance. © 2017, Springer-Verlag Berlin Heidelberg.