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The problem we focus on in this paper is to find a nearly optimal slidingmode controller of continuous-time nonlinear multiple-input multiple-output(MIMO) systems that can both reduce chattering and minimize the cost function,which is a measure of the performance index of dynamics systems. First, thedeficiency of chattering in traditional SMC and the quasi-SMC method areanalyzed in this paper. In quasi-SMC, the signum function of the traditionalSMC is replaced with a continuous saturation function. Then, a chatteringreduction algorithm based on integral reinforcement learning (IRL) is proposed.Under an initial sliding mode controller, the proposed method can learn thenearly optimal saturation function using policy iteration. To satisfy therequirement of the learned saturation function, we treat the problem oftraining the saturation function as the constraint of an optimization problem.The online neural network implementation of the proposed algorithm is presentedbased on symmetric radius basis functions and a regularized batch least-squares(BLS) algorithm to train the control law in this paper. Finally, two examplesare simulated to verify the effectiveness of the proposed method. The secondexample is an application to a real-world dynamics model -- a two-wheeledvariable structure robot.

A Nearly Optimal Chattering Reduction Method of Sliding Mode Control With an Application to a Two-wheeled Mobile Robot