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

The problem we focus on in this paper is to find a nearly optimal sliding mode 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, the deficiency of chattering in traditional SMC and the quasi-SMC method are analyzed in this paper. In quasi-SMC, the signum function of the traditional SMC is replaced with a continuous saturation function. Then, a chattering reduction algorithm based on integral reinforcement learning (IRL) is proposed. Under an initial sliding mode controller, the proposed method can learn the nearly optimal saturation function using policy iteration. To satisfy the requirement of the learned saturation function, we treat the problem of training the saturation function as the constraint of an optimization problem. The online neural network implementation of the proposed algorithm is presented based on symmetric radius basis functions and a regularized batch least-squares (BLS) algorithm to train the control law in this paper. Finally, two examples are simulated to verify the effectiveness of the proposed method. The second example is an application to a real-world dynamics model -- a two-wheeled variable structure robot.