  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.
