Sliding-Mode Control Design for Nonlinear Systems Using Probability Density Function Shaping

摘要

In this paper, we propose a sliding-mode-based stochastic distribution control algorithm for nonlinear systems, where the sliding-mode controller is designed to stabilize the stochastic system and stochastic distribution control tries to shape the sliding surface as close as possible to the desired probability density function. Kullback–Leibler divergence is introduced to the stochastic distribution control, and the parameter of the stochastic distribution controller is updated at each sample interval rather than using a batch mode. It is shown that the estimated weight vector will converge to its ideal value and the system will be asymptotically stable under the rank-condition, which is much weaker than the persistent excitation condition. The effectiveness of the proposed algorithm is illustrated by simulation.