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

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3 Author(s)
Yu Liu ; Inst. of Acoust., Beijing, China ; Hong Wang ; Chaohuan Hou

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.

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Neural Networks and Learning Systems, IEEE Transactions on  (Volume:25 ,  Issue: 2 )