Fast smooth second-order sliding mode control for stochastic systems with enumerable coloured noises

Peng-fei Yang, Yang-wang Fang, You-li Wu, Dan-xu Zhang and Yang Xu

International Journal of Systems Science, 2018, vol. 49, issue 2, 312-323

Abstract: A fast smooth second-order sliding mode control is presented for a class of stochastic systems driven by enumerable Ornstein–Uhlenbeck coloured noises with time-varying coefficients. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the control. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Then the prescribed sliding variable dynamic is presented. The sufficient condition guaranteeing its finite-time convergence is given and proved using stochastic Lyapunov-like techniques. The proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are given comparing with smooth second-order sliding mode control to validate the analysis.

Date: 2018
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DOI: 10.1080/00207721.2017.1410249

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