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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.
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No potential conflict of interest was reported by the authors.
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Notes on contributors
Peng-fei Yang
Peng-fei Yang received his B.E. and M.E. degrees in armament science and technology from Air Force Engineering University, Xi'an, China, where he is currently pursuing the Ph.D. degree. His current research interests include stochastic control, hypersonic vehicle guidance law design, and high-order sliding mode control.
Yang-wang Fang
Yang-wang Fangreceived his Ph.D. degree in control science and engineering from Xi'an Jiaotong University, Xi'an, China, in 1998. From 1999 to 2001, he was a Postdoctoral Research Fellow with the State Key Laboratory of Radar Signal Processing, Xidian University, Xi'an, China. He is currently a Full Professor of the Air Force Engineering University. His research interests include stochastic control, signal processing, and their engineering applications.
You-li Wu
You-li Wu received his Ph.D. degree in armament science and technology from Air Force Engineering University, Xi'an, China, in 2009. He is currently a Associate Professor of the Air Force Engineering University. His research interests include stochastic control, structure stochastic jumping system control, and robotics.
Dan-xu Zhang
Dan-xu Zhang received his M.E. degree in armament science and technology from Air Force Engineering University, Xi'an, China, where he is currently pursuing the Ph.D. degree. His current research interests include global sliding mode control and guidance law design.
Yang Xu
Yang Xu received his M.E. degree in signal processing and communications from Air Force Engineering University, Xi'an, China, where he is currently pursuing the Ph.D. degree. His current research interests include accuracy analysis and evaluation, estimation and detection theory, and signal processing.