Fast smooth second-order sliding mode control for systems with additive colored noises

Pengfei Yang; Yangwang Fang; Youli Wu; Yunxia Liu; Danxu Zhang

doi:10.1371/journal.pone.0178455

Fast smooth second-order sliding mode control for systems with additive colored noises

PLoS One. 2017 May 31;12(5):e0178455. doi: 10.1371/journal.pone.0178455. eCollection 2017.

Authors

Pengfei Yang¹, Yangwang Fang¹, Youli Wu¹, Yunxia Liu², Danxu Zhang¹

Affiliations

¹ School of Aeronautics and Astronautics Engineering, Air Force Engineering University, Xi'an, Shaanxi, China.
² College of Education, Hunan University of Science and Technology, Xiangtan, Hunan, China.

Abstract

In this paper, a fast smooth second-order sliding mode control is presented for a class of stochastic systems with enumerable Ornstein-Uhlenbeck colored noises. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the controller. The finite-time convergence of the prescribed sliding variable dynamics system is proved by using stochastic Lyapunov-like techniques. Then the proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are presented comparing with smooth second-order sliding mode control to validate the analysis.

MeSH terms

Models, Theoretical*
Nonlinear Dynamics
Stochastic Processes

Grants and funding

This work has been supported by the Major Program of the National Natural Science Foundation of China (No. 61627901). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.