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.
Highlights
Sliding mode control (SMC) is well known for its robustness to system parameter variations and external disturbances[1,2]
Using SMC strategy to the nonlinear stochastic systems modeled by the Itostochastic differential equations with multiplicative noise has been gaining much investigation, see [3,4,5,6] and references therein
The existing research findings applying SMC to the stochastic systems always treat the stochastic noise as bounded uncertainties. These methods need to know the upper bound of the noise and they are comparatively more conservative control strategy, which ensure the robustness at the cost of losing control accuracy
Summary
Sliding mode control (SMC) is well known for its robustness to system parameter variations and external disturbances[1,2]. SMC has extensive applications in practice, such as robots, aircrafts, DC and AC motors, power systems, process control and so on. Using SMC strategy to the nonlinear stochastic systems modeled by the Itostochastic differential equations with multiplicative noise has been gaining much investigation, see [3,4,5,6] and references therein. The existing research findings applying SMC to the stochastic systems always treat the stochastic noise as bounded uncertainties. These methods need to know the upper bound of the noise and they are comparatively more conservative control strategy, which ensure the robustness at the cost of losing control accuracy. Wu et al.[8] designed SMC guaranteeing the mean-square exponential stability for the continuous-time switched stochastic systems with multiplicative noise. The control signal in [8] switches frequently and the results cannot be extended to stochastic systems with additive noise
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