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

<div><p>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.</p></div

The block diagram of SFS-SOSM control design.

<p>The block diagram of SFS-SOSM control design.</p

The control signal of SFS-SOSM control.

<p>The control signal of SFS-SOSM control.</p

of SSOSM control.

<p> of SSOSM control.</p

The phase plot of SFS-SOSM control.

<p>The phase plot of SFS-SOSM control.</p

The phase plot of SSOSM control.

<p>The phase plot of SSOSM control.</p

<i>s</i> of SSOSM control.

<p><i>s</i> of SSOSM control.</p

The tracking error of SSOSM control.

<p>The tracking error of SSOSM control.</p