Stochastic Nonlinear Time Delay System Output Feedback Stabilization Problem

When the stochastic disturbance is a standard Wiener noise or a noise of unknown covariance, we consider the output feedback stability for a class of stochastic nonlinear time-varying delayed systems, with strict-feedback form. This paper is made up of three sections:Section 1 introduces some basic concepts, theorems and inequalities, which are important for the paper's finish.Section 2, considers the output feedback control for the stochastic nonlinear time-varying delayed systems driven by noise of unknown covariance, with strict-feedback form, When the stochastic disturbance is a standard Wiener noise. The state observer is firstly designed, and then based on the observed states the controller is designed via Deng and Krstic's quartic Lyapunov function and backstepping method; finally introduce simply the inverse optimal feedback stabilization, the other controller is designed though using Young's inequalities, and the designed controller guarantees that the closed-loop system is not only inverse optimality, but also global asymptotic stability in probability. The effectiveness of the proposed scheme is demonstrated by a simulation example.On the base of section 2, section 3 considers the output feedback adaptive control for the stochastic nonlinear time-varying delayed systems driven by noise of unknown covariance, with strict-feedback form. The observer and controller are designed using the same method as Section 2. Based on Lyapunov and Lasalle theorems, we show that the constructed controller can render the closed-loop system asymptotically stable in probability, and the effectiveness of the proposed scheme is demonstrated by a simulation example.