Adaptive Output Feedback Control for Stochastic Uncertain Nonlinear Time-Delay Systems

In this brief, the adaptive output feedback control problem for stochastic nonlinear time-delay systems with various uncertainties is considered. The unknown output function needs neither to be differentiable, that is, its derivative is limited to known/unknown upper and lower bounds, nor to guarantee its Lipschitz continuity. Besides, the upper bound on the derivative of time-varying delay and the growth rates of the nonlinear functions are proved to be not necessary. An adaptive output feedback control scheme is designed, in which a dynamic gain is embedded in the observer to dominate the time-varying delay and unknown growth rates, and a constant gain is embedded in the controller to dominate the unknown output function. It is proved that all signals of the closed-loop system are globally bounded almost surely and the bounds are ensured to be tuned by design parameters. Finally, a simulation is presented to show the validity of the control scheme.