Neural-observer-based adaptive control for stochastic nonlinear time-delay systems with unknown control directions

The problem of output feedback adaptive stabilization is addressed for a class of stochastic nonlinear systems with unknown time-varying delays and unknown control directions in this paper. Firstly, the unknown control coefficients are lumped together by using a linear state transformation, and the original system is transformed into a new system for which control design becomes feasible. Then, after the design of a novel neural observer, an output feedback adaptive neural network (NN) controller is developed for such systems by combining the Dynamic Surface Control (DSC) technique, the Nussbaum gain function (NGF) method and the Lyapunov-Krasovskii method. The proposed controller ensures that all signals in the closed-loop systems are bounded in probability. Finally, a simulation example is given to verify the effectiveness and applicability of the proposed control design.