Robust adaptive control based on neural state observer for nonlinear time-delay systems

A novel robust adaptive control based on neural state observer is proposed for strict-feedback nonlinear systems with state delays. A state observer with neural networks approximators is established to estimate the system states. By using the backstepping method, adaptive output feedback controller is constructed which can achieve the output trajectory. Both the designed observer and controller are independent of the time delays. It is proven that the proposed a novel Lyapunov-Krasovskii functionals and backstepping method are able to guarantee semi-globally uniform ultimate boundedness of all the signals in the closed-loop systems, while the tracking error converges to a small neighborhood of the origin. The proposed scheme can be applied to the systems which can not satisfy the matching conditions. Simulation results verify the effectiveness of the proposed scheme.