Output feedback control for uncertain nonlinear systems with slowly varying input delay

Output Feedback (OFB) control of a nonlinear system with time-varying actuator delay is a challenging problem because of both the the lack of full state information and the need to develop prediction of the nonlinear dynamics. In this paper, an OFB tracking controller is developed for a general second-order system with time-varying input delay, uncertainties, and additive bounded disturbances. The developed controller is a modified PD controller working in association with a predictor-like feedback term to compensate for the input delay. The PD components are formulated using the difference between a desired trajectory and an estimate of the unknown state, acquired from a dynamic neural network-based observer, to compensate for the unavailability of the true system state. A stability analysis using Lyapunov-Krasovskii functionals is provided to for uniformly ultimately bounded (UUB) tracking and UUB estimation of the unavailable state. A numerical simulation is provided to illustrate the performance of the control design and illustrate its robustness to delay variations.