Adaptive discrete neural observer design for nonlinear systems with unknown time-delay

This paper focuses on the adaptive observer design for nonlinear discrete-time MIMO systems with unknown time-delay and nonlinear dynamics. The delayed states involved in the system are arguments of a nonlinear function and only the estimated delay is utilized. By constructing an appropriate Lyapunov-Krasovskii function, the delay estimation error is considered in the observer parameter design. The proposed method is then extended to the system with a nonlinear output measurement equation and the delayed dynamics. With the help of a high-order neural network (HONN), the requirement for a precise system model, the linear-in-the-parameters (LIP) assumption of the delayed states, the Lipschitz or norm-boundedness assumption of unknown nonlinearities are removed. A novel converse Lyapunov technical lemma is also developed and used to prove the uniform ultimate boundedness of the proposed observer. The effectiveness of the proposed results is verified by simulations.