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 (UUB) of the proposed observer. The effectiveness of the proposed results is verified by simulations.