Adaptive memoryless observer design for nonlinear time-delay systems

Two memoryless adaptive observers are proposed for systems with unknown time-delays and nonlinearities, in which time-delays are not used in the observer. Using high order neural networks (HONN), the precise system model, the Lipschitz, linear-in-parameter or norm-bounded assumptions of nonlinear functions are not needed. A robust term based on the matching condition is introduced in the first observer, such that the observer error converges to the origin. The observer error of the second scheme without the robust compensation is proved to be semi-globally uniformly ultimately bounded (SGUUB). Simulations verify the effectiveness of the proposed methods.