Neural network identification and control for nonlinear dynamic systems with time delay

In this study, a generalized procedure in identification and control of a class of time-varying-delayed nonlinear dynamic systems is developed. Under the framework, recurrent neural network is developed to accommodate the on-line identification, which the weights of the neural network are iteratively and adaptively updated through the model errors. Then indirect adaptive controller is designed based on the adaptive law of the controller, which the adaptive law of the controller is designed for the controller design. It should be noticed that including implicit control variable in design is more challenging, but more generic in theory and practical in applications. To guarantee the correctness, rigorousness, generality of the developed results, Lyapunov stability theory is referred to prove the neural network model identification and the designed closed-loop control systems uniformly ultimately bounded stable. A bench mark test is simulated to demonstrate the effectiveness and efficiency of the procedure.