Adaptive Neural Network Control For Uncertain Nonlinear Time - Delay Systems

This paper mainly studies the controlling problems of adaptive neural network in uncertain nonlinear time-delay systems. The uncertain nonlinear system has gain function with unknown symbols, unknown functions and smooth functions with time-varying delay and un-modeled dynamics. The paper aims at the uncertain nonlinear time-delay systems by using the design method of back-stepping, the function of Nussbaum, neural network and selecting the appropriate functions of Lyapunov and Lyapunov-Krasovskii. The main contents are as follows:The nonlinear time-delay systems with unknown uncertainties in this paper has unknown time-delay smooth function, unmodeled dynamics and unknown control direction. The article gives a new method based on nonlinear adaptive neural network design method combining with the design method of back-stepping, the function of Nussbaum and the function of Lyapunov-Krasovskii. In theory, neural network has very strong approximation ability that it can approximate the unknown nonlinear function to arbitrary precision. The paper designs a class of controllers with uncertain nonlinear time-delay systems and solved the impacts of uncertainties of time-delay nonlinear system. Using the uncertainties of Lyapunov-Krasovskii uncertain nonlinear delay systems and further put the known time-delay problem to time-varying time-delay nonlinear systems, finally using the Young’s inequalities to enlarge the limitation of the time delay. Based on the function of Lyapunov, the design can prove the stability of the closed-loop system and the system output tracking the problem of error convergence while we constantly adjusting the design parameters of system to realize the arbitrary precision of target trajectory tracking control.