On Adaptive Neural Networks Control For A Class Of Nonlinear Time-Delay Systems

Time-delay phenomenon exists quite widely in industrial and engineering problems, such as communication systems, biological systems, chemical systems and electrical networks. The existence of time delay makes the system analysis and synthesis become more complicated and difficult. Meanwhile, time delay is frequently a source of instability and performance degradation in many dynamic systems. Thus, it is of a great importance in theoretical and practical application to study the robust control for the uncertain time-delay systems. Based on the approximate capacity of neural network for unknown functions, the thesis devotes on the stability analysis and the design of controller for a class of nonlinear time-delay systems. The design and analysis procedure is based on a series of control theories, which are Lyapunov stability theory, adaptive control theory, neural network control theory, integral variable structure control theory,Lyapunov-Krasovskii functional method, and so on. The main work in this paper is summarized as follows.Firstly, both direct and indirect supervisory control scheme of adaptive neural network control are proposed for a class of nonlinear time-varying delay systems, respectively. By theoretical analysis, the closed-loop systems are proven to be globally stable in the sense that all signals involved are bounded, with tracking error converging to zero in the two schemes. In the case of direct control, the adaptive compensation term of the optimal approximation error is adopted. The approach does not require the optimal approximation error to be square-integral or the supper bound of the optimal approximation error to be known. While in the indirect case, with the help of a supervisory controller, the adaptive compensation term of the optimal approximation error is introduced to minimize the effects of modeling error.Secondly, a design scheme of adaptive neural network controller for a class of uncertain SISO nonlinear time-delay systems with unknown nonlinear dead-zones and unknown function control gain is proposed. The design is based on the principle of sliding mode control and property of Nussbaum-type functions. This approach relaxes the hypothesis that the upper bound of function control gain is unknown constant in the existing literatures and the supposition further broadness to unknown function. Simultaneously it also relaxes the time-delay uncertainties request. The unknown time-delay uncertainties are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. By theoretical analysis, the closed-loop control systems is proved to be semi-globally uniformly ultimately bounded.Lastly, the results of the SISO are extended to a class of MIMO uncertain nonlinear time-delay systems with unknown dead-zone and function control gain. Two design schemes of adaptive neural network controller are proposed for unknown function control gain sign and known function control gain sign. The design is based on the principle of sliding mode control for known function control gain. The approach relaxes the hypothesis that the upper bound of function control gain is unknown constant. The unknown time-delay uncertainties are compensated for using appropriate Lyapunov- Krasovskii functionals in the design. By theoretical analysis, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded. Moreover, adaptive neural network control is investigated for unknown function control gain. The design is based on the principle of sliding mode control and property of Nussbaum-type functions and a priori knowledge of the control gain sign needn't to be known.Through the research in this paper, the design and analysis problems on adaptive neural networks for a class of nonlinear time-delay systems have been properly solved. Numerical simulation experiments of the control schemes demonstrate their effectiveness and practicability.