Application Of Adaptive Method On Several Classes Of Nonlinear Delayed Systems' Control

In this dissertation, we extend and generalize the existing results on the synchroniza-tion of complex networks, the theory of sliding mode control and the theory of H∞control by combing the adaptive control method, stability theory of differential equations and lin-ear inequality techniques. The contents of this dissertation can be list as the following four chapters.In the first chapter, a review on the theoretical research and practical significance of the control theory of nonlinear delayed systems is presented, the history and basic princi-ples of adaptive control method are described. Then, the development on synchronization of complex networks, variable structure control for nonlinear systems, H∞control for systems with Markovian switching are also briefly addressed. The necessity on the com-bination for adaptive method and the control of nonlinear systems is given in this chapter.In the second chapter, we consider the synchronization of complex networks with time delay. Firstly, for a complex network with time-varying delays, we design the adap-tive laws for instantaneous coupling strength and delayed coupling strength to realize the synchronization without connecting any controller. Secondly, pinning adaptive controllers are designed to make sure the synchronization for time-delayed complex networks. The contents of this chapter improve the results of complex network synchronization and the numerical examples show that our results are correct, effective and feasible.In the third chapter, we consider the adaptive variable structure control problem for three classes of nonlinear systems and realize unification for the robustness of the system and adaptive variable structure control method. In the sliding controller, we can improve reaction rate and control performance by using adaptive method to unknown parameters. At first, we propose the generalized Lipschiz condition for artificial neural networks with discontinuous activation function and design the robust decentralized adaptive controller. Under the assumption that the nonlinear input function satisfies the sector condition, the system can be stable by using this controller. Secondly, we consider the variable struc-ture control of the nonlinear stochastic neural networks for the first time, and discuss the stability in probability for the stochastic Hopfield neural networks. Finally, assumed the nonlinear function satisfies the linear constraints and the measurable output is corrupted by noise, we design a sliding surface with low dimensions and nonlinear input, in which the unknown parameters adopt the adaptive method, to guarantee the stability of the system. Numerical examples show that our results are correct and adaptive method is feasible and effective in sliding mode control for nonlinear delayed systems.In the fourth chapter, we apply the adaptive method to the H∞control for uncer-tain nonlinear systems with time delay and Markov switching. In the first part, based on the assumption that the nonlinear disturbance function is satisfying the linear constraints, where the parameters are known, we design a mixed controller, which is composed by a linear controller and an adaptive controller to guarantee the H∞controllability of the the systems. In this part, the parameter in linear controller is given in terms of linear matrix inequalities and the adaptive controller is used to compensate the disturbance errors. In the second part, assuming the parameters in linear constraints are unknown, we design an adaptive controller to ensure that the system can be H∞controllable. The numerical ex-ample shows our results are correct and prove the designed controllers are effective and feasible.