Stabilization And Synchronization Control For Some Classes Of Complex Dynamical Systems

Currently, in the fields of engineering applications as well as the natural science, the dynamical systems become more and more complex while the control goals present to be increasingly diversified. In this case, it is necessary to propose a more effective control design method and strategy in control theory. Due to the different characters in complex dynamical systems, for example, the inaccuracy of model and measurement errors, the diversity of dynamical behavior in systems (such as limit cycles, chaotic behaviors and so on), as well as the strong coupling of the internal and external states in systems and others, proposing the method of designing controllers and relative analysis of theory has become an important research topic the field of control theory both at home and abroad.Based on the fuzzy logic systems and Lyapunov stabilization theory in this paper, stabilization, tracking and synchronization for some classes of complex dynamical systems are discussed respectively under the condition of model inaccuracy and coupling effect of the internal and external states. At first, for some kinds of complex dynamical systems with uncertain nonlinearities and a class of complex dynamical system with chaotic phenomenon, the adaptive stable and tracking controller are designed by using fuzzy adaptive control, along with liding mode control and other control design methods. Compared to the other existing control design methods, the method of design controllers in this thesis may not only approximate uncertainty effectively and reduce the number of adaptive laws but also be suitable to various forms of fuzzy logic systems. In addition, by designing the adaptive feedback controller with time-variable factor in state quantizers, the stabilization with states quantized is obtained for a class of chaotic systems. Finally, the stabilization and synchronization for complex dynamical networks with similar nodes are discussed in the thesis. Under certain conditions, by using decentralized control strategy, stabilization and synchronization are discussed for complex dynamical networks with different dimensions of nodes. The main work and research results of this thesis are listed in the following aspects: (1) The background and the significance. relevant research and development overview and some dynamical characters on complex dynamical systems are introduced. Some necessary research topics are also presented.(2) Fuzzy logic systems are adopted for some classes of complex dynamical systems with uncertainties, and the stabilization controllers and tracking adaptive controllers are designed respectively. The results in this thesis show that the control design strategy may not only reduce the number of adaptive laws but also guarantee that the states of these close-loop systems are bounded, and the tracking errors and the observer errors converge to a small neighborhood of the origin. The simulation results demonstrate the effectiveness of the proposed control schemes.(3) The drive-response fuzzy adaptive synchronization is investigated for a class of complex dynamical systems with chaotic phenomenon. For the systems with uncertain nonlinearities and external disturbances, the fuzzy logic systems with nonlinear consequents are utilized to approximate the uncertainties and design adaptive controllers, which may partly solve the problem of disaster of dimension for Mamdani type and T-S type fuzzy logic systems.(4) Stabilization with the quantizers is considered for a class of complex dynamical systems with chaotic phenomenon. Some examples show that if the static quantizers are placed in the input passageway of continuous stable state feedback controllers), some examples show that the divergence phenomenon for chaotic systems may happen because that the static quantizers are placed in the input passageway of continuous stable state feedback controllers. In this case, the stabilization can be solved by using quantizers with time-variable parameters and adaptive schemes.(5) Stabilization and synchronization are considered for a class of coupling complex dynamical networks with similar nodes. Based on the similar parameters, the design method of decentralized controllers is proposed, which can guarantee the exponential stabilization and synchronization for the complex dynamical systems. The method removes the shortcoming that the state dimensions of nodes are completely identical in complex dynamic networks presented in other references. Finally, stabilization and synchronization for the complex dynamical systems with both the same coupling time delay and different coupling time delay are discussed respectively.This work was supported by the National Natural Science Foundation of Guangdong Province (No.8151009001000061), and Team Project of the Guangdong Natural Science Foundation (No.8351009001000002).