The Control And Synchronization Of Caputo Fractional-order Chaotic Systems

Chaos is a ubiquitous nonlinear phenomenon in both nature and society.A chaotic system is a nonlinear deterministic system that exhibits chaotic behavior.Since the pioneering work of Pecora and Carroll who proposed a successful method to synchronize two identical chaotic systems,the control and synchronization of chaotic systems has attracted lots of attention in a variety of research fields over the last two decades owing to its potential applications in many fields of physics and engineering,especially in secure communications.In the recent years,fractional-order calculus has drawn a lot of interest and become a hot topic.In comparison with the classical integer-order model,the major merit of fractional-order calculus is that it has infinite memory which can be utilized to characterize different nonlinear phenomena more accurately.In this paper,the control and synchronization of fractional order chaotic systems are mainly studied.Some sufficient conditions for control and synchronization are given and the effectiveness of the proposed method is verified by numerical simulations.The main work and structure of this paper are summarized as follows:In Chapter 1,the background of the development of chaos control and synchronization is introduced,the definition and properties of chaos and the main concepts of fractional calculus are also given.In addition,the purpose and significance of this study are expounded.It is well known that fractional-order systems can be divided into commensurate systems and incommensurate systems.In Chapter 2,the impulse control of incommensurate fractional systems is considered.By constructing a comparison system of the original system,the corresponding impulse controllers are designed and some sufficient conditions for the stability of the system are proposed.By simultaneously considering the convergence speed of exponential synchronization is faster than that of general asymptotic synchronization and the control input can be disturbed by external factors,so Chapter 3 studies the exponential synchronization of a class of fractional-order chaotic systems with discontinuous inputs.The fractional-order financial systems is taken as an example to verify the effectiveness of the proposed synchronization scheme.Since it is difficult to obtain all the state variables of chaotic systems,so in Chapter 4 we assume that only one state variable is available.By using the single output variable,some controllers are designed to achieve the control and synchronization of fractional-order chaotic systems.The fractional-order generalized Lorenz system is taken as an example to verify the feasibility of the proposed scheme.The summaries of this thesis and prospects for future research are given in Chapter 5.