Research Of Synchronization And Consensus Problem For Fractional-Order Nonlinear System

The phenomena of synchronization are widely exist in nature, and the related theoretical research has been for a long time. Its application fields are also dispersed from the theoretical science to life science even more social science. It has become one of the hot issues in current research community at home and abroad. More and more scholars devote to study chaotic synchronization and consensus of multi-agent systems. At the same time, the fractional model has attracted lots of attention of many researchers due to good performance in practice. Switched projective synchronization of hyper-chaotic systems and consensus control of multi-agent systems modeled by fractional-order dynamics posses important academic value and practical significance. The dissertation is divided into four chapters and the organization is as follows:In the first chapter, the outline about research background, research significance and research status of this paper is introduced. Some relevant knowledge about graph theory, fractional-order calculus and numerical method of this dissertation are also introduced.In the second chapter, the switched projective synchronization problem of fractional-order hyper-chaotic systems is researched. According to the stability theory of fractional-order systems and combing the method of matrix configuration, a suitable synchronization controller is designed to realize switched projective synchronization between fractional-order hyper-chaotic Chen system and fractional-order hyper-chaotic Lorenz system. Finally, a numerical simulation proves the validity and feasibility of the scheme.In the third chapter, the consensus problem of fractional-order multi-agent systems with nonlinear dynamics is considered. Because the state variables can not be measured completely in reality control systems, the reconstructed states from the state observer are employed to overcome this obstacle in the state-feedback controller design. Based on the Lyapunov stability theory of fraction-order systems, we show that the nonlinear multiple agents in the network can eventually reach an agreement when the feedback gain matrix satisfies a certain LMI condition.The simulation results demonstrate the effectiveness and validity of the proposed method by using the fractional calculus predictor-corrector algorithm.In the fourth chapter, the robust consensus problem for uncertain fractional-order multi-agent systems with nonlinear dynamics is considered.According to the frequency distributed equivalent model of fractional-order systems, the fractional-order systems is transformed into the integer-order systems. Based on the Lyapunov stability theory, a sufficient condition is given to realize consensus for the nonlinear multi-agent systems with fractional-order dynamics.Theory analysis and numerical simulation results are given to verify the validity and reliability of the scheme.In the last, the research work of this paper is summarized. Furthermore, the prospect of the further research is made.