Study Of Consensus Of Fractional-order Multi-agent System

Consensus of multi-agent systems is a central topic in the investigation of the dynamics of complex networks and has been received munch attention by a lot of scholars. The critical problem of consensus is how to design appropriate protocols or algorithms which describes the process of exchanging information among each agent and its neighbors so that the multi-agent systems can reach to a certain desired state. As a new field of mathematical research, fractional-order calculus has been a hot research topic. The aim of this work is to discuss the leader-following consensus of fractional-order multi-agent by using feedback control, adaptive pinning control and sampled-data control. The work of this thesis includes the following aspects:In the first part, we consider the leader-following consensus of fractional-order multi-agent systems under feedback control. Based on the Lyapunov method and stability theory of fractional-order di?erential system, some su?cient conditions ensuring the leader-following consensus of the model under the undirected and connected topology and strongly connected topology are given, respectively. Finally,four examples are given to demonstrate the e?ectiveness of the proposed method.In the second part, the leader-following consensus problem of fractional-order multi-agent systems is considered via adaptive pinning control. The dynamics of leader and all followers with linear and nonlinear functions are investigated, respectively. Based on the stability theory of fractional-order di?erential systems and Riccati inequality, some leader-following consensus criteria are derived. two simulation examples are presented to demonstrate the e?ectiveness of the results.In the third part, we studies the consensus control problem for a group of fractional-order multi-agent systems(FOMAS) via sampled control over directed communication topology. The sampled control protocol is induced from continuoustime consensus protocol by using sampling technology. First, consensus of FOMAS without leader is considered. In this case, the sampling control without error and with error are studied, respectively. Moreover, the case that consensus of FOMAS with a leader, which is invariable or variable, are also investigated, respectively. By the iterative method, the continuous-time FOMAS can be equivalently transformed into a discrete-time system. Then by applying algebraic graph theory and matrix theory, some algebraic-type necessary and su?cient conditions of consensus for each case are obtained. Finally, several simulation examples are employed to validate the e?ectiveness of the theoretical results.