Consensus Of Fractional-order Multi-agent Systems

Due to general systems has limitations in description the memory and viscosity materials, and unable rdflect the own characteristics. The researcher found the systems of fractional-order can reflect the mate-rial stability and it's own characteristics. And factional-order systems has widely application in fractional-order robots and circuit and so on.Researching on consensus problem of multi-agent systems is a hot and basic topic, via exchange of information of multi-agent, using it design a controller, and the state of multi-agent achieve consensus.This master paper mainly research the consensus problem of fractional-order multiagent systems, the arrangement of the thesis are as follows:In chapter 1, the background and application prospect of fractional-order was introduced, and fractional-order calculus were simply intro-duced. Then preliminary knowledge of this paper was introduced.In chapter 2, the consensus problem of fraction-order multi-agent systems is investigated on the directed graphs which contain a span-ning tree. To solve the fractional-order linear systems'consensus prob-lem,the control cooperative tracking is put forward. A observer-based consensus protocols is proposed which depend on the output measure-ment informations.Some sufficient conditions of consensus are estab-lished to guarantee the fractional-order multi-agent system achieves con-sensus. A numerical simulation is preformed to show the effectiveness of the theoretical results.In chapter 3, the leader-following tracking problem of fractional-order multi-agent systems is addressed. The dynamics of each agent may be heterogeneous and has unknown nonlinearities. By assumptions that the interaction topology is undirected and connected and the unknown nonlinear uncertain dynamics can be parameterized by a neural network,an adaptive learning law is proposed to deal with unknown nonlinear dynamics, based on which a kind of cooperative tracking protocols are constructed. The feedback gain matrix is obtained to solve an algebraic Riccati equation. To construct the fully distributed cooperative tracking protocols, the adaptive law is also adopted to adjust the coupling weight.With the developed control laws, we can prove that all signals in the closed-loop systems are guaranteed to be uniformly ultimately bounded.In chapter 4, the distribute tracking problem of linear multi-agent systems with unknown dynamics under directed graphs is considered.Based on the local state information from Ineighboring agents distribute adaptive protocols are proposed. Neural networks couple with adaptive laws are used for being capable of learning unmodeled uncertainties. A local observer is proposed which on the basis of the output information between the agents. Distribute adaptive control protocols and observer-based adaptive control protocols, are designed to make sure that all the signals in the closed-loop dynamics are uniformly ultimately bounded,the tracking errors and tracking errors of observer converge to a small neighborhood around the origin.Chapter 5 is the summary of the paper.