The Research Of Consensus Of Multi-agengt Systems With Reduced-order Observer

Recently, a great number of researchers focus on the coordination control of themulti-agent systems, which have been investigated in many fields, such as: biolo-gy, physics, information science, computer science, control science and mathematics.Consensus problem is one of the most basic problems and is also an important researchpoint of the coordination control. Experts have made great achievements in theoreticalresearch. The basic idea for the consensus Algorithm is: use the local informationof the neighbor’s to design a distributed protocol, through the simple control lawsenable a group of agents to achieve an agreement on certain quantities of interest.Consensus of multi-agent systems under continuous-time and discrete-time willbe study in this paper. we use the measure output of relative neighbors to design areduced-order observer and construct a distribute protocol. As the same time,we usedGraph theory, matrix theory and the Lyapunov function method to make the multi-agent systems to achieve the consensus.The content and the main results are as follows:1. We correct some slight errors which established in the aforementioned paper[28]and prove the new result by the Jordan decomposition method. The proof in this wayis easier to be understand. Then the multi-agent systems achieve consensus if and onlyif the topology graph of the multi-agent system contain a directed spanning tree.2. We used local information to design a distributed reduced-order observer-based protocol under undirected switching topology with the continuous time and thediscrete time. If the undirected topology is connected, we can translate the consensusproblem into the stability of the subsystem and use the common Lyapunov method tosolve it. The simulation example is also show the effectiveness of our obtained result.3. This parts is on the basis of the second chapter, take the complex and the variable of the real environment into account, as well as the real biological model.We consider the leader-following multi-agent system. Design a new protocol basedon the reduce observer, prove the theory and simulate it. We obtained the sufficien-t and necessary condition of the multi-agent consensus under undirected switchingtopology is that the graph is connected. When the topology is connected, the Neigh-bors’information exchanged between each other and their state will change at thesame time until all the agents track the leader. Then we extend the theory to the di-rected switching topology. If the leader is globally reachable, the multi-agent systemsachieve consensus.