Research On Multi - Autonomous Coherence And Dynamics Behavior Based On Stream Translation Theory

As the emerging discipline in the complex system, the complex networks have attracted extensive attentions of the domestic and international researchers in different fields. As a special kind of complex network model, the multi-agent system has become the focus in many disciplines, such as the information science, management science and control science, and the consensus of the multi-agent systems has been one of the strategic frontier subjects of science and technology. So far, there have been a lot of achievements on the consensus of the multi-agent systems. However, there are still many aspects which are not involved about the research methods and results. According to the research status quo of the problem, the theory for the discontinuous dynamical systems is used to analyze the consensus of the multi-agent systems in this thesis. At the same time, this thesis presents a method for judging the stability of the differential system. The main contributions are as follow:l.The consensus problems of the second-order continuous multi-agent systems within the limited time are investigated through the theory of flow switchability. Each equation in the systems has inherent characteristics of nonlinear dynamics. Through a simple consensus protocol, the consensus within limited time of the system with leader is discussed in the thesis. First of all, based on the theory of flow switchability, the direction field of each individual is divided into several different subdomains according to the restriction of the protocol. In each subdo-main, the individual’s motion has different dynamical characteristics respectively. In order to realize the consensus of the system under the protocol, the individu-al’s motion should be on the boundaries between the subdomains. Therefore, the motions of subsystems near the boundaries are analyzed in detail. By defining the corresponding G function, a variety of situations and possible bifurcations of the subsystems’flow are determined through the sign and variation of the G function. Through the flow switchability of the subsystems, the conditions for the onset and vanishing of the consensus are established. The consensus of the system in partial time intervals can be determined, when the full consensus does not exist. Furthermore, the analytical condition for consensus is presented.2. Using the mapping dynamical theory, the discrete consensus problem of a class of discontinuous systems is studied. The research is on the second order multi-agent system affected by the impulsive function. The definitions of com-panion and consensus under once iteration are established, and the consensus conditions are analyzed. According to the definitions, the composite mapping between the adjacent switch points is presented, and the necessary and sufficient conditions of consensus are discussed by using the mapping. The conditions for the onset and vanishing of the consensus are established.3. The stability of differential systems is investigated. The main research is on the n-dimensional differential systems. Based on the theory of flow switch-ability, we present a new method to study the stability of differential systems. The method takes the advantage of the relationship between the vector field and the first integral. In order to overcome the difficulty that the first integral of differential systems is hard to be determined, we decompose the vector field into two parts. The first integral of the first part can be got easily. When the other part meets the corresponding conditions, the stability of differential systems can be presented. Moreover, we discuss the stability of the impulsive differential sys-tems in this section. On this basis, the uniform stability of differential systems is discussed by using the relationship between the vector field and the generalized measure function. This method overcomes the restriction of the first integral, and presents results of uniform stability of equilibrium solution of the differential sys-tems. Also, we present the stability results for the impulsive differential systems. And the effectiveness of results is illustrated through numerical simulation.