Consensus Of Third-Order Multi-Agent Systems

In recent decade, more and more people have an interest in multi-agent systems, due to its broad applications in the real world, such as unmanned aerial vehicles, Multi-vehicle and robot systems, autonomous underwater submarines and information in network control etc.. Consensus problem is always a core problem in the corresponding theory of multi-agent systems. People firstly study simple first-order multi-agent systems, and scholars gradually begin to study second-order multi-agent systems with the development of the first-order multi-agent systems. But only a few people study third-order and high-order multi-agent systems up to now. Therefore, the theoretical results of first-order and second-order multi-agent systems are more rich and more perfect than the results of third-order and high-order multi-agent systems. In view of the practical application in life and in order to make the theory results perfect, we mainly investigate consensus problem of third-order multi-agent systems in this paper.In this paper, we mainly study the consensus problem of continuous-time third-order multi-agent systems with(without) time-delay and discrete-time third-order multi-agent systems without time-delay. The main contents and contributions of this paper are as follows:In Chapter I, we briefly describe the background and research status of consensus of multi-agent systems. The main content of this paper is also given briefly.In Chapter II, in order to simplify and unify the whole paper, some basic knowledge of graph theory and notations are briefly introduced.In Chapter III, we manly study the consensus problem of continuous–time third-order multi-agent systems without time-delay. According to the algebra graph theory, Hurwitz criterion and the stability criterion of polynomial with complex constant coefficient, we analyzes the characterreistic value of systems' matrix and necessary and sufficient conditions for consensus are established under the directed and undirected graphs, respectively.In Chapter IV, we mainly study the consensus of continuous third-order multi-agent systems with time-delay based on the chapter III. According to the Laplacian transform and frequency domain analysis method, we give some sufficient or necessary and sufficient conditions for consensus of third-order multi-agent systems under the directed or the undirected graphs.In Chapter V, in order to complement the consensus theory, we mainly study consensus problems of third-order discrete-time multi-agent systems. We reduce the order of the original system by a reduced order method. Hence, we study the stability problem of reduced order system instead of the consensus problem of the original system. What's more, some necessary and sufficient conditions for consensus of the system are given under the directed network according to the algebra graph theory, matrix theory and the stability criterion of polynomial with complex constant coefficient.In Chapter VI, we give the summary and outlook. The main work and innovation points of this paper are briefly summarized. Some future research about this paper is also presented.