Cooperative Control Of Several Multi-agent Systems

In recent years, multi-agent systems have received great attention from various scientific fields such as mathematics, automatic control, computer science, physics, biology and so on, which is partly due to its wide applications in sensor networks, unmanned air vehicles, cooperation systems of multi-robots, biological networks, distributed satellites and so forth. As a new discipline, the multi-agent system is related to several scientific fields including applied mathematics and control theory. This paper focuses on the study of the coordination control of several multi-agent systems, which possesses high practical values in the reality.As one of the most important and fundamental issues in the area of coordination control, the consensus problem of multi-agent systems has attracted much interest from scientists. The consensus of multi-agent systems can be described as the states of all the agents converge to the same by communications under the designed control protocol as time goes on, in which the main point is to design the appropriate control protocol. In real situations, due to some external disturbance, there exists damping in systems more or less. Based on this consideration, a general model of multi-agent system with linear decays of both velocity and position of agents is discussed in this paper. By using a combined tools from matrix theory and Lyapunov stability analysis, a new kind of control protocols is first designed and employed. Some necessary and sufficient conditions for the achievement of consensus in the closed-loop multi-agent systems are further obtained. In the reality, the state can be position, velocity, temperature or other physical quantities. However, sometimes the states of agents can not be measured directly. Thus, observers are necessary to obtain the states of agents, which can be used in the control of the system. Nevertheless, in real situations, there may exist many restrictions in the communications of agents, such as the failures of physical devices, unreliability of communication channels and other communication congestions. In most of the time, the agents can not receive information continuously, which can only communicate with their neighbors in some disconnected intervals. Thus, the research for the multi-agent systems with intermittent communications is meaningful. Motivated by above works, a stabilization problem for linear multi-agent systems with time-varying parameter uncertainties and discontinuous observations under is studied.The main work of this paper is presented as follows:In the first chapter, a brief introduction of multi-agent systems, background, research progress of multi-agent systems and meaning of coordination control is given, which is the basis of the main results.In the second chapter, some useful theories used in this paper are introduced, such as graph theory, matrix theory and Lyapunov stability theory, which are basic knowledge of the main results in this paper.A general model of multi-agent systems with second-order dynamics is discussed in the third chapter. Compared with the existing works, the second-order multi-agent systems studied in this chapter contain linear decays of both velocity and position of agents, which makes the problem more general. By analyzing the eigenvalues and using the Lyapunov stability theory, a general control protocol is designed and a necessary and sufficient condition is proposed, which can guarantee the consensus of the system. Finally, simulation examples are provided to verify the theoretical results. The consensus problem studied in this chapter is more practical than some existing works.In the fourth chapter, a linear multi-agent system with intermittent communications and time-varying parameter uncertainties under an undirected topology is discussed. To make the states of all the agents reach the stabilization, a distributed control protocol only based on output information is constructed, as well as the algorithm which shows the method of designing the control protocol. By the use of switching theory, graph theory, matrix analysis and Lyapunov method, a sufficient condition which can guarantee the system can reach the stabilization is derived. A simulation example is provided to verify the effectiveness of the result. The main contribution of this chapter is the combination of intermittent control and time-varying parameter uncertainties, which is more close to the practical situations.The last chapter makes a conclusion of the research work of this dissertation. In addition, the prospect for the further work is proposed.