Research On Consensus Of Networked Multi-agent Systems

Due to actual requirements and rapid developments of engineering control systems, researchers have paid great attention to the consensus problem of multi-agent systems. The purpose to study multi-agent systems is to guarantee that each agent with simple functions can complete the complex tasks together according to distributed coordination mechanism. Multi-agent systems have been applied in many actual engineering areas,such as mobile multi-robot systems, automated highway systems, wireless sensor network, autonomous underwater vehicles and so on. When the multi-agent system executes a task, each agent in the system first needs to satisfy a condition that all states of the system will reach a consensus for the given task or a certain value. The consensus problem means that, each agent contacts and affects others in the system via some control protocols, and the states of all agents eventually come to a desired value. This problem is not only a basic problem of distributed and coordinated control, but also a key problem. Thus, it is valuable and meaningful to study it deeply.According to the existence of time-delays in multi-agent systems, researchers have studied the consensus problem, and some conditions that make the systems achieve the consensus have been given. However, the research works on improvement of the convergence rate under time-delays and convergence analysis under different situations of time-delays have been rarely involved. Moreover, though the existing consensus control protocols can guarantee that the system reaches a consensus ultimately, not all the actual systems can converge in the finite time, so it is worthy and meaningful to study the convergence problem of finite-time consensus. On account of the above-mentioned problems that is needed to solve, the research works on the designs of the consensus control protocols and the analysis of convergence performance under the conditions of time-delays and finite-time in multi-agent systems have been done in this dissertation. Based on the theoretical tools of algebraic graph theory and matrix theory, the consensus problems with different cases of communication-delays and self-delays are studied, the problems of time-delays tolerance and convergence rates are analyzed and discussed. In addition, the finite-time consensus problems are also studied.In actual environments, communication delays often occur because of sending messages among agents and self-delays usually happen due to processing messages by agents themselves. However, these two time-delays will lead to a slower convergence rate for the system. Therefore, under the condition of time-delays, it is necessary and worthy to study the problem that how to improve the performance of convergence in multi-agent systems by using effective control protocols. In this dissertation, firstly, three cases of two time-delays are considered, and a PD consensus protocol is designed in first-order system, the control protocol is that an agent updates its state in the next moment by using its changed trend of a former certain state and its previous obtained information. According to the stability criterion and frequency domain method, three sufficient conditions are obtained that guarantee the system converging to the consensus, and the convergence rates have been increased respectively in a certain extent. In addition, a PD consensus control protocol is designed and used in second-order multi-agent system under the connected network, the tolerance problem of time-delays and convergence rate are analyzed, then the time-delay upper bound that makes the system reach a consensus is derived, the range of derivative regulation parameter of PD controller that accelerates the system to a consensus is gained. On this basis, a consensus control protocol that makes the system achieve a dynamic consensus is presented. The research results show that, whether the system achieves a faster consensus or not, depends on the eigenvalues of Laplacian matrix and the connectivity of the system graph. In simulations, it is shown that the presented consensus control protocols can indeed improve the convergent performance of the system.In present, many existing consensus control protocols can make multi-agent systems converge to the consensus asymptotically, but the convergence time may be infinite, that is to say, these protocols can not always make the system achieve the equilibrium state in the finite time. While in the real system, the convergence time must be finite. Thus, it is worthy to further study and analyze the finite-time consensus problem. In this dissertation, the finite-time consensus problem of multi-agent system is analyzed in the cases of undirected and directed network. A consensus control protocol is proposed first. According to the finite-time Lyapunov stability theorem, this presented protocol is proved to make the system converge to a finite-time consensus, and the specific expression of convergence time is obtained. On this basis, the protocol is then summarized in common sense, and the sufficient conditions that make the system reach a finite-time consensus are derived under undirected and directed network respectively. The research results illustrate that, these conditions have less conservativeness than the ones in former literature. After that, from the perspective of convergence rate, a new nonlinear consensus protocol is designed with no time-delay. When a given Lyapunov function satisfies with some assumptions, this protocol can make the undirected system achieve a faster consensus compared with the standard protocol. Moreover, this improved consensus protocol is generally extended further. The simulation results show that, the proposed consensus protocols with time-delays and no time-delays can indeed guarantee the system reaching a finite-time consensus and make the system achieve a faster consensus respectively.Finally, the contents of research works in the dissertation are summarized, and the main research results are given, then the future research works are presented.