Research On Several Problems Of Consensus In Multi-agent Systems

In recent years, distributed coordination of multi-agent systems has attracted great attention due to several technological advances in the fields of communication and computation. As a fundamental problem in distributed coordination of networks of dynamic agents, the consensus problem is to design appropriate protocols such that the group of vehicles can reach consensus on the shared information in the presence of limited and unreliable information exchange and dynamically changing interaction topologies. Based on garph theory, the fast consensus protocols, finite-time consensus problems and the group motion stability problems of autonomous underwater vehicle (AUV) systems are studied in this dissertation, the main work and research results lie in the following.The analysis of convergence rate is very important in the consensus control of multi-agent systems. In most engineering systems, a fast convergence rate is necessary. Based on the local information, agents automatically converge to a common consensus state and the convergence rate is determined by the algebraic connectivity of the communication network. Without changing the network topology and without requiring extra communication, this dissertation proposes solutions to fast consensus of first-order systems and second-order systems. Aimed at first-order systems, the PI controller is used in fast consensus. With out increasing the maximum control effort, the systems using the PI controller can reach a faster consensus than using the standard consensus protocol. The main idea is to employ a more useful package of information to make sure the agents' next state. Based on the frequency-domain analysis, the sufficient condition to guarantee a faster consensus convergence has been obtained. The disturbance of communication delay is unavoidable and might cause multi-agent systems to diverge or oscillation, the stability analyses of the systems using the proposed protocol with input delays and communication delays are also given. Aimed at second-order systems, a PI controller is used in undirected topologies; the sufficient conditions for the multi-agent systems converging to a fast stationary consensus and a fast dynamical consensus are obtained. Under directed topologies, a fast consensue protocol using both current states and outdated states is proposed. The stability analysis of the systems using the protocol is given, and the sufficient conditions for the system converging to a fast stationary consensus and a fast dynamical consensus are obtained, respectively. What's more, the consensus protocols are applied to the formation control of the multi-vehicle system. The theoretic results show that the fast consensus of the systems is related to the eigenvalues of the Laplacian matrix, the structure of the network and the interconnection topology of the network. Simulations show that the proposed fast protocols can improve the convergence rate significantly.Most of the existing protocols (including those appeared in the aforementioned works) can not result in state consensus in a finite time, that is, consensus is only achieved asymptotically. Hence, finite-time consensus is more appealing and there are a number of settings where finite-time convergence is a desirable property. Based on the theory of finite-time Lyapunov stability and matrix theory, the finite-time consensus problems are studied in this dissertation. Finite-time consensus protocol for continuous multi-agent systems with communication constraints is proposed. The sufficient conditions which guarantee the multi-agent systems to reach a consensus in finite time are given, provided that the undirected network is connected. Moreover, the settling time for the system to reach a consensus is given, it is important to know that the settling time depends on the Lyapunov function, the Laplacian matrix of the undirected graph and the initial state of the system. In order to identify general criteria for solving finite-time consensus problems of multi-agent systems with communication constraints, we show that under protocols satisfying our conditions, the states of agents reach a consensus in finite time when the interaction topology is connected. The methods to design finite-time consensus protocols for systems consider mass are given. The finite-time tracking problems of multi-agent systems with leader-follower models are studied. To track a time-varying leader, a nonlinear finite-time tracking control protocol is proposed for multi-agent systems under fixed network topologies. The sufficient conditions which guarantee the system to reach a finite-time tracking are obtained. Moreover, for the system under switching network topologies, another tracking control protocol is proposed. We show that the followers can track the time-invariant leader in finite time. Simulation results demonstrate that designed protocols can make the system reach consensus in finite time and meeting corresponding performance.Motivated by recent advances in consensus theory of multi-agent systems, based on the leader-follower model, we present corresponding motion model about the formation control and group motion control of AUVs for three different communication conditions. Based on the models and the consensus theory, the conditions for the followers to track the leader steadily are presented and proved. For the systems with communication constraints, a distributed consensus controller for each AUV is designed. It is proved that if the communication time delay between two AUVs is smaller than a certain upper bound, then the velocity vectors of all AUV and the group formation converge to the same desired velocity vector and the desired formation globally asymptotically, and the commen upper bound of the time delay is dependent on the parameters of the network, so it can reduce the conservatism.Finally, a summary has been done for all discussions in the dissertation. The research works in future study are presented.