Research On Some Problems In Consensus Control Of Multi-agent Systems

With the development of computer science, information science and automation, the coordinated control of multi-agent systems shows a promising potential in actual application. Consensus problem is a foundational problem in coordinated control of multi-agent systems, which has become a hot topic in system and control science community. In this dissertation, graph theory and matrix analysis are used to study the consensus problem of multi-agent systems. The main contributions of this dissertation are as follows:1. The consensus problem of second-order nonlinear multi-agent systems with communication delay under time-controlled switching topology is investigated. By introducing a state transformation, a reduced-order consensus error system is obtained,which implies that the consensus problem can be analyzed by the stability problem of the error system. Finally, Lyapunov-Krasovskii functionals are constructed to derived the consensus protocol and the minimum average dwell time of the switching signal.2. The consensus problem of second-order nonlinear multi-agent systems under state-controlled is studied. A kind of state transformation is proposed, which turns the second-order system to a first-order system with nodes in the new system doubled. First, a consensus protocol is proposed and is proved to be effective theoretically under fixed topology. Then, the state-controlled switching laws is designed. Finally, by constructing a common Lyapunov function, it is proved that consensus of multi-agent system under switching topologies which jointly contains a spanning tree is reached with the designed consensus protocol and the state-controlled switching laws.3. The consensus problems of high-order nonlinear multi-agent systems in complex environment are studied. On one hand, actuator with Backlash-like hysteresis and unknown direction is considered. By exploiting the property of backlash-like hysteresis,output of the hysteresis actuator can be the combination of linear input and bounded disturbance. Then,a new kind of Nussbaum function is employed to confront with the unknown control direction. Finally, by using the backstepping technique and adaptive neural networks, a distributed adaptive neural consensus protocol is proposed. On the other hand, the consensus problem of high-order nonlinear multi-agent systems with state time-delay is studied. Neural networks are employed to compensate the nonlinearities in the systems. Then norm of the weight matrix of the neural network is estimated, in this way, the number of adaptive parameters are reduced and thus the computation burden is relieved. Finally, Lyapunov-Krasovskii functionals are constructed to show the effectiveness of the proposed consensus protocol.4. The cluster consensus of heterogeneous multi-agent systems is studied where there are negative weights of edges representing competitions among agents. First, the cluster consensus problem of a class of semi-heterogeneous multi-agent, where only agents in different clusters may have different dynamics, is studied. By using the linear small gain theory, a distributed cluster consensus protocol is proposed. Second, the cluster consensus problem of heterogenous multi-agent systems, in which dynamics of all agents can be different, is studied. Based on the output regulation theory and small gain theory, state feedback and dynamic output feedback consensus protocols are proposed. Finally, the underlying secret of inter cluster couplings and intra cluster couplings for cluster consensus problem is revealed.