| In recent years, the development of the coordinated control of the multi-agent system is more and more quickly. The flocking problem is a hot topic in multi-agent coordination control, which has attracted experts and scholars attention. In the study of flocking in the multi-agent system, second-order multi-agent systems are usually considered. To prove the feasibility of the flocking algorithm, the Lyapunov stability theory and the LaSalle’s invariance principle are used. However, in practice, many physical systems are nonlinear. And, there is the time delay among the agents in the communication process. While, it varies with the change of time. From the above considerations, this paper mainly studies the flocking control problem of the second-order multi-agent system with the communication delay and nonlinear dynamics.1. The flocking control problems of the multi-agent system with a leader and nonlinear dynamics are studied. The topology of system is switched. And, the control algorithm is proposed in the case of the communication of agents with the time-varying delay. Nonlinear dynamics satisfy the local Lipschitz condition. Assume that the initial state of the network topology being connected, the corresponding potential function and energy function are constructed. At the same time, the size of the agent is considered. When time-varying delays satisfying certain conditions, agents reach the flocking behavior, proved by using the Lyapunov stability method.2. The flocking problems of the second-order multi-agent system with nonlinear dynamics are studied. Considering the system with and without a leader, time delays are considered in the communication of agents, which vary with the time changes. As the initial state of switched network topology being connected, the flocking control protocol is designed. Nonlinear dynamics satisfies the local Lipschitz condition. And, the event-triggered control method is adopted. Giving the potential function and the energy function, the Lyapunov stability method and the LaSalle invariance principle are used to prove the flocking stability of system. Finally, the numerical simulation is made to verify the effectiveness of the control protocol. |
