Finite-time Consensus Problems Of Multi-agent Systems

In recent years, distributed coordinated control of multi-agent systems has received considerable attention from a lot of researches because it can reveal the physical phenomena in the nature and some engineering problems. In distributed coordinated control area,consensus is the basic problem, which has become a hot research topic in the control field.Leader-follower consensus or consensus tracking is investigated in this paper which requires that all followers communicating with their local neighbors eventually converge to the leader’s state. Although there are many results which can accelerate the convergence speed of achieving the consensus, the achievement of consensus is asymptotic, which means that consensus can never be reached in finite time. However, in many situations, it is often required that consensus is reached in finite time. In addition, the convergence time is expected to be shorter. Besides the faster convergence speed, other advantages of ?nite-time consensus include better disturbance rejection and robustness against uncertainties. Therefore, it is actually significant to study how to accelerate the convergence speed of finite-time consensus tracking of heterogeneous multi-agent systems.This paper investigates the fast finite-time consensus tracking problems of different multi-agent systems with a virtual leader, obtaining the following results:(1) We study the fast finite-time consensus tracking problems of first-order multi-agent systems with a virtual leader. With adding the asymptotic coordination and tracking mechanisms into the traditional finite time tracking control algorithm, we propose a novel finite-time consensus tracking protocol. The algebra graph theory, Lyapunov function method,and some other techniques are employed to acquire the convergence condition of reaching fast finite-time consensus tracking. Furthermore, numerical simulations show that compared with the traditional finite-time consensus tracking protocol, the proposed protocol can accelerate the convergence speed.(2) We study the fast finite-time consensus tracking problems of second-order multi-agent systems with a virtual leader. With adding the asymptotic coordination and tracking mechanisms into the traditional finite time tracking control algorithm, we propose a novel finite-time consensus tracking protocol. The Lyapunov function method, algebra graph theory, homogeneity with dilation and some other techniques are employed to acquire the convergence condition of reaching fast finite-time consensus tracking. Furthermore,numerical simulations show that compared with the traditional finite-time consensus tracking protocol, the proposed protocol can accelerate the convergence speed.(3) We study the fast finite-time consensus tracking problems of heterogeneous multi-agent systems with a virtual leader. In the heterogeneous multi-agent systems, the leader can be either first-order or second order. With adding the asymptotic coordination and tracking mechanisms into the traditional finite time tracking control algorithm, we propose a novel finite-time consensus tracking protocol. The Lyapunov function method, algebra graph theory, homogeneity with dilation and some other techniques are employed to acquire the convergence condition of reaching fast finite-time consensus tracking. Furthermore,numerical simulations show that compared with the traditional finite-time consensus tracking protocol, the proposed protocol can accelerate the convergence speed.