Study On Flocking For Multi-agent Systems

Flocking is a universal phenomenon of multi-agent systems. The common feature of flocking is that velocities converge to a common one, and distances keep in a limited range.Based on previous studies, this article studied flocking of multi-agent systems with time delays. The main contents are as follows:This paper studied the flocking behaviors of multi-agent systems with asymmetric time delays. We used the method of steps in each time strip and integral inequality skills to obtain the asymptotic velocity. And the asymptotic velocity is only related to the initial conditions and time delay. Then using the Lyapunov method, we deduced a sufficient condition of flocking behaviors.In reality, besides asymmetric communication time delays, there is also symmetric communication time delays in the systems. In response to this phenomenon, we also analyzed flocking behavior of multi-agent systems with symmetric time delays. By transforming a general system to the mean value differential system, we derived total momentum of the system is unchanged. Then using a differential inequality system that denote the fluctuations of distances and velocities, a sufficient framework was established. And we deduced that all agents tending to the average speed.At present, in most flocking models, the values of velocities are changing. But there may be some flocking models with constants values and changing directions of velocities. So this paper discussed the flocking behaviors for a class of time-delayed multi-agent system under the speed constraint. At first, the general time delay system was transformed into a time delay system under speed constraints. Then using a system of differential inequalities, we showed that time delay is no qualitative effect on flocking behavior under certain conditions. At the same time, a sufficient framework in terms of initial states, coupling strength and time delay was established to achieve flocking behaviors. At last, we derived avoidance of collisions between agents by using an nonmonotonic increasing function.In order to demonstrate the effectiveness of analytical results, we gave some simulation examples in each chapter.