Swarming Behaviors And Stability Analysis Of Multi-agent Systems

This paper considers the behaviors of multi-agent systems and analyzes the stability of the multi-agent systems. Firstly, we investigate first-order system model of multi-agent systems. In order to describe the interaction between agents, we define a fixed linear attraction function and a bounded repulsion function. The coupling weight matrix is used to describe the potency betw-een the agents. Under some assumptions, for quadratic attractant/repellent profiles and the Gau-ssion attractant/repellent profiles we research the behaviors of the multi-agent systems with co-mmunication delays and lyapunov stability. It prove that each agent of multi-agent systems will converge to our virtual leader and steady in the virtual leader's limited scope no longer move out of the scope, which is decided by the parameters of environment and attraction-repulsion function.etc.In nature, the velocity of each agent affects the behaviors of multi-agent systems. But first-order system model does not consider this factor, then in the second part of this paper, we found second-order system model. The multi-agent systems are affected by the environment or other multi-agent systems in motion, but not each agent can obtain the information from the environment, therefore the agents of swarms are divided into two parts: one part can get the information from the environment; another part can not. When the gradient of the environment is bounded, the agents whether can obtain the information from the environment or not will aggregate around the center of the position with a fixed speed. In above conclusions, we all expend the special attraction-repulsion function to general attraction-repulsion function, which do not consider the space dimension. Our conclusions also hold.For verify the accuracy of our conclusion, we give a large number of simulations. In sim-ulations,we can easy observe the trend of movement, and can obviously see the different envi-ronmental effects on multi-agent systems behaviors are different. Finally, we give the conclusions.