Dynamical Behavior Of Swarms Under Communicate Network

This thesis devotes to the study of dynamical behavior of multi-agent systems in network by the means of graph theory, matrix analysis, control theory and so on.The multi-agent systems in network is a kind of swarms, which consists of many identical dynamical agents. The dynamics of each agent is Lyapunov stable when it is disconnected with other agents. We design a linear distributed protocol for the dynamical agents in communication network. When the communicated network is of fixed topology structure, we show that the dynamic behavior of swarms depends not only on the dynamical equations of agents, but also on the algebraic characteristic associated with the topology of the network. Moreover, we provide with the conditions under which the agents will gradually achieve aggregation, periodically stable or divergent trajectories. The similar results are extended to the case that the communication network is with transmission time-delay. The time-delay could be constant or time-varying. In this transmission time-delay case, we give in detail algorithms to estimate the upper bounds, for both cases: constant delays and time-varying delays, by means of transfer function and linear matrix inequality, respectively.Under the condition of digital communicated network, we study the dynamic behavior of the swarms which is described by hybrid systems. It is shown that the behavior of the swarms will appear gradually aggregation if the sampling period and dynamic feedback of each agent are satisfied certain conditions. Fixing dynamic feedback gain, we show that there exists an unique sampling period such that the swarms achieve critical periodic stability. Moreover, if we fix sampling period, we also show that there exists an unique dynamic feedback gain such that the swarms achieve critical period stability.Finally, we discuss the nonlinear swarm model where the interactions between any two agents are described by means of physical field. We use some nonlinear functions to define the interactions that governs a long range attraction and short range repulsion nature. It is shown that the members of swarms will asymptotically form a cohesive cluster with finite size if their communication network is an undirected weight topology structure. The similar results can be obtained under the condition that the topology structure of their communication network is a directed weight detailed balance. Meanwhile, we show that there exist various aggregation behaviors of swarms in nonlinear cases by numerical simulations.Moreover, while the communication network of the agents is a directed weight topology structure, the dynamic behaviors of swarms are discussed by simulation examples. We show that the complex behaviors of swarms depend on the choices of the nonlinear attraction and repulsion functions in its mathematical models.