Multi-Agent Systems with Local Rules: Towards a Theory of Analysis and Control

Multi-agent systems enjoy some basic characteristics of complex systems, which arise from diverse fields in natural and artificial systems, such as flocking of birds, schools of fish, traffic systems and robots formation. A basic problem is to understand how locally interacting rules lead to collective behaviors (e.g., synchronization) of the overall system. The so-called Vicsek's model is a simple, typical, and well-known model in describing and comprehending the collective behaviors of a wide class of multi-agent systems. It captures some basic features of complex multi-agent systems, such as local rules, dynamic behaviors, and changing neighborhood. The model looks very simple, but the analysis is quite complicated, because there are nonlinear interactions among the agents of this model. In fact, most of the existing results on synchronization need to impose a certain connectivity condition on the global behaviors of the agents' trajectories, which are quite hard to verify in general. The main purpose of this talk is: (1) to present some recent progress in the analysis of the Vicsek's model. First, we will show that each agent's heading has a limit in any cases; then, replace the previously used connectivity conditions by some easily verifiable ones, imposed only on the agents' initial conditions and the parameters of the model in both deterministic and stochastic frameworks; after that we will also consider both simplifications and generalizations of the Vicsek's model.