Collective behavior of mobile agents with state-dependent interactions

In this paper, we develop a novel self-propelled particle model to describe the emergent behavior of a group of mobile agents. Each agent coordinates with its neighbors through a local force accounting for velocity alignment and collision avoidance. The interactions between agents are governed by path loss influence and state-dependent rules, which results in topology changes as well as discontinuities in the local forces. By using differential inclusion technique and algebraic graph theory, we show that collective behavior emerges while collisions between agents can be avoided, if the interaction topology is jointly connected. A trade-off between the path loss influence and connectivity condition to guarantee the collective behavior is discovered and discussed. Numerical simulations are given to validate the theoretical results.