Distributed Safety-Critical Control of Multi-Agent Systems with Time-Varying Communication Topologies

Coordinating multiple autonomous agents to reach a target region while avoiding collisions and maintaining communication connectivity is a core problem in multi-agent systems. In practice, agents have a limited communication range. Thus, network links appear and disappear as agents move, making the topology state-dependent and time-varying. Existing distributed solutions to multi-agent reach-avoid problems typically assume a fixed communication topology, and thus are not applicable when encountering discontinuities raised by time-varying topologies. This paper presents a distributed optimization-based control framework that addresses these challenges through two complementary mechanisms. First, we introduce a truncation function that converts the time-varying communication graph into a smoothly state-dependent one, ensuring that constraints remain continuous as communication links are created or removed. Second, we employ auxiliary mismatch variables with two-time-scale dynamics to decouple globally coupled state-dependent constraints, yielding a singular perturbation system that each agent can solve using only local information and neighbor communication. Through singular perturbation analysis, we prove that the distributed controller guarantees collision avoidance, connectivity preservation, and convergence to the target region. We validate the proposed framework through numerical simulations involving multi-agent navigation with obstacles and time-varying communication topologies.