Distributed Potential-Based Coordination within Open Multi-Agent Systems

Potential-based coordination frameworks represent a fundamental paradigm for distributed coordination in multi-agent systems, enabling stable collective behaviors through gradient-based local updates. However, their conventional formulations typically assume a fixed agent set, limiting applicability in dynamic settings where agents may enter or exit the network. This paper introduces a generalized potential-based coordination framework tailored for open multi-agent systems (OMASs) in discrete time. Fundamental properties that such potential-based open systems must satisfy are formally established, and a distributed protocol is presented to ensure their fulfillment. Specifically, the proposed approach extends classical gradient-based laws by incorporating cumulative dissipation mechanisms to handle time-varying network cardinality. Numerical simulations validate the effectiveness of the proposed framework compared to different baselines.