Finite-Time Multi-Parameter Smoothing Distributed Algorithm for Delayed Multi-Agent Systems Subject to Switching Topology

This brief tackles the finite-time consensus and distributed optimization issues in multi-agent systems (MASs) affected by time-varying delays (TDs). It centers on scenarios where the agents' communication network topology is characterized by a switching undirected graph. Distributed time-varying optimization involves a collective effort by multiple agents to collaboratively minimize the aggregate of local objective functions that change over time. This process is subject to time-dependent equality constraints and relies solely on information available at the local level and from neighboring agents. First, a finite-time multi-parameter smooth distributed algorithm with input TDs is proposed to solve the optimization problem of MASs with arbitrary switching topologies. Secondly, combined with the Lyapunov stability theory, the states of each agent can achieve consensus and asymptotically track the optimal solution trajectory within a finite-time is proved. At last, an illustrative simulation example of target tracking with MASs is given to verify the effectiveness and applicability of the theoretical results.