Zero-Gradient-Sum Algorithm-Based Distributed Optimization in Finite Time for Agents on Signed Networks

Based on zero-gradient-sum (ZGS) algorithm, this paper studies the finite-time distributed optimization problem for multi-agent systems (MASs) over signed networks. First, a finite-time distributed control protocol is designed to ensure all agent states to realize bipartite consensus in a finite time under undirected signed graphs. Meanwhile, the optimized solutions of minimizing global convex objective functions under undirected signed graphs also converge to the bipartite consensus values. Moreover, the finite-time upper bound is given, which depends on the initial states and also the choice of the parameters in the proposed protocols. Then, extend the results to the case of signed digraphs. Finally, simulation results show the validity of the proposed methods.