Distributed Zero-Gradient-Sum (ZGS) consensus optimisation over networks with time-varying topologies

This paper addresses a distributed consensus optimisation problem over networks with time-varying topologies based on Zero-Gradient-Sum (ZGS) algorithm. First, the exponential convergence of the algorithm is guaranteed under a new condition on network topologies, called cooperatively connected. This condition does not require the topology constantly connected or jointly connected but only requires the integral of the Laplacian matrix of the network topology over a period of time is connected. Hence, it is suitable for more general time-varying topologies. Second, by establishing a key mathematical lemma, we develop a convergence analysis technique which is based on the difference of the Lyapunov function rather than its differentiation. Finally, a simulation example is also provided to verify the results obtained in this paper.