Topology Optimization for Sampled-Data Consensus to Improve the Convergence Rate and Increase the Sampling Period

This paper considers the network topology optimization problem for first-order multi-agent systems (MASs) under the sampled-data consensus protocol, so that MASs can achieve a faster convergence rate and set a longer sampling period, which leads to less information exchanges for reaching consensus. An edge swapping operation (ESO) method is introduced to optimize the communication topology of MASs with undirected graphs as their communication topologies, which keeps the degree of each vertex constant. Based on properties of Laplacian eigenvectors, conditions are proposed for determining an effective ESO which can lead a graph with a larger algebraic connectivity and a smaller Laplacian spectral radius. Numerical results on random graphs show that only ten percent of ESOs are effective. Then an iterative algorithm for optimizing the communication topology for any given MAS is designed. Finally, simulations for MASs under graphs before and after optimization are given, which show that our approach is efficient.