A Unified Optimization-Based Framework to Adjust Consensus Convergence Rate and Optimize the Network Topology in Uncertain Multi-Agent Systems

摘要

This paper deals with the consensus problem in an uncertain multi-agent system whose agents communicate with each other through a weighted undirected(primary)graph.The considered multi-agent system is described by an uncertain state-space model in which the involved matrices belong to some matrix boxes.As the main contribution of the paper,a unified optimization-based framework is proposed for simultaneously reducing the weights of the edges of the primary communication graph(optimizing the network topology)and synthesizing a controller such that the consensus in the considered uncertain multi-agent system is ensured with an adjustable convergence rate.Considering the NP-hardness nature of the optimization problem related to the aforementioned framework,this problem is relaxed such that it can be solved by regular LMI solvers.Numerical/practical-based examples are presented to verify the usefulness of the obtained results.