Optimal Control Nodes Selection for Consensus in Multi-Agent Systems

In a resource limited multi-agent system, it is of practical importance to select a fraction of nodes (agents) to provide control inputs such that consensus can be achieved with optimized performance in terms of network cost and/or convergence speed. In this paper, we investigate the problem of how to select control nodes so as to minimize the network cost, where the control nodes are selected at the beginning and will be fixed all the time. This problem can be transformed to a combinatorial optimization problem, and further relaxed to a convex optimization problem with reweighted l1 norm. We propose a suboptimal algorithm to solve the convex optimization problem. Finally, we offer several numerical examples to illustrate the efficiency of the proposed strategies, and investigate the relationship how the degrees of control nodes will influence network cost and convergence speed.