Time and Energy Costs for Consensus of Multi-Agent Networks With Undirected and Directed Topologies

Time and energy costs are two important indicators to evaluate the consensus protocols of networking agent systems. However, the relationship between time and energy costs for achieving consensus is far from clear. In this paper, combining the benefits of the linear feedback and finite-time control technologies, a new switching protocol is proposed to solve the finite-time consensus problem of multi-agent networks with undirected and detail-balanced directed topologies. The analytical estimates of time and energy costs are obtained, which unveil the network characteristics and control parameters that can reduce the time and energy costs. Especially, it is shown, both analytically and numerically, that there is a trade-off between time and energy costs, i.e., reducing the time cost will inevitably increase the energy cost.