Specified-Time Distributed Control for Multiagent Systems Over Undirected and Directed Graphs: A Linear Operator Theoretic Framework

This article focuses on the performance analysis of distributed controllers for general linear multiagent systems in the sense of convergence time and energy consumption. First, the specified-time optimal controller is obtained using the linear operator theory-based method, and then the optimal topology is deduced. Second, to analyze the impact of communication topology on energy consumption, two distributed, suboptimal specified-time controllers are developed for undirected and directed graphs, respectively. By utilizing the inverse optimality method and Lyapunov function scaling, the performance in terms of the bounds of the gaps between the energy consumption of the suboptimal and optimal control laws is derived, which evaluates the effectiveness of the suboptimal controllers. Finally, as the simulation results show, the performance can specify appropriate settling times for applications with different energy budgets and facilitate optimizing the communication topology to reduce the energy gap.