Guaranteed Cost Consensus for Multi‐Agent Systems with Fixed Topologies

Abstract

Abstract Guaranteed cost consensus analysis and design problems for multi‐agent systems with fixed interaction topologies are investigated. Guaranteed cost consensus problems for multi‐agent systems are introduced to obtain a tradeoff between the consensus regulation performance and the energy consumption, where a cost function is constructed based on state errors among neighboring agents and control inputs of all agents. Sufficient conditions for guaranteed cost consensus and consensualization are given by the state space decomposition approach and the Lyapunov method, an upper bound of the cost function and the consensus value are determined respectively. It should be pointed out that these criteria of guaranteed cost consensus and consensualization are only related to the maximum eigenvalue of the Laplacian matrix associated with the interaction topology. A numerical simulation is given to show the effectiveness of the theoretical results.