Distributed Event-Triggered Consensus Control of Discrete-Time Linear Multi-Agent Systems under LQ Performance Constraints
This paper proposes a distributed event-triggered control method that not only guarantees consensus of multi-agent systems but also satisfies a given LQ performance constraint. Taking the standard distributed control scheme with all-time communication as a baseline, we consider the problem of designing an event-triggered communication rule such that the resulting LQ cost satisfies a performance constraint with respect to the baseline cost while consensus is achieved. The main difficulty is that the performance requirement is global, whereas triggering decisions are made locally and asynchronously by individual agents, which cannot directly evaluate the global performance degradation. To address this issue, we decompose allowable degradation across agents and design a triggering rule that uses only locally available information to satisfy the given LQ performance constraint. For general linear agents on an undirected graph, we derive a sufficient condition that guarantees both consensus and the prescribed performance level. We also develop a tractable offline design method for the triggering parameters. Numerical examples illustrate the effectiveness of the proposed method.