Predefined Time Proportional Consensus for Second-order Multi-agent Systems with Dynamic Event Triggering

A distributed predefined-time control strategy based on dynamic event-triggered mechanisms was designed using the backward method, to investigate the predefined time proportional consensus problem for general linear second-order multi-agent systems. Proportional parameters were set for the position and velocity states to enable agents to rapidly achieve proportionate consensus within a predefined time. By selecting appropriate proportional parameters, the proportionate consensus can be extended to ordinary, bipartite consensus, or clustered consensus.An internal dynamic variable was introduced to realize real-time variation of the event triggering condition, thereby reducing system energy consumption and control update frequency. Through algebraic graph theory, linear matrix inequalities, and Lyapunov stability theory,it was proven that under this control strategy, the second-order multi-agent system can achieve proportional consensus within the predefined time, and the dynamic event-triggered moments can avoid Zeno behavior.Through numerical simulation experiments of consensus control, the effectiveness and superiority of the proposed strategy were verified by comparing convergence rates and system performance metrics.The results indicate that, compared with fixed-time control strategies, the convergence time of the system with the proposed strategy is easier to obtain and adjust, and the actual convergence time is closer to the estimated value, offering better convergence rates and system performance metrics. Compared with static event-triggered control strategies, the proposed method can effectively reduce system communication energy consumption while maintaining the performance of the communication system.