Distributed Two-Stage Fixed-Time Optimization Algorithm for Formation Control of Multi-Agent System Based on Local Voting Event-Triggered Mechanism

This article proposes a two-stage fixed-time distributed optimization algorithm based on a local voting event-triggered mechanism for continuous-time multiagent systems, which simultaneously guarantees fast convergence, high 3D formation precision, and communication efficiency. This algorithm consists of two stages: the gradient-driven stage ensures each agent quickly converges from the initial position to the local optimal solution, and the event-triggered consensus stage realizes coordinated formation and cuts down communication frequency. In this case, this algorithm avoids the insufficient convergence speed existing in single-stage counterparts. First, an exponential trajectory compensation term is introduced into the second stage, aiming to eliminate precision loss induced by spatial dimensional conversion in formation control. Second, a local voting-based event-triggered mechanism that adopts exponential decay thresholds and introduces neighbor state feedback is developed, under which an agent can only trigger communication when its local state error exceeds the threshold and at least one neighbor satisfies the same triggering condition. The designed cooperative triggering strategy eliminates isolated triggering and stale information utilization, which reduces controller updates and communication consumption. Furthermore, a timeout fallback module is embedded to avoid triggering deadlock caused by strict neighbor-consensus constraints, ensuring stable and reliable triggering performance. Third, theoretical analysis is demonstrated that the proposed algorithm achieves the fixed time convergence, while achieving optimal formation control for multi-agent systems. It is also strictly proven that the proposed event-triggered mechanism avoids Zeno behavior. Finally, numerical simulations verified the precise convergence of the proposed algorithm to the optimal value in 3D formation tasks.