Event-Triggered Practical Finite-Time Distributed Optimization for Networked Multiagent Systems With Edge-Based Noise

This article addresses the time-varying distributed optimization problem (DOP) for networked multiagent systems (NMASs) operating over directed graphs, considering the impact of edge-based additive measurement noise (EBAMN). First, a finite-time stochastic stability framework is established to demonstrate the global stochastic practical finite-time attraction of the origin, enabling robust control design for stochastic nonlinear systems. The proposed method achieves faster convergence rates and provides bounded finite convergence time estimates, outperforming asymptotic methods. Second, a novel distributed optimization algorithm (DOA) is introduced, incorporating consensus-gain function, state-dependent optimization gains, and integral information of the gradient of local objective functions. Using the It $\mathrm {\hat {o}}$ lemma and Lyapunov theory, the continuous-time DOA guarantees the $p$ th moment convergence for all agents, ensures practical finite-time consensus in probability, and drives that states of NMASs converge to the time-varying optimal solution, even in the presence of EBAMN interferences. Furthermore, a new adaptive dynamic event-triggered mechanism (ETM) integrated with the DOA is proposed. This mechanism significantly enhances communication efficiency and reduces resource consumption throughout the process of tracking the optimal solution while preventing Zeno behavior. Finally, numerical simulations in multiuncrewed aerial vehicle (UAV) target tracking validate the effectiveness of the robust continuous-time DOA against random EBAMN.