Prescribed-Time Convergent Distributed Multiobjective Optimization With Dynamic Event-Triggered Communication

This article addresses distributed constrained multiobjective resource allocation problems (DCMRAPs) in multiagent networks, where agents face multiple conflicting local objectives under local and global constraints. By reformulating DCMRAPs as single-objective weighted $L\!_p$ problems, the proposed approach enables distributed solutions without relying on predefined weighting coefficients or centralized decision-making. Leveraging prescribed-time control and dynamic event-triggered mechanisms (ETMs), a novel distributed algorithm is proposed within a prescribed time through sampled communication. Using generalized time-based generators (TBGs), the algorithm provides more flexibility in optimizing solution accuracy and trajectory smoothness without the constraints of initial conditions. Novel dynamic ETMs, integrated with generalized TBGs, improve communication efficiency by adapting to local error metrics and network-based disagreements, while providing enhanced flexibility in balancing solution accuracy and communication frequency. The Zeno behavior is excluded. Validated by Lyapunov analysis and simulation experiments, our method demonstrates superior control performance and efficiency compared to existing methods, advancing distributed optimization (DO) across diverse applications.