Fully Distributed Prescribed-Time Optimization of Multi-Agent Systems

This paper investigates fully distributed prescribed-time control methods for the convex optimization of continuous-time first-order multi-agent systems (MAS). We propose a novel distributed control scheme that eliminates the necessity for global communication topology information while ensuring prescribed-time convergence to the global minimizer of the objective function. First, we design a new prescribed-time estimator to compute the average gradients and Hessians of the objective function. Concurrently, we introduce a fully distributed consensus control scheme that enables all agents to achieve consensus. Second, utilizing the estimated gradients and Hessians, and with consensus achieved among the MAS, we develop a prescribed-time optimization controller that ensures the convergence of all agents' states to the global minimizer. A numerical simulation is included to demonstrate the effectiveness of the proposed control methods.