Fixed-Time Distributed Optimization via Edge-Based Adaptive Algorithms

This article presents two fixed-time (FXT) distributed adaptive algorithms to solve a class of convex optimization problems for multiagent systems. First, a distributed adaptive protocol based on edge weights is developed to achieve global FXT optimization, in which the initial states are the local optimal points. Subsequently, an adaptive power-law algorithm is designed to realize local FXT optimization for each agent with arbitrary initial state. In the convergence analysis, unlike previous analysis method based on Lyapunov FXT stability criteria, this study employs the definition of FXT stability with Laplace transformation and a method of contradiction, several sufficient conditions are obtained to ensure that the states of all agents converge to the global optimal value within a fixed time, and the upper bound of convergence time is estimated. Furthermore, these adaptive algorithms on undirected graphs are extended to weight-balanced digraphs. Finally, the validity of the proposed edge-based adaptive distributed algorithms is demonstrated through numerical simulations of two packet-level charge-state balance problems.