Distributed Optimization on Matrix‐Weighted Networks

ABSTRACT This article is intended to tackle the optimization problems for continuous‐time first‐order and second‐order multi‐agent systems (MASs) operating over matrix‐weighted networks. A matrix‐weighted network serves as a powerful framework to model the interdependence among agents' multidimensional states, providing an effective approach to analyze smart grids, intelligent transportation systems, and so forth. Our optimization objective is to facilitate the convergence of all agents toward the optimal value of a global cost function, which is formed by a sum of local cost functions. To achieve this goal, distributed optimization algorithms based on Hessian matrix and gradient information are constructed. Additionally, an edge‐based event‐triggered mechanism is utilized to avoid communicating with all neighbors at the time of event triggering. It is proved that this mechanism theoretically excludes Zeno behavior. The results show that the proposed algorithms ensure that the agents can achieve the optimization goal while reducing energy consumption. Finally, an application is presented to substantiate the theoretical results.