Distributed Optimization of Multiagent Systems Over Uniform Hypergraphs

Distributed optimization of multiagent systems over uniform hypergraphs is considered in this article. Given a global objective function in advance, an ideal design method of utility functions for each agent is put forward to convert a multiagent system into a budget-balanced potential network game (BBPNG) with the preassigned objective function as its potential function. First, the verification of BBPNGs is simplified to verify whether its fundamental network game is a budget-balanced potential game (BBPG). Next, the algebraic and geometric expressions of BBPGs are obtained, respectively. Finally, a necessary and sufficient condition is given about the utility design.