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.

Publication:

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 69, NO. 5, MAY 2024

http://dx.doi.org/10.1109/TAC.2023.3337688

Author:

Yaqi Hao

School of Mathematics, Shandong University, Shandong 250100, China

Email: hoayaqi@outlook.com

Ji-Feng Zhang

Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Beijing 100190, China

Chinese Academy of Sciences and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100149, China

Email: jif@iss.ac.cn