Distributed Optimization and State Based Ordinal Potential Games - Intelligent Computing for Sustainable Energy and Environment - page 113

Distributed Optimization and State Based
Ordinal Potential Games
Jianliang Zhang, Guangzhou Zhao, and Donglian Qi
Department of Electrical Engineering, Zhejiang Uinversity, Hangzhou 310027, China
{jlzhang,zhaogz,qidl}@zju.edu.cn
Abstract. The focus of this paper is to develop a theoretical framework
to analyze and address distributed optimization problem in multi-agent
systems based on the cooperative control methodology and game theory.
First the sensing/communication matrix is introduced and the minimal
communication requirement among the agents is provided. Based on the
matrix communication model, the state based ordinal potential game is
designed to capture the optimal solution. It is worth noting that the pro-
posed methodology can guarantee the distributed optimization problem
converge to desired system level objective, even though the corresponding
communication topologies may be local, time-varying and intermittent.
Simulations on a multi-agent consensus problem are provided to verify
the validness of the proposed methodology.
Keywords: Distributed optimization, multi-agent system, potential
games, consensus problem.
1 Introduction
Distributed coordination of dynamic agents in a group plays an important role in
many practical applications ranging from unmanned vehicles, automated high-
way systems, weapon target assignment and wireless sensor networks communi-
cation, etc. As a result, the central problem for multi-agent system is to design
local control laws such that the group of agents can reach consensus on the shared
information in the presence of limited and unreliable information exchange as
well as dynamically changing interaction topologies [1]. In the past decades, nu-
merous studies have been conducted on the consensus problems [1-7]. However,
designing local control laws with real-time adaption and robustness to dynamic
uncertainties would come with several underlying challenges[7][14].
Recently, the appeal of applying game theoretic methodology to multi-agent
systems is receiving significant attention [4-9]. The most advantage of the game
theoretic approach is that it provides a hierarchical decomposition between the
game design and the distributed learning algorithm design. Marden [4] estab-
lished a relationship between cooperative control and potential game by using
the potential function to capture the global objective in game model. Based on
but different from the trial and error learning procedure of Young [11], Pradelski
[12] propose a variant of log linear learning in order to simply compute the states