期刊
AUTOMATICA
卷 50, 期 12, 页码 3038-3053出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2014.10.047
关键词
Dynamic graphical games; Optimal control; Nash equilibrium; Best response; Reinforcement learning
资金
- NSF [ECCS-1128050]
- ONR [N00014-13-1-0562]
- AFOSR EOARD [13-3055]
- ARO [W911NF-11-D-0001]
- China NNSF [61120106011]
- China Education Ministry Project 111 [B08015]
- Directorate For Engineering
- Div Of Electrical, Commun & Cyber Sys [1405173] Funding Source: National Science Foundation
- Directorate For Engineering
- Div Of Electrical, Commun & Cyber Sys [1128050] Funding Source: National Science Foundation
This paper introduces a new class of multi-agent discrete-time dynamic games, known in the literature as dynamic graphical games. For that reason a local performance index is defined for each agent that depends only on the local information available to each agent. Nash equilibrium policies and best-response policies are given in terms of the solutions to the discrete-time coupled Hamilton-Jacobi equations. Since in these games the interactions between the agents are prescribed by a communication graph structure we have to introduce a new notion of Nash equilibrium. It is proved that this notion holds if all agents are in Nash equilibrium and the graph is strongly connected. A novel reinforcement learning value iteration algorithm is given to solve the dynamic graphical games in an online manner along with its proof of convergence. The policies of the agents form a Nash equilibrium when all the agents in the neighborhood update their policies, and a best response outcome when the agents in the neighborhood are kept constant. The paper brings together discrete Hamiltonian mechanics, distributed multi-agent control, optimal control theory, and game theory to formulate and solve these multi-agent dynamic graphical games. A simulation example shows the effectiveness of the proposed approach in a leader-synchronization case along with optimality guarantees. (C) 2014 Elsevier Ltd. All rights reserved.
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