Title: Policy iteration and coupled Riccati solutions for dynamic graphical games

Authors: Mohammed I. Abouheaf; Magdi Sadek Mahmoud

Addresses: Group for Research in Decision Analysis (GERAD), Electrical Engineering, Polytechnique Montreal, Canada on leave from College of Energy Engineering, Aswan University, Aswan, Egypt ' Systems Engineering Department, King Fahd University of Petroleum and Minerals, P.O. Box 5067, Dhahran 31261, Saudi Arabia

Abstract: A novel online adaptive learning technique is developed to solve the dynamic graphical games in real-time. The players or agents exchange the information on a communication graph. Hamiltonian mechanics are used to derive the constrained minimum conditions for the graphical game. Novel coupled Riccati equations are developed for this type of games. Convergence of the adaptive learning technique is studied given the graph topology. Nash equilibrium solution for the graphical game is found by solving the underlying Hamilton-Jacobi-Bellman equations. Actor-Critic neural network structures are used to implement the adaptive learning solution using local information available to the players.

Keywords: dynamic games; optimal control; game theory; cooperative control; reinforcement learning; adaptive critics.

DOI: 10.1504/IJDSSS.2017.088058

International Journal of Digital Signals and Smart Systems, 2017 Vol.1 No.2, pp.143 - 162

Received: 25 Oct 2016
Accepted: 08 Mar 2017
Published online: 20 Nov 2017 *

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