Policy iteration and coupled Riccati solutions for dynamic graphical games

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.