Discrete-Time Nonzero-Sum Games for Multiplayer Using Policy-Iteration-Based Adaptive Dynamic Programming Algorithms.

Area of Science:

• Control Theory
• Game Theory
• Machine Learning

Background:

• Nonzero-sum games are complex in discrete-time nonlinear systems.
• Existing methods may not guarantee stability or optimal performance for all players.

Purpose of the Study:

• To develop a novel policy iteration adaptive dynamic programming method for discrete-time nonlinear nonzero-sum games.
• To ensure system stability and minimize individual player performance indices.

Main Methods:

• Integration of game theory, optimal control, and reinforcement learning.
• Design of three actor-critic algorithms (one offline, two online) within the policy iteration framework.
• Implementation using neural networks with stability analysis via Lyapunov theory.

Main Results:

• The proposed policy iteration adaptive dynamic programming method effectively handles discrete-time nonlinear nonzero-sum games.
• Achieved system stability and minimized performance index functions for each player.
• Numerical simulations validated the approach's effectiveness.

Conclusions:

• The novel policy iteration adaptive dynamic programming method provides a robust solution for discrete-time nonlinear nonzero-sum games.
• The integration of AI and control theory offers a powerful framework for complex game scenarios.
• The approach demonstrates practical applicability through simulation examples.