Approximate N-Player Nonzero-Sum Game Solution for an Uncertain Continuous Nonlinear System.

Area of Science:

• Control Theory
• Game Theory
• Machine Learning

Background:

• N-player nonzero-sum games present complex control challenges due to nonlinear dynamics and infinite horizons.
• Approximating equilibrium solutions in such systems requires robust methods for handling unknown system dynamics and disturbances.

Purpose of the Study:

• To develop an approximate online equilibrium solution for N-player nonzero-sum games.
• To address continuous-time nonlinear unknown dynamics and infinite horizon quadratic costs.
• To implement a novel actor-critic-identifier structure for robust control.

Main Methods:

• Utilizing a robust dynamic neural network for asymptotic system identification with additive disturbances.
• Employing actor and critic neural networks (NNs) to approximate value functions and equilibrium policies.
• Deriving weight update laws via gradient-descent and least-square regression based on a dynamics-independent modified Bellman error.

Main Results:

• Achieving uniformly ultimately bounded tracking through Lyapunov-based stability analysis.
• Demonstrating convergence of approximate control policies to a neighborhood of optimal solutions.
• Real-time, continuous, and simultaneous implementation of actor, critic, and identifier structures.

Conclusions:

• The developed actor-critic-identifier method provides an effective approach for solving complex N-player games.
• The method ensures stability and convergence to near-optimal policies even with uncertain system dynamics.
• Simulations confirm the practical performance of the proposed real-time control strategy.