Distributed Nash Equilibrium Seeking for Aggregative Games With Nonlinear Dynamics Under External Disturbances

Area of Science:

• Control Theory
• Game Theory
• Distributed Systems

Background:

• Distributed Nash equilibrium (NE) seeking is crucial for multi-agent systems with complex dynamics.
• Players in aggregative games face challenges due to uncertain perturbed nonlinear dynamics.
• Existing methods may struggle with disturbance rejection in such environments.

Purpose of the Study:

• To develop a distributed algorithm for Nash equilibrium seeking in uncertain nonlinear aggregative games.
• To ensure the proposed algorithm can effectively reject external disturbances.
• To analyze the convergence properties of the algorithm for achieving NE.

Main Methods:

• A distributed gradient-based algorithm is proposed, integrating the internal model principle.
• Average consensus techniques are employed for information exchange among neighboring players.
• The algorithm utilizes local cost function information and neighbor communications.

Main Results:

• The proposed algorithm successfully achieves Nash equilibrium seeking for the studied class of games.
• Effective rejection of external disturbances is demonstrated.
• Theoretical analysis confirms the algorithm's convergence properties.

Conclusions:

• The developed distributed algorithm provides a robust solution for Nash equilibrium seeking in uncertain nonlinear aggregative games.
• The integration of internal model principle and average consensus is effective for disturbance rejection.
• This work advances the state-of-the-art in distributed optimization and control for multi-agent systems.