Incomplete-Information Dynamic Stackelberg Equilibrium Seeking by A Distributed Distributionally Robust Feedback...

Area of Science:

• Control Theory
• Game Theory
• Optimization

Background:

• Traditional Stackelberg games assume leaders possess complete information about followers' objectives.
• Leaders often face challenges with unknown follower behaviors and random system disturbances.
• Existing methods struggle with distributional uncertainty in follower responses.

Purpose of the Study:

• To develop a robust framework for multileader Stackelberg games with incomplete information.
• To address distributional uncertainty in follower objective functions.
• To enable leaders to manipulate physical plant states effectively despite unknown follower strategies.

Main Methods:

• Reformulation of the game as a distributionally robust equilibrium-seeking problem.
• Development of a fully distributed Federated Learning (FL) algorithm.
• Data-driven state estimation via neighbor communication and local gradient updates.

Main Results:

• Characterization of equilibrium existence in nonconvex settings.
• Establishment of the relationship between communication/gradient errors and system energy function.
• Rigorous analysis of the upper bound of regret for the proposed algorithm.

Conclusions:

• The proposed FL algorithm effectively achieves distributionally robust solutions against uncertain stochastic perturbations.
• The data-driven approach operates without prior knowledge of system models or disturbance distributions.
• Demonstrated effectiveness through a case study, highlighting practical applicability.