Target-Attackers-Defenders Linear-Quadratic Exponential Stochastic Differential Games With Distributed Control.

Area of Science:

• Control Theory
• Game Theory
• Networked Systems

Background:

• Traditional differential games often require global information, limiting their applicability in decentralized systems.
• Stochastic elements introduce complexities not addressed in deterministic game models.

Purpose of the Study:

• To develop distributed control strategies for multi-agent stochastic differential games.
• To minimize system coupling and computational complexity in target-attackers-defenders scenarios.

Main Methods:

• Leveraging topological graph theory for distributed design.
• Applying the direct method of completing the square and Radon-Nikodym derivative.
• Analyzing scenarios with predefined and free-maneuvering targets.

Main Results:

• Optimal distributed control strategies were derived for both target scenarios.
• The designed strategies effectively drive the system towards a Nash equilibrium.
• The need to solve coupled Hamilton-Jacobi equations was eliminated, reducing computational load.

Conclusions:

• The proposed distributed control strategies are effective for stochastic differential games.
• The method offers a computationally efficient alternative to traditional approaches.
• Numerical simulations validate the practical applicability of the developed algorithms.