Adaptive multi-player pursuit-evasion games with unknown general quadratic objectives

Area of Science:

• Control Theory
• Game Theory
• Robotics

Background:

• Multi-player pursuit-evasion games present complex control challenges.
• Unknown objectives and parameters complicate achieving stable equilibrium solutions.

Purpose of the Study:

• To develop an adaptive parameter estimation scheme for multi-player pursuit-evasion games.
• To ensure stability and convergence to a Nash equilibrium despite unknown objectives.

Main Methods:

• An adaptive method is employed for players to estimate opponent parameters.
• Controller strategies are updated iteratively to approach the Nash equilibrium.
• Stability is analyzed using the contraction mapping method.

Main Results:

• A sufficient condition for the stability of the adaptive procedure is established.
• The stability of the closed-loop Nash strategy with the adaptive estimator is guaranteed.
• Simulations demonstrate the effectiveness in an all-against-one scenario.

Conclusions:

• The proposed adaptive estimation scheme effectively addresses unknown objectives in pursuit-evasion games.
• The method ensures stable controller strategies and convergence to a Nash equilibrium.
• Validated through simulation, the methodology offers a robust solution for complex game dynamics.