Advanced optimal tracking integrating a neural critic technique for asymmetric constrained zero-sum games

Area of Science:

• Control Theory
• Game Theory
• Artificial Intelligence

Background:

• Nonlinear continuous-time zero-sum games (ZSGs) present complex optimal tracking challenges.
• Existing methods for asymmetric constraints often impose strict limitations on control matrices.

Purpose of the Study:

• To develop an improved algorithm for optimal tracking in nonlinear continuous-time multiplayer ZSGs with asymmetric constraints.
• To address limitations of previous methods in handling asymmetric constraints.

Main Methods:

• Exploitation of the neural critic technique for tracking control.
• Development of a novel nonquadratic function to manage asymmetric constraints.
• Utilizing a single critic neural network and normalized steepest descent for weight updates.

Main Results:

• Derivation of optimal controls, worst disturbances, and the tracking Hamilton-Jacobi-Isaacs equation.
• Approximation of optimal controls and worst disturbances using the critic network.
• Demonstration of stability for tracking and weight estimation errors via Lyapunov method.

Conclusions:

• The proposed neural critic method effectively solves the optimal tracking problem for nonlinear CT ZSGs with asymmetric constraints.
• The novel approach relaxes restrictions on control matrices, offering broader applicability.
• Theoretical results are validated through two illustrative examples.