Asymmetric Constrained Optimal Tracking Control With Critic Learning of Nonlinear Multiplayer Zero-Sum Games

Area of Science:

• Control Theory
• Game Theory
• Artificial Intelligence

Background:

• Investigating optimal tracking control for nonlinear continuous-time (CT) multiplayer zero-sum games (ZSGs) presents challenges due to asymmetric constraints.
• Traditional analytical solutions for the Hamilton-Jacobi-Isaacs (HJI) equation are often intractable.

Purpose of the Study:

• To develop an effective method for optimal tracking control in nonlinear CT multiplayer ZSGs with asymmetric constraints.
• To address the difficulty in obtaining analytical solutions to the HJI equation.

Main Methods:

• An augmented system combining tracking error and reference systems was constructed.
• A novel nonquadratic function was introduced to handle asymmetric constraints.
• A neural-network-based adaptive critic mechanism was employed to estimate the optimal cost function and derive control policies.

Main Results:

• The study derived the tracking HJI equation for the constrained nonlinear multiplayer ZSG.
• A single critic neural network with a new weight updating rule was utilized.
• The Lyapunov approach verified the uniform ultimate boundedness stability of the tracking error and weight estimation error.

Conclusions:

• The proposed neural-network-based adaptive critic mechanism provides a viable approach for solving optimal tracking control problems in complex multiplayer ZSGs.
• Simulation examples confirmed the efficacy of the developed mechanism in achieving near-optimal control and disturbance policies.