Model-Free Adaptive Control for Unknown Nonlinear Zero-Sum Differential Game.

Area of Science:

• Control Systems Engineering
• Artificial Intelligence
• Game Theory

Background:

• Discrete-time nonlinear zero-sum games present significant control challenges.
• Solving the associated Hamilton-Jacobi-Isaacs equation is crucial for optimal regulation.
• Existing methods often require system dynamics or identifiers, limiting applicability.

Purpose of the Study:

• To introduce a model-free globalized dual heuristic dynamic programming (GDHP) approach for discrete-time nonlinear zero-sum games.
• To develop an online learning algorithm for solving the Hamilton-Jacobi-Isaacs equation.
• To relax the need for explicit system dynamics or identifiers in optimal control problems.

Main Methods:

• An online learning algorithm based on GDHP is proposed.
• Three neural networks approximate the optimal control law, disturbance law, and performance index.
• Explicit updating rules are derived from online learning data and system trajectories.
• Lyapunov stability analysis is used to address neural network approximation errors.

Main Results:

• The proposed GDHP method effectively solves discrete-time nonlinear zero-sum games without requiring a model.
• The online learning algorithm successfully approximates optimal saddle point feedback control and performance index.
• Stability is demonstrated concerning neural network approximation errors.
• Simulation examples validate the method's effectiveness.

Conclusions:

• The presented model-free GDHP approach offers a viable solution for complex zero-sum game control problems.
• The use of neural networks and online learning simplifies the optimal control design.
• The method's ability to relax system dynamics requirements enhances its practical applicability.