Control Design With Optimization for Fuzzy Steering-by-Wire System Based on Nash Game Theory

Area of Science:

• Control Theory
• Fuzzy Systems
• Game Theory

Background:

• Dynamical systems often exhibit time-varying, bounded uncertainty.
• Fuzzy logic provides a framework to describe uncertain parameters as fuzzy numbers.
• Lyapunov theory is a standard for analyzing system stability.

Purpose of the Study:

• To develop a high-order control strategy for uncertain dynamical systems.
• To enhance system performance and minimize control input.
• To verify the proposed control method using numerical simulations.

Main Methods:

• Applying a high-order controller to a dynamical system with fuzzy uncertainty.
• Utilizing noncooperative game theory and Nash game to optimize controller parameters.
• Introducing the D-operation for handling fuzzy number uncertainties.
• Employing Lyapunov theory for stability analysis.

Main Results:

• The proposed deterministic controller ensures uniform boundedness and ultimate boundedness of the system.
• Nash game optimization effectively improves system performance and reduces control input.
• The D-operation successfully addresses fuzzy number-related uncertainties.
• Numerical simulations validate the effectiveness of the control strategy.

Conclusions:

• The developed high-order control method effectively manages fuzzy uncertainty in dynamical systems.
• The integration of fuzzy logic, game theory, and Lyapunov stability analysis offers a robust control solution.
• The steering-by-wire system simulation demonstrates practical applicability and improved performance.