Neural Network-Based Model-Free Adaptive Near-Optimal Tracking Control for a Class of Nonlinear Systems

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Adaptive Control Theory

Background:

• Receding horizon control for nonlinear systems presents challenges due to unknown dynamics in both state feedback and input channels.
• Solving optimal control for nonlinear systems typically requires nonlinear Hamilton-Jacobi-Bellman equations, lacking systematic solution approaches.

Purpose of the Study:

• To develop a novel model-free adaptive near-optimal control method for continuous-time nonlinear systems with fully unknown dynamics.
• To address limitations in existing control methods by considering unknown input channel parameters.

Main Methods:

• Utilizes Taylor expansion for problem relaxation, approximating the performance index into a solvable linear algebraic equation.
• Employs sigmoid neural networks for their universal approximation property.
• Designs an auxiliary system to reconstruct unknown input-to-output dynamics.
• Integrates sliding mode control concepts to derive an explicit adaptive control law.

Main Results:

• The auxiliary system demonstrates convergence.
• The closed-loop system achieves asymptotic stability.
• The performance index converges asymptotically to the optimal value.

Conclusions:

• The proposed model-free adaptive near-optimal control method effectively handles nonlinear systems with unknown dynamics.
• The method provides a systematic approach to near-optimal tracking control, validated by theoretical analysis and experimental results.