Novel optimal trajectory tracking for nonlinear affine systems with an advanced critic learning structure

Area of Science:

• Control Engineering
• Artificial Intelligence

Background:

• Optimal tracking control is crucial for affine nonlinear systems.
• Existing methods often struggle with stable control input computation and tracking error minimization.

Purpose of the Study:

• To develop a critic learning structure for optimal tracking control in affine nonlinear systems.
• To improve convergence speed and reduce tracking error compared to existing methods.

Main Methods:

• A novel utility function defined as the quadratic form of the next moment's error is proposed.
• Theoretical derivation with convergence and stability analysis using value iteration.
• Dual heuristic dynamic programming (DHP) algorithm with a single neural network and polynomial approximation for the costate function.

Main Results:

• The proposed critic learning structure demonstrates faster convergence than the heuristic dynamic programming (HDP) algorithm.
• The method effectively avoids solving for stable control input.
• Achieves tracking error closer to zero compared to traditional tracking control strategies.

Conclusions:

• The novel critic learning structure offers an effective solution for optimal tracking control in affine nonlinear systems.
• The DHP-based approach enhances computational efficiency and performance.
• This method provides superior tracking accuracy and avoids complex control input calculations.