Convergence Analysis of Saturated Iterative Learning Control Systems With Locally Lipschitz Nonlinearities

Area of Science:

• Control Engineering
• Nonlinear System Analysis
• Robotics

Background:

• Iterative learning control (ILC) is crucial for repetitive tasks in uncertain nonlinear systems.
• Challenges include locally Lipschitz nonlinearities, input saturation, and nonzero relative degrees.
• Robust trajectory tracking is essential for precision in dynamic systems.

Purpose of the Study:

• To develop a robust iterative learning control (ILC) algorithm for uncertain nonlinear systems.
• To address the impact of locally Lipschitz nonlinearities, input saturation, and nonzero relative degrees.
• To guarantee pointwise and uniform convergence of tracking errors.

Main Methods:

• A saturated ILC algorithm is proposed.
• Convergence analysis is performed using a composite energy function-based approach.
• The method is demonstrated through two illustrative examples.

Main Results:

• The proposed ILC algorithm guarantees pointwise and uniform convergence of the tracking error.
• The input updating signal converges within saturation limits over iterations.
• The algorithm effectively handles systems with relative degree one, input saturation, and local Lipschitz nonlinearities.

Conclusions:

• The developed saturated ILC algorithm provides robust trajectory tracking for uncertain nonlinear systems.
• The composite energy function approach effectively proves convergence properties.
• The findings are validated for systems with specific challenging characteristics, including input saturation.