Adaptive Iterative Learning Control for a Class of Nonlinear Strict-Feedback Systems With Unknown State Delays

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Robotics

Background:

• Nonlinear parametric strict-feedback systems often exhibit unknown state delays, complicating control design.
• Achieving precise trajectory tracking in finite intervals remains a significant challenge for such systems.
• Traditional control methods struggle with differential explosion and singularity issues in high-order systems.

Purpose of the Study:

• To develop an adaptive iterative learning control (ILC) scheme for nonlinear systems with unknown state delays.
• To achieve point-wise trajectory tracking for a desired trajectory within a finite time interval.
• To address challenges like differential explosion and input signal discontinuity.

Main Methods:

• Utilizing Lyapunov-Krasovskii functions to manage time-delay uncertainties.
• Integrating a command filter into the backstepping procedure to mitigate differential explosion.
• Employing hyperbolic tangent functions in the learning controller to handle singularities and ensure continuity.

Main Results:

• Theoretical analysis and numerical simulations confirm convergence of tracking errors to a compact set.
• The proposed adaptive ILC scheme effectively compensates for unknown state delays.
• The controller demonstrates robustness against system nonlinearities and uncertainties.

Conclusions:

• The presented adaptive iterative learning control scheme offers improved performance and practicality for nonlinear systems with state delays.
• The integration of command filters and hyperbolic tangent functions successfully addresses key control challenges.
• This approach provides a promising solution for precise trajectory tracking in complex dynamic systems.