Adaptive iterative learning control for high-order nonlinear systems with random initial state shifts.

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Robotics

Background:

• High-order nonlinear systems present significant challenges in control due to complex dynamics.
• Iterative learning control (ILC) typically requires precise initial state positioning, limiting its application.
• Arbitrary initial state errors in ILC hinder accurate system tracking and performance.

Purpose of the Study:

• To develop novel initial state rectification schemes for high-order nonlinear systems.
• To enable complete tracking over specified intervals despite arbitrary initial state errors.
• To relax the stringent initial positioning requirements in iterative learning control.

Main Methods:

• Proposing distinct initial state shift rectification schemes tailored to system orders.
• Utilizing differential equation solving techniques for state correction.
• Incorporating the arctangent function to prevent control signal and variable flutter.

Main Results:

• Theoretical analysis confirms bounded system signals under the proposed schemes.
• Demonstrated convergence of tracking error to zero within a preset interval with increasing iterations.
• Simulation results validate the effectiveness of the developed algorithms.

Conclusions:

• The proposed methods successfully address the tracking problem for high-order nonlinear systems with arbitrary initial states.
• The novel schemes enhance the applicability of iterative learning control by removing initial state constraints.
• The integration of the arctangent function ensures smooth control signal behavior and robust system performance.