A Data-Driven ILC Framework for a Class of Nonlinear Discrete-Time Systems

Area of Science:

• Control Engineering
• Nonlinear Systems Theory
• Machine Learning for Control

Background:

• Repetitive discrete-time single-input-single-output (SISO) systems present control challenges due to unknown nonlinear nonaffine dynamics.
• Existing iterative learning control (ILC) methods often require prior knowledge of system dynamics.

Purpose of the Study:

• To develop a purely data-driven ILC framework for unknown nonlinear nonaffine repetitive discrete-time SISO systems.
• To achieve guaranteed convergence of tracking errors without explicit system identification.

Main Methods:

• Application of the dynamic linearization (DL) technique to approximate system dynamics.
• Construction of the ILC law based on the equivalent DL expression.
• Adaptive update of the learning control gain vector using a Newton-type optimization method.

Main Results:

• Theoretical guarantee of monotonic convergence of tracking errors in the 2-norm under specified conditions.
• Demonstration that the proposed framework encompasses existing ILC types (PID, higher-order) as special cases.
• Validation through simulations on a complex unknown nonlinear system and a linear time-varying system.

Conclusions:

• The proposed data-driven ILC framework effectively controls unknown nonlinear systems using only input-output data.
• The independence from physical system dynamics makes the approach broadly applicable.
• The adaptive gain update ensures robust and efficient learning control performance.