Robust Closed–Open Loop Iterative Learning Control for MIMO Discrete-Time Linear Systems with Dual-Varying Dynamics and Nonrepetitive Uncertainties

Iterative learning control (ILC) typically requires strict repeatability in initial states, trajectory length, external disturbances, and system dynamics. However, these assumptions are often difficult to fully satisfy in practical applications. While most existing studies have achieved limited progress in relaxing either one or two of these constraints simultaneously, this work aims to eliminate the restrictions imposed by all four strict repeatability conditions in ILC. For general finite-duration multi-input multi-output (MIMO) linear discrete-time systems subject to multiple non-repetitive uncertainties—including variations in initial states, external disturbances, trajectory lengths, and system dynamics—an innovative open- closed loop robust iterative learning control law is proposed. The feedforward component is used to make sure the tracking error converges as expected mathematically, while the feedback control part compensates for missing tracking data from previous iterations by utilizing real-time tracking information from the current iteration. The convergence analysis employs an input-to-state stability (ISS) theory for discrete parameterized systems. Detailed explanations are provided on adjusting key parameters to satisfy the derived convergence conditions, thereby ensuring that the anticipated tracking error will eventually settle into a compact neighborhood that meets the required standards for robustness and convergence speed. To thoroughly assess the viability of the proposed ILC framework, computer simulations effectively illustrate the strategy’s effectiveness. Further simulation on a real system, a piezoelectric motor system, verifies that the ILC tracking error converges to a small neighborhood in the sense of mathematical expectation. Extending the ILC to complex real-world applications provides new insights and approaches.