Linearly Monotonic Convergence and Robustness of P-Type Gain-Optimized Iterative Learning Control for Discrete-Time Singular Systems

Abstract

In this article, the repetitive finite-length linear discrete-time singular system is formulated as an input-output equation by virtue of the lifted-vector method and a gain-optimized P-type iterative learning control profile is architected by sequentially arguing the learning-gain vector in minimizing the addition of the quadratic norm of the tracking-error vector and the weighed quadratic norm of the compensation vector. By virtue of the elementary permutation matrix and the property of the quadratic function, the optimized-gain vector is solved and explicitly expressed by the system Markov matrix and the iterationwise tracking error. Then the linearly monotonic convergence of the tracking error is derived under the assumption that the initial state of the dynamic subsystem is resettable. Furthermore, for the circumstance that the system parameters uncertainties exist, the quasi scheme is established by replacing the exact system Markov matrix with the approximated one in the optimized gain. Rigorous analysis conveys that the proposed gain-optimized scheme is robust to the system internal disturbance within a suitable range. The validity and effectiveness are demonstrated numerically. INDEX TERMS Discrete-time singular systems, iterative learning control, linearly monotonic convergence, robustness, the optimized-gain vector, tuning factor.

Static Iterative Learning Control Over Finite Frequency Domain for Actuator Failure Uncertain Systems

“…I TERATIVE learning control (ILC) is well-suited for systems exhibiting cyclical motion and inherent periodicity, enabling the achievement of precise tracking within a finite time interval [1]. By manipulating the input of the controlled system based on the error signal derived from the disparity between the system output and the desired trajectory, ILC effectively rectifies imperfect control signals, thereby enhancing the overall tracking performance of the system [2], [3].…”