Document Type : Research Articles
Authors
Department of Electrical Engineering, Tafresh University
Abstract
This paper introduces a novel optimal iterative learning control scheme for continuous-time systems with multiple-inputs and multiple-outputs and linear time-varying dynamics. While iterative learning control has been extensively studied in the discrete-time domain, the development of optimal iterative learning control for continuous-time systems remains limited due to the lack of lifted-formulations and associated mathematical challenges. The proposed method transforms the original optimal iterative learning control problem into a linear quadratic tracking-like problem, enabling the derivation of an explicit close-loop control law that ensures both tracking performance and control effort minimization. Unlike many existing approaches that rely on learning algorithms involving derivative terms, which are often sensitive to measurement noise, the proposed design avoids such terms and remains computationally efficient. Moreover, the monotonic convergence of the tracking error and the associated cost function are proved by rigorous mathematical analysis. Theoretical results are supported by four comprehensive simulation examples, including comparisons with several existing iterative learning control methods. Quantitative evaluations confirm that the proposed optimal scheme significantly outperforms previous techniques in terms of convergence speed and error reduction rate. This contribution offers a new framework for the optimal control of continuous-time systems with multiple inputs and outputs in repetitive tasks and provides a foundation for future extensions to constrained, nonlinear, or partially measurable systems.
Keywords
- Iterative learning control (ILC)
- Linear time-variant systems
- Linear quadratic tracking (LQT)
- Monotonic convergence
- Trajectory tracking
Main Subjects
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