Convergence analysis of feedback-based iterative learning control with input saturation

For linear continuous multiple-input multiple-output systems with vector relative degree, which operate repetitively with an input-driven motion and a following autonomous motion over a finite time interval, this article proposes an iteratively moving average operator (IMAO) based D-type iterative learning control (ILC) method to address the iteratively varying input trail lengths and random initial state shifts. The proposed ILC algorithm has a rectifying action to random initial state shifts at the designed initial time interval. From the terminal time of rectifying action to the end of control input, it makes the ILC tracking error convergent into a bounded range, the bound of which is proportional to the initial state shifts. Specifically, as the initial state shifts remain fixed, the ILC tracking error can be driven to zero at the relevant time interval along the iteration axis. An example manifests the validity of the proposed IMAO based D-type ILC algorithm.

Section: Discussionmentioning

confidence: 99%

Robust iterative learning control for linear continuous systems with vector relative degree under varying input trail lengths and random initial state shifts

Wei

2020

“…For system with IOCM being full-row rank and the output dimension being less than the input dimension, the existing literature mainly focuses on the convergence of system output sequence and ignores the convergence of system input sequence. 18,19,21,22 However, this does not mean that the convergence of system input sequence is irrelevant. The main reason is that under the constraint on the input and output dimensions, it is easy to analyze the convergence of system output sequence, but it is a challenge to analyze the convergence of system input sequence.…”

Section: Problem Formulationmentioning

confidence: 99%

“…where ūP 1 (2, t) = P 2 ū1 (t) and P = [(P 1 ) ⊤ , (P 2 ) ⊤ ] ⊤ satisfies (22). Here, P 1 ∈ R q×p and P 1 ∈ R (p−q)×p .…”

Section: Convergencementioning

confidence: 99%

Equivalence and convergence of two iterative learning control schemes with state feedback

Zhang

Liu

Ruan

2021

This article considers the equivalence and convergence of two iterative learning control (ILC) schemes with state feedback for a class of multi-input-multi-output discrete-time nonlinear systems in which each desired trajectory corresponds to a unique desired input or an infinite number of desired inputs. First, we strictly prove that the two ILC schemes are equivalent if they have the identical initial system inputs. Moreover, by the input space transformation method and mathematical induction we establish the necessary and sufficient criterion for the convergence of system output, input and state sequences. It is shown that the (locally Lipschitz) continuity is enough to guarantee the (exponential) convergence. Generally, the learned desired input depends on the values of the initial signals, the learning gain matrix and the state feedback item. By designing them with appropriate structures, the dependence is disappeared. Third, we show how to leverage the available information of system dynamics to design the learning gain matrix and state feedback for better tracking performance. Finally, we provide an example to illustrate the usefulness of our findings, in which we introduce the energy of learnable desired input to evaluate the learning performance.

“…The principle of iterative learning control is: through the control attempt of the controlled system, the deviation between the output signal and the desired target is corrected to improve the tracking performance of the system. At the same time, it attracts a large number of researchers and has achieved a large number of scientific research results 3‐10 …”

Section: Introductionmentioning

confidence: 99%

Iterative learning control for one‐sided Lipschitz nonlinear singular conformable differential equations

Wang

2020

This article contributes to a detailed convergence analysis of iterative learning control for singular conformable differential equations with one-sided Lipschitz nonlinearity. In order to track the desired reference trajectory in a finite time interval, a closed-loop D-type learning update law is proposed for such nonlinear systems. Here, the strict convergence analysis is derived under the condition of identical initial state. A numerical example is provided to verify the effectiveness of the proposed controller. K E Y W O R D S convergence, iterative learning control, singular conformable differential equations 1 INTRODUCTION Iterative learning control is an accurate technology, which is suitable for the systems with repetitive motion in a finite time interval. Its goal is to achieve perfect tracking task. The concept of iterative learning control was first mentioned by Uchiyama, a Japanese scholar, in a paper on robot control. 1 A few years later, Arimoto and others formally proposed iterative learning control based on Reference 2. The principle of iterative learning control is: through the control attempt of the controlled system, the deviation between the output signal and the desired target is corrected to improve the tracking performance of the system. At the same time, it attracts a large number of researchers and has achieved a large number of scientific research results. 3-10 Singular system is a kind of system described by differential and algebraic equations. Compared with the regular system described only by differential or difference equations, it has algebraic equation description part. Because of different research fields, singular systems are called by different scholars in different fields, such as generalized state space system, descriptor system, and so on. The singular system includes the description of algebraic equation. Therefore, the applicability of singular system is much wider than that of normal system. The original singular system model was proposed by Ardema in 1962 when studied the dynamic model of spacecraft. Since then, the majority of research enthusiasts have carried out extensive research on singular systems, and obtained many very valuable theoretical results. In the field of Physics, Solimene et al 11 dealt with the calculation of the singular system of radiation operators related to the banded current case. And it can be easily used to describe biological systems in practice. 12,13 Ma and Boukas, 14 based on a singular