Iterative Learning Control for Linear Time-varying Systems with Input and Output Constraints

This paper integrates a previously developed iterative learning identification (ILI) (Liu, N., and Alleyne, A. G., 2016, “Iterative Learning Identification for Linear Time-Varying Systems,” IEEE Trans. Control Syst. Technol., 24(1), pp. 310–317) and iterative learning control (ILC) algorithms (Bristow, D. A., Tharayil, M., and Alleyne, A. G., 2006, “A Survey of Iterative Learning Control,” IEEE Control Syst. Mag., 26(3), pp. 96–114), into a single norm-optimal framework. Similar to the classical separation principle in linear systems, this work provides conditions under which the identification and control can be combined and guaranteed to converge. The algorithm is applicable to a class of linear time-varying (LTV) systems with parameters that vary rapidly and analysis provides a sufficient condition for algorithm convergence. The benefit of the integrated ILI/ILC algorithm is a faster tracking error convergence in the iteration domain when compared with an ILC using fixed parameter estimates. A simple example is introduced to illustrate the primary benefits. Simulations and experiments are consistent and demonstrate the convergence speed benefit.

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Data-Driven Networked Optimal Iterative Learning Control for Discrete Linear Time-Varying Systems with One-Operation Bernoulli-Type Communication Delays

Discrete Dynamics in Nature and Society ◽

10.1155/2017/9846846 ◽

2017 ◽

Vol 2017 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Yan Geng ◽

Xiaoe Ruan ◽

Hyo-Sung Ahn

Keyword(s):

Iterative Learning Control ◽

Linear Time ◽

Tracking Error ◽

Learning Control ◽

Iterative Learning ◽

Data Driven ◽

Time Varying ◽

Communication Delays ◽

System Matrix ◽

Time Varying Systems

This paper develops a type of data-driven networked optimal iterative learning control strategy for a class of discrete linear time-varying systems with one-operation Bernoulli-type communication delays. In terms of the stochastic Bernoulli-type one-operation communication delayed inputs and outputs, the previous-iteration synchronous compensations are adopted. By means of deriving gradients of two types of objective functions that express the optimal approximation of the system matrix and the minimal tracking error, the strategy approximates the system matrix and upgrades the control inputs in an interact mode as the iteration evolves. By taking advantage of matrix theory and statistical technique, it is derived that the approximation discrepancy of the system matrix is bounded and the mathematical expectation of the tracking error vanishes as the iteration goes on. Numerical simulations manifest the validity and effectiveness.

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A high-order internal model based iterative learning control scheme for discrete linear time-varying systems

International Journal of Automation and Computing ◽

10.1007/s11633-015-0886-x ◽

2015 ◽

Vol 12 (3) ◽

pp. 330-336 ◽

Cited By ~ 28

Author(s):

Wei Zhou ◽

Miao Yu ◽

De-Qing Huang

Keyword(s):

Iterative Learning Control ◽

Internal Model ◽

Linear Time ◽

Learning Control ◽

Iterative Learning ◽

High Order ◽

Time Varying ◽

Model Based ◽

Control Scheme ◽

Time Varying Systems

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Kernel-based Regularized Iterative Learning Control of Repetitive Linear Time-varying Systems

IFAC-PapersOnLine ◽

10.1016/j.ifacol.2021.08.449 ◽

2021 ◽

Vol 54 (7) ◽

pp. 738-743

Author(s):

Xian Yu ◽

Tianshi Chen ◽

Biqiang Mu ◽

Lennart Ljung

Keyword(s):

Iterative Learning Control ◽

Linear Time ◽

Learning Control ◽

Iterative Learning ◽

Time Varying ◽

Time Varying Systems

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Adaptive iterative learning control for unknown linear time-varying continuous systems

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331219880110 ◽

2019 ◽

Vol 42 (5) ◽

pp. 981-996

Author(s):

Fateme Afsharnia ◽

Ali Madady ◽

Mohammad Bagher Menhaj

Keyword(s):

Iterative Learning Control ◽

Reference Model ◽

Linear Time ◽

Learning Control ◽

Iterative Learning ◽

Gronwall Lemma ◽

Continuous Systems ◽

Time Varying ◽

Adaptive Iterative Learning Control ◽

Time Varying Systems

This paper presents a novel model reference adaptive iterative learning control (ILC) for unknown continuous-time linear time-varying systems. The unknown time-varying parameters of the system are neither required to vary slowly nor to have known bounds. The system is not required to be minimum-phase, stable, controllable or observable. The input of the system is determined by a differentiator-free control law. The used reference model is time-invariant and first order and thus choosing its parameters is easily possible, even though, the system under control is high order and time variant. Almost all of the components of the system initial condition can be iteration variant. By introducing a novel kind of Lyapunov function the convergence of the proposed adaptive ILC (AILC) and achieving asymptotic tracking are proved. Also, by rigorous mathematical analysis and with the help of some mathematical key techniques such as Bellman-Gronwall lemma, it is shown that all signals and quantities in the closed-loop system are bounded in the sense of at least one norm. Finally, the effectiveness of the proposed method is verified by two simulation examples.

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