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(searched for: doi:10.1016/s1004-4132(06)60103-5)
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International Journal of Control, Automation and Systems, Volume 19, pp 777-787; https://doi.org/10.1007/s12555-019-1033-1

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Furqan Memon,
International Journal of Systems Science, Volume 52, pp 263-276; https://doi.org/10.1080/00207721.2020.1825872

Abstract:
The paper presents model-free proportional–integral–derivative (PID) type iterative learning control (ILC) approach for the nonlinear batch process. The dynamic linearisation method is considered, which uses the input-output (I/O) measurements to update the model at each iteration. Based on the newly updated model and error information of the previous iteration, optimal PID gains are updated iteratively. The quadratic performance index is employed to optimise the parameters of the PID controller, and then an optimal PID type data-driven iterative learning control (DDILC) scheme is established for nonlinear batch process. The convergence analysis of optimal PID type DDILC is also discussed which can be enhanced by the proper choice of penalty matrices. Simulation examples are also given to demonstrate the effectiveness of the proposed scheme.
, Wei He
Surrogate Model-Based Engineering Design and Optimization pp 1-13; https://doi.org/10.1007/978-981-15-2784-5_1

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Furqan Memon,
International Journal of Control, Automation and Systems, Volume 18, pp 1926-1935; https://doi.org/10.1007/s12555-018-0840-0

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Meryem Hamidaoui, ,
International Journal of Control, Automation and Systems, Volume 18, pp 1045-1052; https://doi.org/10.1007/s12555-019-0094-5

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, Boško Cvetković,
Scientific Technical Review, Volume 68, pp 17-25; https://doi.org/10.5937/str1802017l

Abstract:
U ovom radu razmatrano je iterativno upravljanje učenjem u zatvorenoj petlji (ILC) - PDα tip linearnim singularnim sistemom sa kašnjenjem necelog reda. Dati su dovoljni uslovi za konvergenciju u vremenskom domenu predloženog PD-alfa tipa ILC za datu klasu linearnog singularnog sistema sa kašnjenjem necelog reda zajedno sa odgovarajućom teoremom i dokazom. Takođe, po prvi put je u ovom radu predloženi tip PDα ILC primenjen za datu klasu linearnih singularnih sistema sa kašnjenjem necelog reda sa neizvesnošću. Konačno, valjanost predloženog ILC algoritma upravljanja za razmatranu klasu singularnih sistema je potvrđena sa adekvatnom numeričkom simulacijom. singularni sistem; linearni sistem; sistem sa kašnjenjem; robotizovani sistem; zatvorena petlja; konvergencija; algoritam upravljanja; iterativno upravljanje
Zhuoyan Gao, ,
Discrete Dynamics in Nature and Society, Volume 2017, pp 1-15; https://doi.org/10.1155/2017/9050289

Abstract:
We address existence and Ulam-Hyers and Ulam-Hyers-Mittag-Leffler stability of fractional nonlinear multiple time-delays systems with respect to two parameters’ weighted norm, which provides a foundation to study iterative learning control problem for this system. Secondly, we design PID-type learning laws to generate sequences of output trajectories to tracking the desired trajectory. Two numerical examples are used to illustrate the theoretical results.
Jianhuan Su, Yinjun Zhang, Yinghui Li
2016 Chinese Control and Decision Conference (CCDC) pp 4252-4256; https://doi.org/10.1109/ccdc.2016.7531728

Abstract:
The work is connected with the development of stability theory methods for a class of second order strong hyperbolic distributed parameter systems for iterative learning control. This research works out the specific P-type control law for the system and proves its robustness and convergence via mapping and semi group method. The system state mild solution is built. The paper used mapping method with the P-type learning law, thus can guarantee the output tracking errors on L2 space converge along the iteration axis. An example has been shown to verify the effectiveness of the new proposed algorithm.
Ke Xi, Xiangjie Liu
Proceedings of the 33rd Chinese Control Conference pp 7752-7757; https://doi.org/10.1109/chicc.2014.6896293

Abstract:
As advanced control strategies, both iterative learning control (ILC) and model predictive control (MPC) are widely used in industrial process. Because ILC cannot eliminate the non-repetitive disturbances, ILC and MPC are integrated as model predictive iterative learning control (MPILC) to improve the capability of rejecting disturbances. Although the typical MPILC has a good tracking performance, there is also left some aspects to be developed. Based on a fuzzy model, a modified nonlinear model predictive iterative learning control (NMPILC) is proposed to achieve a better tracking performance and speed up the learning rate. The performance of the modified NMPILC is illustrated by a PH neutralization process.
ICFDA'14 International Conference on Fractional Differentiation and Its Applications 2014 pp 1-6; https://doi.org/10.1109/icfda.2014.6967421

Abstract:
A feedback-feedforward PDalpha type iterative learning control (ILC) of fractional order uncertain time delay system is considered. Particularly, we discuss fractional order time delay systems in state space form with uncertain bounded constant time delay. Sufficient conditions for the convergence of a proposed PDalpha type of learning control algorithm for a class of fractional state space time delay system are given in time domain. Finally, a simulation example shows the feasibility and effectiveness of the approach.
Published: 10 May 2014
Journal of Process Control, Volume 24, pp 64-77; https://doi.org/10.1016/j.jprocont.2014.04.013

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International Journal of Control, Automation and Systems, Volume 11, pp 470-481; https://doi.org/10.1007/s12555-012-0350-4

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Inam Ul Hasan Shaikh, Martin Brown
Proceedings of 2012 UKACC International Conference on Control pp 778-783; https://doi.org/10.1109/control.2012.6334728

Abstract:
ILC is an emerging technique for learning control. The D-ILC algorithm is the generic ILC scheme which captures the error trend of a batch to update the control input for the next batch or batches. The 2-dimensional nature requires in-depth convergence analysis of the algorithm. This paper addresses these issues in detail. This paper deals with the convergence properties of ILC algorithms with emphasis on control input. Discrete-time linear state space representation of a linear time-invariant system has been considered along with usual assumptions which ensure D-type ILC algorithm converges in terms of output error. The convergence for control input sequence is investigated up to component level.
Zhai Chun-Yan, Xue Ding-Yu, Li Ping, Li Shu-Chen
2012 24th Chinese Control and Decision Conference (CCDC) pp 2031-2034; https://doi.org/10.1109/ccdc.2012.6244327

Abstract:
An algorithm of iterative learning control(ILC) based on predictive model is proposed for a kind of repetitive tracking process of the discrete time system with CARMA model. The repetitive tracking process is operated along with the reference trajectory with performance of predictive control based on predictive model of the one step minimum variance. The convergence of this algorithm is analyzed and convergence conditions are derived. The algorithm for linear stable process can be achieved one iteration unbiased tracking for any changing trajectory when the estimation of model parameters is unbiased. In the car suspension system as an example, the simulation results demonstrate this algorithm can achieve fast unbiased tracking for the changing trajectory. It can still achieve unbiased tracking by 4~5 times of iterative learning control while errors of model parameters estimation are changing in ±30%.
Published: 13 January 2012
Cybernetics and Systems, Volume 43, pp 48-61; https://doi.org/10.1080/01969722.2012.637016

Abstract:
This article addresses an iterative learning control (ILC) design for a class of linear discrete-time systems with multiple time delays. In order to improve the tracking performance, we introduce a P-type high-order iterative learning algorithm that makes use of information from several previous iterations. An initial state learning scheme is proposed to eliminate the effect of the initialization error on the final tracking error. Furthermore, we establish a sufficient condition to ensure asymptotic convergence. A simulation example is also provided to illustrate the effectiveness of the proposed result.
Published: 15 December 2011
Applied Mathematics and Computation, Volume 218, pp 4333-4340; https://doi.org/10.1016/j.amc.2011.10.008

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Hamid-Reza Reza-Alikhani, Ali Madady
2011 19th Mediterranean Conference on Control & Automation (MED) pp 189-194; https://doi.org/10.1109/med.2011.5982987

Abstract:
In this paper, we present a proportional - derivative (PD) type iterative learning control (ILC) for discrete-time systems, performing repetitive tasks. That is, the input of controlled system in current cycle is modified by using the PD strategy on the error achieved between the system output and the desired trajectory in the previous iteration. The convergence of the presented scheme is analyzed and an optimal design method is obtained to determine the PD learning coefficients. Furthermore a condition is achieved in terms of the system parameters so that the monotonic convergence of the presented method is guaranteed. An illustrative example is given to demonstrate the effectiveness of the proposed ILC.
Journal of Computational and Nonlinear Dynamics, Volume 6; https://doi.org/10.1115/1.4002384

Abstract:
Iterative learning control (ILC) is a simple and effective technique of tracking control aiming at improving system tracking performance from trial to trial in a repetitive mode. In this paper, we propose a new ILC called switching gain PD-PD (SPD-PD)-type ILC for trajectory tracking control of time-varying nonlinear systems with uncertainty and disturbance. In the developed control scheme, a PD feedback control with switching gains in the iteration domain and a PD-type ILC based on the previous iteration combine together into one updating law. The proposed SPD-PD ILC takes the advantages of feedback control and classical ILC and can also be viewed as online-offline ILC. It is theoretically proven that the boundednesses of the state error and the final tracking error are guaranteed in the presence of uncertainty, disturbance, and initialization error of the nonlinear systems. The convergence rate is adjustable by the adoption of the switching gains in the iteration domain. Simulation experiments are conducted for trajectory tracking control of a nonlinear system and a robotic system. The results show that fast convergence and small tracking error bounds can be observed by using the SPD-PD-type ILC.
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