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Volume 34, Issue 4
Iterative Learning Control for a Class of Linear Continuous-Time Switched Systems with Fixed Initial Shifts

Guangzhao Xu, Qin Fu, Lili Du, Jianrong Wu & Pengfei Yu

Commun. Math. Res., 34 (2018), pp. 309-328.

Published online: 2019-12

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  • Abstract

This paper deals with the problem of iterative learning control for a class of linear continuous-time switched systems in the presence of a fixed initial shift. Here, the considered switched systems are operated during a finite time interval repetitively. According to the characteristics of the systems, a PD-type learning scheme is proposed for such switched systems with arbitrary switching rules, and the corresponding output limiting trajectories under the action of the PD-type learning scheme are given. Based on the contraction mapping method, it is shown that this scheme can guarantee the outputs of the systems converge uniformly to the output limiting trajectories of the systems over the whole time interval. Furthermore, the initial rectifying strategies are applied to the systems for eliminating the effect of the fixed initial shift. When the learning scheme is applied to the systems, the outputs of the systems can converge to the desired reference trajectories over a pre-specified interval. Finally, simulation examples illustrate the effectiveness of the proposed method.

  • Keywords

iterative learning control, switched system, PD-type learning scheme, fixed initial shift, output limiting trajectory

  • AMS Subject Headings

68T05, 93C05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

2825418339@qq.com (Guangzhao Xu)

fuqin925@sina.com (Qin Fu)

  • BibTex
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@Article{CMR-34-309, author = {Guangzhao and Xu and 2825418339@qq.com and 5996 and School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, Jiangsu, 215009 and Guangzhao Xu and Qin and Fu and fuqin925@sina.com and 5997 and School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, Jiangsu, 215009 and Qin Fu and Lili and Du and and 5998 and School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, Jiangsu, 215009 and Lili Du and Jianrong and Wu and and 6000 and School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, Jiangsu, 215009 and Jianrong Wu and Pengfei and Yu and and 6002 and School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, Jiangsu, 215009 and Pengfei Yu}, title = {Iterative Learning Control for a Class of Linear Continuous-Time Switched Systems with Fixed Initial Shifts}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {34}, number = {4}, pages = {309--328}, abstract = {

This paper deals with the problem of iterative learning control for a class of linear continuous-time switched systems in the presence of a fixed initial shift. Here, the considered switched systems are operated during a finite time interval repetitively. According to the characteristics of the systems, a PD-type learning scheme is proposed for such switched systems with arbitrary switching rules, and the corresponding output limiting trajectories under the action of the PD-type learning scheme are given. Based on the contraction mapping method, it is shown that this scheme can guarantee the outputs of the systems converge uniformly to the output limiting trajectories of the systems over the whole time interval. Furthermore, the initial rectifying strategies are applied to the systems for eliminating the effect of the fixed initial shift. When the learning scheme is applied to the systems, the outputs of the systems can converge to the desired reference trajectories over a pre-specified interval. Finally, simulation examples illustrate the effectiveness of the proposed method.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2018.04.04}, url = {http://global-sci.org/intro/article_detail/cmr/13514.html} }
TY - JOUR T1 - Iterative Learning Control for a Class of Linear Continuous-Time Switched Systems with Fixed Initial Shifts AU - Xu , Guangzhao AU - Fu , Qin AU - Du , Lili AU - Wu , Jianrong AU - Yu , Pengfei JO - Communications in Mathematical Research VL - 4 SP - 309 EP - 328 PY - 2019 DA - 2019/12 SN - 34 DO - http://doi.org/10.13447/j.1674-5647.2018.04.04 UR - https://global-sci.org/intro/article_detail/cmr/13514.html KW - iterative learning control, switched system, PD-type learning scheme, fixed initial shift, output limiting trajectory AB -

This paper deals with the problem of iterative learning control for a class of linear continuous-time switched systems in the presence of a fixed initial shift. Here, the considered switched systems are operated during a finite time interval repetitively. According to the characteristics of the systems, a PD-type learning scheme is proposed for such switched systems with arbitrary switching rules, and the corresponding output limiting trajectories under the action of the PD-type learning scheme are given. Based on the contraction mapping method, it is shown that this scheme can guarantee the outputs of the systems converge uniformly to the output limiting trajectories of the systems over the whole time interval. Furthermore, the initial rectifying strategies are applied to the systems for eliminating the effect of the fixed initial shift. When the learning scheme is applied to the systems, the outputs of the systems can converge to the desired reference trajectories over a pre-specified interval. Finally, simulation examples illustrate the effectiveness of the proposed method.

Guangzhao Xu, Qin Fu, Lili Du, Jianrong Wu & Pengfei Yu. (2019). Iterative Learning Control for a Class of Linear Continuous-Time Switched Systems with Fixed Initial Shifts. Communications in Mathematical Research . 34 (4). 309-328. doi:10.13447/j.1674-5647.2018.04.04
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