Linearly Monotonic Convergence and Robustness of P-Type Gain-Optimized Iterative Learning Control for Discrete-Time Singular Systems
In this article, the repetitive finite-length linear discrete-time singular system is formulated as an input-output equation by virtue of the lifted-vector method and a gain-optimized P-type iterative learning control profile is architected by sequentially arguing the learning-gain vector in minimiz...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2021-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9374450/ |
| _version_ | 1831684848032415744 |
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| author | Ijaz Hussain Xiaoe Ruan Chen Liu Yan Liu |
| author_facet | Ijaz Hussain Xiaoe Ruan Chen Liu Yan Liu |
| author_sort | Ijaz Hussain |
| collection | DOAJ |
| description | In this article, the repetitive finite-length linear discrete-time singular system is formulated as an input-output equation by virtue of the lifted-vector method and a gain-optimized P-type iterative learning control profile is architected by sequentially arguing the learning-gain vector in minimizing the addition of the quadratic norm of the tracking-error vector and the weighed quadratic norm of the compensation vector. By virtue of the elementary permutation matrix and the property of the quadratic function, the optimized-gain vector is solved and explicitly expressed by the system Markov matrix and the iteration-wise tracking error. Then the linearly monotonic convergence of the tracking error is derived under the assumption that the initial state of the dynamic subsystem is resettable. Furthermore, for the circumstance that the system parameters uncertainties exist, the quasi scheme is established by replacing the exact system Markov matrix with the approximated one in the optimized gain. Rigorous analysis conveys that the proposed gain-optimized scheme is robust to the system internal disturbance within a suitable range. The validity and effectiveness are demonstrated numerically. |
| first_indexed | 2024-12-20T08:08:20Z |
| format | Article |
| id | doaj.art-a3cab449bf9644cb81cbb692ce8b0ac6 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-20T08:08:20Z |
| publishDate | 2021-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-a3cab449bf9644cb81cbb692ce8b0ac62022-12-21T19:47:20ZengIEEEIEEE Access2169-35362021-01-019583375835010.1109/ACCESS.2021.30651429374450Linearly Monotonic Convergence and Robustness of P-Type Gain-Optimized Iterative Learning Control for Discrete-Time Singular SystemsIjaz Hussain0Xiaoe Ruan1https://orcid.org/0000-0003-3049-4075Chen Liu2Yan Liu3School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, ChinaSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, ChinaSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, ChinaSchool of Mathematics and Information Science, North Minzu University, Yinchuan, ChinaIn this article, the repetitive finite-length linear discrete-time singular system is formulated as an input-output equation by virtue of the lifted-vector method and a gain-optimized P-type iterative learning control profile is architected by sequentially arguing the learning-gain vector in minimizing the addition of the quadratic norm of the tracking-error vector and the weighed quadratic norm of the compensation vector. By virtue of the elementary permutation matrix and the property of the quadratic function, the optimized-gain vector is solved and explicitly expressed by the system Markov matrix and the iteration-wise tracking error. Then the linearly monotonic convergence of the tracking error is derived under the assumption that the initial state of the dynamic subsystem is resettable. Furthermore, for the circumstance that the system parameters uncertainties exist, the quasi scheme is established by replacing the exact system Markov matrix with the approximated one in the optimized gain. Rigorous analysis conveys that the proposed gain-optimized scheme is robust to the system internal disturbance within a suitable range. The validity and effectiveness are demonstrated numerically.https://ieeexplore.ieee.org/document/9374450/Discrete-time singular systemsiterative learning controllinearly monotonic convergencerobustnessthe optimized-gain vectortuning factor |
| spellingShingle | Ijaz Hussain Xiaoe Ruan Chen Liu Yan Liu Linearly Monotonic Convergence and Robustness of P-Type Gain-Optimized Iterative Learning Control for Discrete-Time Singular Systems IEEE Access Discrete-time singular systems iterative learning control linearly monotonic convergence robustness the optimized-gain vector tuning factor |
| title | Linearly Monotonic Convergence and Robustness of P-Type Gain-Optimized Iterative Learning Control for Discrete-Time Singular Systems |
| title_full | Linearly Monotonic Convergence and Robustness of P-Type Gain-Optimized Iterative Learning Control for Discrete-Time Singular Systems |
| title_fullStr | Linearly Monotonic Convergence and Robustness of P-Type Gain-Optimized Iterative Learning Control for Discrete-Time Singular Systems |
| title_full_unstemmed | Linearly Monotonic Convergence and Robustness of P-Type Gain-Optimized Iterative Learning Control for Discrete-Time Singular Systems |
| title_short | Linearly Monotonic Convergence and Robustness of P-Type Gain-Optimized Iterative Learning Control for Discrete-Time Singular Systems |
| title_sort | linearly monotonic convergence and robustness of p type gain optimized iterative learning control for discrete time singular systems |
| topic | Discrete-time singular systems iterative learning control linearly monotonic convergence robustness the optimized-gain vector tuning factor |
| url | https://ieeexplore.ieee.org/document/9374450/ |
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