Parameter-Optimal-Gain-Arguable Iterative Learning Control for Linear Time-Invariant Systems with Quantized Error
In this paper, a parameter optimal gain-arguable iterative learning control algorithm is proposed for a class of linear discrete-time systems with quantized error. Based on the lifting model description for ILC systems, the iteration time-variable derivative learning gain in the algorithm is optimiz...
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MDPI AG
2023-08-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/13/17/9551 |
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| author | Yan Liu Xiaoe Ruan |
| author_facet | Yan Liu Xiaoe Ruan |
| author_sort | Yan Liu |
| collection | DOAJ |
| description | In this paper, a parameter optimal gain-arguable iterative learning control algorithm is proposed for a class of linear discrete-time systems with quantized error. Based on the lifting model description for ILC systems, the iteration time-variable derivative learning gain in the algorithm is optimized by resolving a minimization problem regarding the tracking error energy and the learning effort amplified by a weighting factor. Further, the tracking error can be monotonically convergent to zero when the condition is guaranteed and the rate of convergence can be adjusted by scaling the weighting factor of an optimization problem. This algorithm is more innovative when compared with the existing iterative learning control algorithm for quantization systems. The innovations of this algorithm are as follows: (i) this optimization-based strategy for selecting learning gains can improve the active learning ability of the control mechanism and avoid the passivity of existing selective learning gains; (ii) the algorithm of POGAILC with data quantization can improve the convergence performance of tracking errors and reduce the negative effects of data quantization on the control performance of the logarithmic quantizer; and (iii) we provide a rigorous algorithm convergence analysis by deriving the existence of the unique solution for the optimal learning-gain vector under a singular and nonsingular tracking-error diagonalized matrix. Finally, numerical simulations are used to demonstrate the effectiveness of the algorithm. |
| first_indexed | 2024-03-10T23:29:10Z |
| format | Article |
| id | doaj.art-e4375e3056b14bf19be5ec78c71b0a9f |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T23:29:10Z |
| publishDate | 2023-08-01 |
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| record_format | Article |
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| spelling | doaj.art-e4375e3056b14bf19be5ec78c71b0a9f2023-11-19T07:48:36ZengMDPI AGApplied Sciences2076-34172023-08-011317955110.3390/app13179551Parameter-Optimal-Gain-Arguable Iterative Learning Control for Linear Time-Invariant Systems with Quantized ErrorYan Liu0Xiaoe Ruan1School of Mathematics and Information Sciences, North Minzu University, Yinchuan 750021, ChinaDepartment of Applied Mathematics, School of Mathematics and Statistics, Xi′an Jiaotong University, Xi’an 710049, ChinaIn this paper, a parameter optimal gain-arguable iterative learning control algorithm is proposed for a class of linear discrete-time systems with quantized error. Based on the lifting model description for ILC systems, the iteration time-variable derivative learning gain in the algorithm is optimized by resolving a minimization problem regarding the tracking error energy and the learning effort amplified by a weighting factor. Further, the tracking error can be monotonically convergent to zero when the condition is guaranteed and the rate of convergence can be adjusted by scaling the weighting factor of an optimization problem. This algorithm is more innovative when compared with the existing iterative learning control algorithm for quantization systems. The innovations of this algorithm are as follows: (i) this optimization-based strategy for selecting learning gains can improve the active learning ability of the control mechanism and avoid the passivity of existing selective learning gains; (ii) the algorithm of POGAILC with data quantization can improve the convergence performance of tracking errors and reduce the negative effects of data quantization on the control performance of the logarithmic quantizer; and (iii) we provide a rigorous algorithm convergence analysis by deriving the existence of the unique solution for the optimal learning-gain vector under a singular and nonsingular tracking-error diagonalized matrix. Finally, numerical simulations are used to demonstrate the effectiveness of the algorithm.https://www.mdpi.com/2076-3417/13/17/9551parameter optimal gain-arguableiterative learning controlquantized errorconvergence analysislinear discrete-time system |
| spellingShingle | Yan Liu Xiaoe Ruan Parameter-Optimal-Gain-Arguable Iterative Learning Control for Linear Time-Invariant Systems with Quantized Error Applied Sciences parameter optimal gain-arguable iterative learning control quantized error convergence analysis linear discrete-time system |
| title | Parameter-Optimal-Gain-Arguable Iterative Learning Control for Linear Time-Invariant Systems with Quantized Error |
| title_full | Parameter-Optimal-Gain-Arguable Iterative Learning Control for Linear Time-Invariant Systems with Quantized Error |
| title_fullStr | Parameter-Optimal-Gain-Arguable Iterative Learning Control for Linear Time-Invariant Systems with Quantized Error |
| title_full_unstemmed | Parameter-Optimal-Gain-Arguable Iterative Learning Control for Linear Time-Invariant Systems with Quantized Error |
| title_short | Parameter-Optimal-Gain-Arguable Iterative Learning Control for Linear Time-Invariant Systems with Quantized Error |
| title_sort | parameter optimal gain arguable iterative learning control for linear time invariant systems with quantized error |
| topic | parameter optimal gain-arguable iterative learning control quantized error convergence analysis linear discrete-time system |
| url | https://www.mdpi.com/2076-3417/13/17/9551 |
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