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Finite‐dimensional, output‐predictor‐based, adaptive observer for heat PDEs with sensor delay.

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Title: Finite‐dimensional, output‐predictor‐based, adaptive observer for heat PDEs with sensor delay.
Authors: Rafia, H.1 (AUTHOR), Benabdelhadi, A.1 (AUTHOR), Giri, F.2 (AUTHOR) fouad.giri@yahoo.fr, Ouadi, H.1 (AUTHOR), Chaoui, F. Z.1 (AUTHOR)
Source: International Journal of Adaptive Control & Signal Processing. Apr2024, Vol. 38 Issue 4, p1153-1171. 19p.
Subjects: Mathematical decoupling, Ordinary differential equations, Partial differential equations, Detectors
Abstract: Summary: We are considering the problem of designing observers for heat partial differential equations (PDEs) that are subject to sensor delay and parameter uncertainty. In order to get finite‐dimensional observers, described by ordinary differential equations (ODE), we develop a design method based on the modal decomposition approach. The approach is extended so that both parameter uncertainty and sensor delay effects are compensated for. To cope more effectively with sensor delay, an output predictor is designed and the online provided output predictions are substituted to the future output values in the observer. To compensate for parameter uncertainty, we design a parameter estimator providing online parameter estimates, which are substituted to the unknown parameters in the observer. The parameter estimator design is made decoupled from the observer gain design by using an appropriate decoupling transformation. Using an analysis of the small‐gain‐theorem type, the whole (state and parameter) estimation error system is shown to be exponentially stable, under well‐defined conditions on the observer dimension, the sensor delay, and signal persistent excitation (PE). [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Adaptive Control & Signal Processing is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Finite‐dimensional, output‐predictor‐based, adaptive observer for heat PDEs with sensor delay.
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Adaptive+Control+%26+Signal+Processing%22">International Journal of Adaptive Control & Signal Processing</searchLink>. Apr2024, Vol. 38 Issue 4, p1153-1171. 19p.
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  Data: <searchLink fieldCode="DE" term="%22Mathematical+decoupling%22">Mathematical decoupling</searchLink><br /><searchLink fieldCode="DE" term="%22Ordinary+differential+equations%22">Ordinary differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Detectors%22">Detectors</searchLink>
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  Data: Summary: We are considering the problem of designing observers for heat partial differential equations (PDEs) that are subject to sensor delay and parameter uncertainty. In order to get finite‐dimensional observers, described by ordinary differential equations (ODE), we develop a design method based on the modal decomposition approach. The approach is extended so that both parameter uncertainty and sensor delay effects are compensated for. To cope more effectively with sensor delay, an output predictor is designed and the online provided output predictions are substituted to the future output values in the observer. To compensate for parameter uncertainty, we design a parameter estimator providing online parameter estimates, which are substituted to the unknown parameters in the observer. The parameter estimator design is made decoupled from the observer gain design by using an appropriate decoupling transformation. Using an analysis of the small‐gain‐theorem type, the whole (state and parameter) estimation error system is shown to be exponentially stable, under well‐defined conditions on the observer dimension, the sensor delay, and signal persistent excitation (PE). [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Adaptive Control & Signal Processing is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1002/acs.3740
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      – Code: eng
        Text: English
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        PageCount: 19
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      – SubjectFull: Mathematical decoupling
        Type: general
      – SubjectFull: Ordinary differential equations
        Type: general
      – SubjectFull: Partial differential equations
        Type: general
      – SubjectFull: Detectors
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      – TitleFull: Finite‐dimensional, output‐predictor‐based, adaptive observer for heat PDEs with sensor delay.
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            NameFull: Rafia, H.
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              M: 04
              Text: Apr2024
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              Y: 2024
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              Value: 38
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            – TitleFull: International Journal of Adaptive Control & Signal Processing
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