Time-limited Gramians Based Model Reduction Framework for 1-D and 2-D Systems
Abstract Gawronski and Juang provide an unstable reduced-order model formulation without a priori error bounds for the original one- and two-dimensional models. Several strategies were put forth for the standard linear discrete-time one-dimensional models to guarantee the stability of the reduced-or...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Imran, Muhammad [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© ICROS, KIEE and Springer 2022 |
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| Übergeordnetes Werk: |
Enthalten in: International Journal of Control, Automation and Systems - Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers, 2009, 20(2022), 11 vom: 29. Sept., Seite 3540-3548 |
|---|---|
| Übergeordnetes Werk: |
volume:20 ; year:2022 ; number:11 ; day:29 ; month:09 ; pages:3540-3548 |
| Links: |
|---|
| DOI / URN: |
10.1007/s12555-021-0764-y |
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| Katalog-ID: |
SPR051102994 |
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| 520 | |a Abstract Gawronski and Juang provide an unstable reduced-order model formulation without a priori error bounds for the original one- and two-dimensional models. Several strategies were put forth for the standard linear discrete-time one-dimensional models to guarantee the stability of the reduced-order model over a given time-intervals. These frameworks produce significant truncation mistakes and lack time-domain error-bound expressions. For discrete-time, two-dimensional Gramians models, there are no stability-preserving frameworks that the authors are aware of. This study suggests a Gramian-based model reduction strategy for discrete-time models. One- and two-dimensional discrete-time models can be employed with the framework. The suggested model reduction approach is applied using time-limited Gramians after the discrete-time two-dimensional causal recursive separable denominator models are split into two sub-models (two one-dimensional cascaded models). The framework ensures reduced-order model stability and offers time-domain a priori error-bound expressions for one- and two-dimensional models. Comparisons and numerical results demonstrate the usefulness of the proposed framework. | ||
| 650 | 4 | |a Minimal realization |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a minimal-rank decomposition |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a model reduction |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a time-limited Gramians |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Hamdani, Syeda Fizza |0 (orcid)0000-0001-7870-8701 |4 aut | |
| 700 | 1 | |a Imran, Muhammad |4 aut | |
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10.1007/s12555-021-0764-y doi (DE-627)SPR051102994 (SPR)s12555-021-0764-y-e DE-627 ger DE-627 rakwb eng Imran, Muhammad verfasserin (orcid)0000-0002-7122-8454 aut Time-limited Gramians Based Model Reduction Framework for 1-D and 2-D Systems 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © ICROS, KIEE and Springer 2022 Abstract Gawronski and Juang provide an unstable reduced-order model formulation without a priori error bounds for the original one- and two-dimensional models. Several strategies were put forth for the standard linear discrete-time one-dimensional models to guarantee the stability of the reduced-order model over a given time-intervals. These frameworks produce significant truncation mistakes and lack time-domain error-bound expressions. For discrete-time, two-dimensional Gramians models, there are no stability-preserving frameworks that the authors are aware of. This study suggests a Gramian-based model reduction strategy for discrete-time models. One- and two-dimensional discrete-time models can be employed with the framework. The suggested model reduction approach is applied using time-limited Gramians after the discrete-time two-dimensional causal recursive separable denominator models are split into two sub-models (two one-dimensional cascaded models). The framework ensures reduced-order model stability and offers time-domain a priori error-bound expressions for one- and two-dimensional models. Comparisons and numerical results demonstrate the usefulness of the proposed framework. Minimal realization (dpeaa)DE-He213 minimal-rank decomposition (dpeaa)DE-He213 model reduction (dpeaa)DE-He213 time-limited Gramians (dpeaa)DE-He213 Hamdani, Syeda Fizza (orcid)0000-0001-7870-8701 aut Imran, Muhammad aut Enthalten in International Journal of Control, Automation and Systems Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers, 2009 20(2022), 11 vom: 29. Sept., Seite 3540-3548 (DE-627)SPR026303256 nnns volume:20 year:2022 number:11 day:29 month:09 pages:3540-3548 https://dx.doi.org/10.1007/s12555-021-0764-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_21 GBV_ILN_24 GBV_ILN_72 GBV_ILN_181 GBV_ILN_496 GBV_ILN_2002 GBV_ILN_2003 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2060 GBV_ILN_2470 AR 20 2022 11 29 09 3540-3548 |
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10.1007/s12555-021-0764-y doi (DE-627)SPR051102994 (SPR)s12555-021-0764-y-e DE-627 ger DE-627 rakwb eng Imran, Muhammad verfasserin (orcid)0000-0002-7122-8454 aut Time-limited Gramians Based Model Reduction Framework for 1-D and 2-D Systems 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © ICROS, KIEE and Springer 2022 Abstract Gawronski and Juang provide an unstable reduced-order model formulation without a priori error bounds for the original one- and two-dimensional models. Several strategies were put forth for the standard linear discrete-time one-dimensional models to guarantee the stability of the reduced-order model over a given time-intervals. These frameworks produce significant truncation mistakes and lack time-domain error-bound expressions. For discrete-time, two-dimensional Gramians models, there are no stability-preserving frameworks that the authors are aware of. This study suggests a Gramian-based model reduction strategy for discrete-time models. One- and two-dimensional discrete-time models can be employed with the framework. The suggested model reduction approach is applied using time-limited Gramians after the discrete-time two-dimensional causal recursive separable denominator models are split into two sub-models (two one-dimensional cascaded models). The framework ensures reduced-order model stability and offers time-domain a priori error-bound expressions for one- and two-dimensional models. Comparisons and numerical results demonstrate the usefulness of the proposed framework. Minimal realization (dpeaa)DE-He213 minimal-rank decomposition (dpeaa)DE-He213 model reduction (dpeaa)DE-He213 time-limited Gramians (dpeaa)DE-He213 Hamdani, Syeda Fizza (orcid)0000-0001-7870-8701 aut Imran, Muhammad aut Enthalten in International Journal of Control, Automation and Systems Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers, 2009 20(2022), 11 vom: 29. Sept., Seite 3540-3548 (DE-627)SPR026303256 nnns volume:20 year:2022 number:11 day:29 month:09 pages:3540-3548 https://dx.doi.org/10.1007/s12555-021-0764-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_21 GBV_ILN_24 GBV_ILN_72 GBV_ILN_181 GBV_ILN_496 GBV_ILN_2002 GBV_ILN_2003 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2060 GBV_ILN_2470 AR 20 2022 11 29 09 3540-3548 |
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10.1007/s12555-021-0764-y doi (DE-627)SPR051102994 (SPR)s12555-021-0764-y-e DE-627 ger DE-627 rakwb eng Imran, Muhammad verfasserin (orcid)0000-0002-7122-8454 aut Time-limited Gramians Based Model Reduction Framework for 1-D and 2-D Systems 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © ICROS, KIEE and Springer 2022 Abstract Gawronski and Juang provide an unstable reduced-order model formulation without a priori error bounds for the original one- and two-dimensional models. Several strategies were put forth for the standard linear discrete-time one-dimensional models to guarantee the stability of the reduced-order model over a given time-intervals. These frameworks produce significant truncation mistakes and lack time-domain error-bound expressions. For discrete-time, two-dimensional Gramians models, there are no stability-preserving frameworks that the authors are aware of. This study suggests a Gramian-based model reduction strategy for discrete-time models. One- and two-dimensional discrete-time models can be employed with the framework. The suggested model reduction approach is applied using time-limited Gramians after the discrete-time two-dimensional causal recursive separable denominator models are split into two sub-models (two one-dimensional cascaded models). The framework ensures reduced-order model stability and offers time-domain a priori error-bound expressions for one- and two-dimensional models. Comparisons and numerical results demonstrate the usefulness of the proposed framework. Minimal realization (dpeaa)DE-He213 minimal-rank decomposition (dpeaa)DE-He213 model reduction (dpeaa)DE-He213 time-limited Gramians (dpeaa)DE-He213 Hamdani, Syeda Fizza (orcid)0000-0001-7870-8701 aut Imran, Muhammad aut Enthalten in International Journal of Control, Automation and Systems Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers, 2009 20(2022), 11 vom: 29. Sept., Seite 3540-3548 (DE-627)SPR026303256 nnns volume:20 year:2022 number:11 day:29 month:09 pages:3540-3548 https://dx.doi.org/10.1007/s12555-021-0764-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_21 GBV_ILN_24 GBV_ILN_72 GBV_ILN_181 GBV_ILN_496 GBV_ILN_2002 GBV_ILN_2003 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2060 GBV_ILN_2470 AR 20 2022 11 29 09 3540-3548 |
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10.1007/s12555-021-0764-y doi (DE-627)SPR051102994 (SPR)s12555-021-0764-y-e DE-627 ger DE-627 rakwb eng Imran, Muhammad verfasserin (orcid)0000-0002-7122-8454 aut Time-limited Gramians Based Model Reduction Framework for 1-D and 2-D Systems 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © ICROS, KIEE and Springer 2022 Abstract Gawronski and Juang provide an unstable reduced-order model formulation without a priori error bounds for the original one- and two-dimensional models. Several strategies were put forth for the standard linear discrete-time one-dimensional models to guarantee the stability of the reduced-order model over a given time-intervals. These frameworks produce significant truncation mistakes and lack time-domain error-bound expressions. For discrete-time, two-dimensional Gramians models, there are no stability-preserving frameworks that the authors are aware of. This study suggests a Gramian-based model reduction strategy for discrete-time models. One- and two-dimensional discrete-time models can be employed with the framework. The suggested model reduction approach is applied using time-limited Gramians after the discrete-time two-dimensional causal recursive separable denominator models are split into two sub-models (two one-dimensional cascaded models). The framework ensures reduced-order model stability and offers time-domain a priori error-bound expressions for one- and two-dimensional models. Comparisons and numerical results demonstrate the usefulness of the proposed framework. Minimal realization (dpeaa)DE-He213 minimal-rank decomposition (dpeaa)DE-He213 model reduction (dpeaa)DE-He213 time-limited Gramians (dpeaa)DE-He213 Hamdani, Syeda Fizza (orcid)0000-0001-7870-8701 aut Imran, Muhammad aut Enthalten in International Journal of Control, Automation and Systems Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers, 2009 20(2022), 11 vom: 29. Sept., Seite 3540-3548 (DE-627)SPR026303256 nnns volume:20 year:2022 number:11 day:29 month:09 pages:3540-3548 https://dx.doi.org/10.1007/s12555-021-0764-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_21 GBV_ILN_24 GBV_ILN_72 GBV_ILN_181 GBV_ILN_496 GBV_ILN_2002 GBV_ILN_2003 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2060 GBV_ILN_2470 AR 20 2022 11 29 09 3540-3548 |
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10.1007/s12555-021-0764-y doi (DE-627)SPR051102994 (SPR)s12555-021-0764-y-e DE-627 ger DE-627 rakwb eng Imran, Muhammad verfasserin (orcid)0000-0002-7122-8454 aut Time-limited Gramians Based Model Reduction Framework for 1-D and 2-D Systems 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © ICROS, KIEE and Springer 2022 Abstract Gawronski and Juang provide an unstable reduced-order model formulation without a priori error bounds for the original one- and two-dimensional models. Several strategies were put forth for the standard linear discrete-time one-dimensional models to guarantee the stability of the reduced-order model over a given time-intervals. These frameworks produce significant truncation mistakes and lack time-domain error-bound expressions. For discrete-time, two-dimensional Gramians models, there are no stability-preserving frameworks that the authors are aware of. This study suggests a Gramian-based model reduction strategy for discrete-time models. One- and two-dimensional discrete-time models can be employed with the framework. The suggested model reduction approach is applied using time-limited Gramians after the discrete-time two-dimensional causal recursive separable denominator models are split into two sub-models (two one-dimensional cascaded models). The framework ensures reduced-order model stability and offers time-domain a priori error-bound expressions for one- and two-dimensional models. Comparisons and numerical results demonstrate the usefulness of the proposed framework. Minimal realization (dpeaa)DE-He213 minimal-rank decomposition (dpeaa)DE-He213 model reduction (dpeaa)DE-He213 time-limited Gramians (dpeaa)DE-He213 Hamdani, Syeda Fizza (orcid)0000-0001-7870-8701 aut Imran, Muhammad aut Enthalten in International Journal of Control, Automation and Systems Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers, 2009 20(2022), 11 vom: 29. Sept., Seite 3540-3548 (DE-627)SPR026303256 nnns volume:20 year:2022 number:11 day:29 month:09 pages:3540-3548 https://dx.doi.org/10.1007/s12555-021-0764-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_21 GBV_ILN_24 GBV_ILN_72 GBV_ILN_181 GBV_ILN_496 GBV_ILN_2002 GBV_ILN_2003 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2060 GBV_ILN_2470 AR 20 2022 11 29 09 3540-3548 |
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Time-limited Gramians Based Model Reduction Framework for 1-D and 2-D Systems |
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Time-limited Gramians Based Model Reduction Framework for 1-D and 2-D Systems |
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Imran, Muhammad |
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Imran, Muhammad Hamdani, Syeda Fizza |
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Elektronische Aufsätze |
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time-limited gramians based model reduction framework for 1-d and 2-d systems |
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Time-limited Gramians Based Model Reduction Framework for 1-D and 2-D Systems |
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Abstract Gawronski and Juang provide an unstable reduced-order model formulation without a priori error bounds for the original one- and two-dimensional models. Several strategies were put forth for the standard linear discrete-time one-dimensional models to guarantee the stability of the reduced-order model over a given time-intervals. These frameworks produce significant truncation mistakes and lack time-domain error-bound expressions. For discrete-time, two-dimensional Gramians models, there are no stability-preserving frameworks that the authors are aware of. This study suggests a Gramian-based model reduction strategy for discrete-time models. One- and two-dimensional discrete-time models can be employed with the framework. The suggested model reduction approach is applied using time-limited Gramians after the discrete-time two-dimensional causal recursive separable denominator models are split into two sub-models (two one-dimensional cascaded models). The framework ensures reduced-order model stability and offers time-domain a priori error-bound expressions for one- and two-dimensional models. Comparisons and numerical results demonstrate the usefulness of the proposed framework. © ICROS, KIEE and Springer 2022 |
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Abstract Gawronski and Juang provide an unstable reduced-order model formulation without a priori error bounds for the original one- and two-dimensional models. Several strategies were put forth for the standard linear discrete-time one-dimensional models to guarantee the stability of the reduced-order model over a given time-intervals. These frameworks produce significant truncation mistakes and lack time-domain error-bound expressions. For discrete-time, two-dimensional Gramians models, there are no stability-preserving frameworks that the authors are aware of. This study suggests a Gramian-based model reduction strategy for discrete-time models. One- and two-dimensional discrete-time models can be employed with the framework. The suggested model reduction approach is applied using time-limited Gramians after the discrete-time two-dimensional causal recursive separable denominator models are split into two sub-models (two one-dimensional cascaded models). The framework ensures reduced-order model stability and offers time-domain a priori error-bound expressions for one- and two-dimensional models. Comparisons and numerical results demonstrate the usefulness of the proposed framework. © ICROS, KIEE and Springer 2022 |
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Abstract Gawronski and Juang provide an unstable reduced-order model formulation without a priori error bounds for the original one- and two-dimensional models. Several strategies were put forth for the standard linear discrete-time one-dimensional models to guarantee the stability of the reduced-order model over a given time-intervals. These frameworks produce significant truncation mistakes and lack time-domain error-bound expressions. For discrete-time, two-dimensional Gramians models, there are no stability-preserving frameworks that the authors are aware of. This study suggests a Gramian-based model reduction strategy for discrete-time models. One- and two-dimensional discrete-time models can be employed with the framework. The suggested model reduction approach is applied using time-limited Gramians after the discrete-time two-dimensional causal recursive separable denominator models are split into two sub-models (two one-dimensional cascaded models). The framework ensures reduced-order model stability and offers time-domain a priori error-bound expressions for one- and two-dimensional models. Comparisons and numerical results demonstrate the usefulness of the proposed framework. © ICROS, KIEE and Springer 2022 |
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Time-limited Gramians Based Model Reduction Framework for 1-D and 2-D Systems |
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