State estimation for coupled reaction-diffusion PDE systems using modulating functions

Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossib...
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Autor*in:	Pumaricra Rojas, David [verfasserIn] Noack, Matti [verfasserIn] Reger, Johann - 1971- [verfasserIn] Pérez-Zúñiga, Gustavo [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Rechteinformationen:	Open Access Namensnennung 4.0 International ; CC BY 4.0

Übergeordnetes Werk:	Enthalten in: Sensors - Basel : MDPI, 2001, 22(2022), 13, Artikel-ID 5008, Seite 1-24
Übergeordnetes Werk:	volume:22 ; year:2022 ; number:13 ; elocationid:5008 ; pages:1-24

Links:	Volltext Volltext

DOI / URN:	10.3390/s22135008

Katalog-ID:	1810700809

Internformat


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allfields	10.3390/s22135008 doi (DE-627)1810700809 (DE-599)KXP1810700809 DE-627 ger DE-627 rda eng Pumaricra Rojas, David verfasserin aut State estimation for coupled reaction-diffusion PDE systems using modulating functions David Pumaricra Rojas, Matti Noack, Johann Reger and Gustavo Pérez-Zúñiga 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier DE-Ilm1 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossible to obtain full state information with physical sensors only. For this problem, observers are developed to estimate the state based on boundary measurements. The method presented applies the so-called modulating function method, relying on an orthonormal function basis representation. Auxiliary systems are generated from the original system by applying modulating functions and formulating annihilation conditions. It is extended by a decoupling matrix step. The calculated kernels are utilized for modulating the input and output signals over a receding time window to obtain the coefficients for the basis expansion for the desired state estimation. The developed algorithm and its real-time functionality are verified via simulation of an example system related to the dynamics of chemical tubular reactors and compared to the conventional backstepping observer. The method achieves a successful state reconstruction of the system while mitigating white noise induced by the sensor. Ultimately, the modulating function approach represents a solution for the distributed state estimation problem without solving a PDE online. DE-Ilm1 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ Noack, Matti verfasserin (DE-588)1298783550 (DE-627)1854652613 aut Reger, Johann 1971- verfasserin (DE-588)129394947 (DE-627)394707214 (DE-576)297639110 aut Pérez-Zúñiga, Gustavo verfasserin aut Enthalten in Sensors Basel : MDPI, 2001 22(2022), 13, Artikel-ID 5008, Seite 1-24 Online-Ressource (DE-627)331640910 (DE-600)2052857-7 (DE-576)281205191 1424-8220 nnns volume:22 year:2022 number:13 elocationid:5008 pages:1-24 https://doi.org/10.3390/s22135008 Verlag Resolving-System kostenfrei Volltext https://www.db-thueringen.de/receive/dbt_mods_00053161 Archivierung kostenfrei Volltext GBV_USEFLAG_U GBV_ILN_32 ISIL_DE-Ilm1 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2111 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 22 2022 13 5008 1-24 32 01 3400 4169412265 OpenAccess-GoldWay-ProcessingCharges x 18-07-22 2403 01 DE-LFER 4190965111 00 --%%-- --%%-- n --%%-- l01 22-09-22 2403 01 DE-LFER https://doi.org/10.3390/s22135008 32 00 DE-Ilm1 00 ilm <2022> 32 00 DE-Ilm1 01 (DE-627)479728933 Fachgebiet Regelungstechnik <Ilmenau> 32 00 DE-Ilm1 02 (DE-627)476645433 Verfasser 32 00 DE-Ilm1 03 (DE-627)476643090 Zeitschriftenaufsatz 32 00 DE-Ilm1 04 (DE-627)480733066 referiert 32 01 3400 OpenAccess-GoldWay-ProcessingCharges
spelling	10.3390/s22135008 doi (DE-627)1810700809 (DE-599)KXP1810700809 DE-627 ger DE-627 rda eng Pumaricra Rojas, David verfasserin aut State estimation for coupled reaction-diffusion PDE systems using modulating functions David Pumaricra Rojas, Matti Noack, Johann Reger and Gustavo Pérez-Zúñiga 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier DE-Ilm1 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossible to obtain full state information with physical sensors only. For this problem, observers are developed to estimate the state based on boundary measurements. The method presented applies the so-called modulating function method, relying on an orthonormal function basis representation. Auxiliary systems are generated from the original system by applying modulating functions and formulating annihilation conditions. It is extended by a decoupling matrix step. The calculated kernels are utilized for modulating the input and output signals over a receding time window to obtain the coefficients for the basis expansion for the desired state estimation. The developed algorithm and its real-time functionality are verified via simulation of an example system related to the dynamics of chemical tubular reactors and compared to the conventional backstepping observer. The method achieves a successful state reconstruction of the system while mitigating white noise induced by the sensor. Ultimately, the modulating function approach represents a solution for the distributed state estimation problem without solving a PDE online. DE-Ilm1 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ Noack, Matti verfasserin (DE-588)1298783550 (DE-627)1854652613 aut Reger, Johann 1971- verfasserin (DE-588)129394947 (DE-627)394707214 (DE-576)297639110 aut Pérez-Zúñiga, Gustavo verfasserin aut Enthalten in Sensors Basel : MDPI, 2001 22(2022), 13, Artikel-ID 5008, Seite 1-24 Online-Ressource (DE-627)331640910 (DE-600)2052857-7 (DE-576)281205191 1424-8220 nnns volume:22 year:2022 number:13 elocationid:5008 pages:1-24 https://doi.org/10.3390/s22135008 Verlag Resolving-System kostenfrei Volltext https://www.db-thueringen.de/receive/dbt_mods_00053161 Archivierung kostenfrei Volltext GBV_USEFLAG_U GBV_ILN_32 ISIL_DE-Ilm1 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2111 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 22 2022 13 5008 1-24 32 01 3400 4169412265 OpenAccess-GoldWay-ProcessingCharges x 18-07-22 2403 01 DE-LFER 4190965111 00 --%%-- --%%-- n --%%-- l01 22-09-22 2403 01 DE-LFER https://doi.org/10.3390/s22135008 32 00 DE-Ilm1 00 ilm <2022> 32 00 DE-Ilm1 01 (DE-627)479728933 Fachgebiet Regelungstechnik <Ilmenau> 32 00 DE-Ilm1 02 (DE-627)476645433 Verfasser 32 00 DE-Ilm1 03 (DE-627)476643090 Zeitschriftenaufsatz 32 00 DE-Ilm1 04 (DE-627)480733066 referiert 32 01 3400 OpenAccess-GoldWay-ProcessingCharges
allfields_unstemmed	10.3390/s22135008 doi (DE-627)1810700809 (DE-599)KXP1810700809 DE-627 ger DE-627 rda eng Pumaricra Rojas, David verfasserin aut State estimation for coupled reaction-diffusion PDE systems using modulating functions David Pumaricra Rojas, Matti Noack, Johann Reger and Gustavo Pérez-Zúñiga 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier DE-Ilm1 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossible to obtain full state information with physical sensors only. For this problem, observers are developed to estimate the state based on boundary measurements. The method presented applies the so-called modulating function method, relying on an orthonormal function basis representation. Auxiliary systems are generated from the original system by applying modulating functions and formulating annihilation conditions. It is extended by a decoupling matrix step. The calculated kernels are utilized for modulating the input and output signals over a receding time window to obtain the coefficients for the basis expansion for the desired state estimation. The developed algorithm and its real-time functionality are verified via simulation of an example system related to the dynamics of chemical tubular reactors and compared to the conventional backstepping observer. The method achieves a successful state reconstruction of the system while mitigating white noise induced by the sensor. Ultimately, the modulating function approach represents a solution for the distributed state estimation problem without solving a PDE online. DE-Ilm1 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ Noack, Matti verfasserin (DE-588)1298783550 (DE-627)1854652613 aut Reger, Johann 1971- verfasserin (DE-588)129394947 (DE-627)394707214 (DE-576)297639110 aut Pérez-Zúñiga, Gustavo verfasserin aut Enthalten in Sensors Basel : MDPI, 2001 22(2022), 13, Artikel-ID 5008, Seite 1-24 Online-Ressource (DE-627)331640910 (DE-600)2052857-7 (DE-576)281205191 1424-8220 nnns volume:22 year:2022 number:13 elocationid:5008 pages:1-24 https://doi.org/10.3390/s22135008 Verlag Resolving-System kostenfrei Volltext https://www.db-thueringen.de/receive/dbt_mods_00053161 Archivierung kostenfrei Volltext GBV_USEFLAG_U GBV_ILN_32 ISIL_DE-Ilm1 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2111 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 22 2022 13 5008 1-24 32 01 3400 4169412265 OpenAccess-GoldWay-ProcessingCharges x 18-07-22 2403 01 DE-LFER 4190965111 00 --%%-- --%%-- n --%%-- l01 22-09-22 2403 01 DE-LFER https://doi.org/10.3390/s22135008 32 00 DE-Ilm1 00 ilm <2022> 32 00 DE-Ilm1 01 (DE-627)479728933 Fachgebiet Regelungstechnik <Ilmenau> 32 00 DE-Ilm1 02 (DE-627)476645433 Verfasser 32 00 DE-Ilm1 03 (DE-627)476643090 Zeitschriftenaufsatz 32 00 DE-Ilm1 04 (DE-627)480733066 referiert 32 01 3400 OpenAccess-GoldWay-ProcessingCharges
allfieldsGer	10.3390/s22135008 doi (DE-627)1810700809 (DE-599)KXP1810700809 DE-627 ger DE-627 rda eng Pumaricra Rojas, David verfasserin aut State estimation for coupled reaction-diffusion PDE systems using modulating functions David Pumaricra Rojas, Matti Noack, Johann Reger and Gustavo Pérez-Zúñiga 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier DE-Ilm1 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossible to obtain full state information with physical sensors only. For this problem, observers are developed to estimate the state based on boundary measurements. The method presented applies the so-called modulating function method, relying on an orthonormal function basis representation. Auxiliary systems are generated from the original system by applying modulating functions and formulating annihilation conditions. It is extended by a decoupling matrix step. The calculated kernels are utilized for modulating the input and output signals over a receding time window to obtain the coefficients for the basis expansion for the desired state estimation. The developed algorithm and its real-time functionality are verified via simulation of an example system related to the dynamics of chemical tubular reactors and compared to the conventional backstepping observer. The method achieves a successful state reconstruction of the system while mitigating white noise induced by the sensor. Ultimately, the modulating function approach represents a solution for the distributed state estimation problem without solving a PDE online. DE-Ilm1 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ Noack, Matti verfasserin (DE-588)1298783550 (DE-627)1854652613 aut Reger, Johann 1971- verfasserin (DE-588)129394947 (DE-627)394707214 (DE-576)297639110 aut Pérez-Zúñiga, Gustavo verfasserin aut Enthalten in Sensors Basel : MDPI, 2001 22(2022), 13, Artikel-ID 5008, Seite 1-24 Online-Ressource (DE-627)331640910 (DE-600)2052857-7 (DE-576)281205191 1424-8220 nnns volume:22 year:2022 number:13 elocationid:5008 pages:1-24 https://doi.org/10.3390/s22135008 Verlag Resolving-System kostenfrei Volltext https://www.db-thueringen.de/receive/dbt_mods_00053161 Archivierung kostenfrei Volltext GBV_USEFLAG_U GBV_ILN_32 ISIL_DE-Ilm1 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2111 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 22 2022 13 5008 1-24 32 01 3400 4169412265 OpenAccess-GoldWay-ProcessingCharges x 18-07-22 2403 01 DE-LFER 4190965111 00 --%%-- --%%-- n --%%-- l01 22-09-22 2403 01 DE-LFER https://doi.org/10.3390/s22135008 32 00 DE-Ilm1 00 ilm <2022> 32 00 DE-Ilm1 01 (DE-627)479728933 Fachgebiet Regelungstechnik <Ilmenau> 32 00 DE-Ilm1 02 (DE-627)476645433 Verfasser 32 00 DE-Ilm1 03 (DE-627)476643090 Zeitschriftenaufsatz 32 00 DE-Ilm1 04 (DE-627)480733066 referiert 32 01 3400 OpenAccess-GoldWay-ProcessingCharges
allfieldsSound	10.3390/s22135008 doi (DE-627)1810700809 (DE-599)KXP1810700809 DE-627 ger DE-627 rda eng Pumaricra Rojas, David verfasserin aut State estimation for coupled reaction-diffusion PDE systems using modulating functions David Pumaricra Rojas, Matti Noack, Johann Reger and Gustavo Pérez-Zúñiga 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier DE-Ilm1 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossible to obtain full state information with physical sensors only. For this problem, observers are developed to estimate the state based on boundary measurements. The method presented applies the so-called modulating function method, relying on an orthonormal function basis representation. Auxiliary systems are generated from the original system by applying modulating functions and formulating annihilation conditions. It is extended by a decoupling matrix step. The calculated kernels are utilized for modulating the input and output signals over a receding time window to obtain the coefficients for the basis expansion for the desired state estimation. The developed algorithm and its real-time functionality are verified via simulation of an example system related to the dynamics of chemical tubular reactors and compared to the conventional backstepping observer. The method achieves a successful state reconstruction of the system while mitigating white noise induced by the sensor. Ultimately, the modulating function approach represents a solution for the distributed state estimation problem without solving a PDE online. DE-Ilm1 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ Noack, Matti verfasserin (DE-588)1298783550 (DE-627)1854652613 aut Reger, Johann 1971- verfasserin (DE-588)129394947 (DE-627)394707214 (DE-576)297639110 aut Pérez-Zúñiga, Gustavo verfasserin aut Enthalten in Sensors Basel : MDPI, 2001 22(2022), 13, Artikel-ID 5008, Seite 1-24 Online-Ressource (DE-627)331640910 (DE-600)2052857-7 (DE-576)281205191 1424-8220 nnns volume:22 year:2022 number:13 elocationid:5008 pages:1-24 https://doi.org/10.3390/s22135008 Verlag Resolving-System kostenfrei Volltext https://www.db-thueringen.de/receive/dbt_mods_00053161 Archivierung kostenfrei Volltext GBV_USEFLAG_U GBV_ILN_32 ISIL_DE-Ilm1 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2111 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 22 2022 13 5008 1-24 32 01 3400 4169412265 OpenAccess-GoldWay-ProcessingCharges x 18-07-22 2403 01 DE-LFER 4190965111 00 --%%-- --%%-- n --%%-- l01 22-09-22 2403 01 DE-LFER https://doi.org/10.3390/s22135008 32 00 DE-Ilm1 00 ilm <2022> 32 00 DE-Ilm1 01 (DE-627)479728933 Fachgebiet Regelungstechnik <Ilmenau> 32 00 DE-Ilm1 02 (DE-627)476645433 Verfasser 32 00 DE-Ilm1 03 (DE-627)476643090 Zeitschriftenaufsatz 32 00 DE-Ilm1 04 (DE-627)480733066 referiert 32 01 3400 OpenAccess-GoldWay-ProcessingCharges
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authorswithroles_txt_mv	Pumaricra Rojas, David @@aut@@ Noack, Matti @@aut@@ Reger, Johann @@aut@@ Pérez-Zúñiga, Gustavo @@aut@@
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spellingShingle	Pumaricra Rojas, David 32 ilm <2022> 32 Fachgebiet Regelungstechnik <Ilmenau> 32 Verfasser 32 Zeitschriftenaufsatz 32 referiert State estimation for coupled reaction-diffusion PDE systems using modulating functions
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title	State estimation for coupled reaction-diffusion PDE systems using modulating functions
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title_full	State estimation for coupled reaction-diffusion PDE systems using modulating functions David Pumaricra Rojas, Matti Noack, Johann Reger and Gustavo Pérez-Zúñiga
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title_sort	state estimation for coupled reaction-diffusion pde systems using modulating functions
title_auth	State estimation for coupled reaction-diffusion PDE systems using modulating functions
abstract	Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossible to obtain full state information with physical sensors only. For this problem, observers are developed to estimate the state based on boundary measurements. The method presented applies the so-called modulating function method, relying on an orthonormal function basis representation. Auxiliary systems are generated from the original system by applying modulating functions and formulating annihilation conditions. It is extended by a decoupling matrix step. The calculated kernels are utilized for modulating the input and output signals over a receding time window to obtain the coefficients for the basis expansion for the desired state estimation. The developed algorithm and its real-time functionality are verified via simulation of an example system related to the dynamics of chemical tubular reactors and compared to the conventional backstepping observer. The method achieves a successful state reconstruction of the system while mitigating white noise induced by the sensor. Ultimately, the modulating function approach represents a solution for the distributed state estimation problem without solving a PDE online.
abstractGer	Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossible to obtain full state information with physical sensors only. For this problem, observers are developed to estimate the state based on boundary measurements. The method presented applies the so-called modulating function method, relying on an orthonormal function basis representation. Auxiliary systems are generated from the original system by applying modulating functions and formulating annihilation conditions. It is extended by a decoupling matrix step. The calculated kernels are utilized for modulating the input and output signals over a receding time window to obtain the coefficients for the basis expansion for the desired state estimation. The developed algorithm and its real-time functionality are verified via simulation of an example system related to the dynamics of chemical tubular reactors and compared to the conventional backstepping observer. The method achieves a successful state reconstruction of the system while mitigating white noise induced by the sensor. Ultimately, the modulating function approach represents a solution for the distributed state estimation problem without solving a PDE online.
abstract_unstemmed	Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossible to obtain full state information with physical sensors only. For this problem, observers are developed to estimate the state based on boundary measurements. The method presented applies the so-called modulating function method, relying on an orthonormal function basis representation. Auxiliary systems are generated from the original system by applying modulating functions and formulating annihilation conditions. It is extended by a decoupling matrix step. The calculated kernels are utilized for modulating the input and output signals over a receding time window to obtain the coefficients for the basis expansion for the desired state estimation. The developed algorithm and its real-time functionality are verified via simulation of an example system related to the dynamics of chemical tubular reactors and compared to the conventional backstepping observer. The method achieves a successful state reconstruction of the system while mitigating white noise induced by the sensor. Ultimately, the modulating function approach represents a solution for the distributed state estimation problem without solving a PDE online.
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title_short	State estimation for coupled reaction-diffusion PDE systems using modulating functions
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State estimation for coupled reaction-diffusion PDE systems using modulating functions

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