A Luenberger-Like Observer for Multistable Kapitaniak Chaotic System
The objective of this paper is to estimate the unmeasurable variables of a multistable chaotic system using a Luenberger-like observer. First, the observability of the chaotic system is analyzed. Next, a Lipschitz constant is determined on the attractor of this system. Then, the methodology proposed...
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| Main Authors: | , , , , , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/9531431 |
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| author | J. Humberto Pérez-Cruz Jacobo Marcos Allende Peña Christian Nwachioma Jose de Jesus Rubio Jaime Pacheco Jesus Alberto Meda-Campaña David Ávila-González Olivia Guevara Galindo Ignacio Adrian Romero Salvador Isidro Belmonte Jiménez |
| author_facet | J. Humberto Pérez-Cruz Jacobo Marcos Allende Peña Christian Nwachioma Jose de Jesus Rubio Jaime Pacheco Jesus Alberto Meda-Campaña David Ávila-González Olivia Guevara Galindo Ignacio Adrian Romero Salvador Isidro Belmonte Jiménez |
| author_sort | J. Humberto Pérez-Cruz |
| collection | DOAJ |
| description | The objective of this paper is to estimate the unmeasurable variables of a multistable chaotic system using a Luenberger-like observer. First, the observability of the chaotic system is analyzed. Next, a Lipschitz constant is determined on the attractor of this system. Then, the methodology proposed by Raghavan and the result proposed by Thau are used to try to find an observer. Both attempts are unsuccessful. In spite of this, a Luenberger-like observer can still be used based on a proposed gain. The performance of this observer is tested by numerical simulation showing the convergence to zero of the estimation error. Finally, the chaotic system and its observer are implemented using 32-bit microcontrollers. The experimental results confirm good agreement between the responses of the implemented and simulated observers. |
| format | Article |
| id | doaj-art-cda03280e62f47d08fcb0f29f8966e08 |
| institution | DOAJ |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-cda03280e62f47d08fcb0f29f8966e082025-08-20T03:19:38ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/95314319531431A Luenberger-Like Observer for Multistable Kapitaniak Chaotic SystemJ. Humberto Pérez-Cruz0Jacobo Marcos Allende Peña1Christian Nwachioma2Jose de Jesus Rubio3Jaime Pacheco4Jesus Alberto Meda-Campaña5David Ávila-González6Olivia Guevara Galindo7Ignacio Adrian Romero8Salvador Isidro Belmonte Jiménez9SEPI, ESIME Azcapotzalco, Instituto Politécnico Nacional, Ciudad de México 02250, MexicoSEPI, ESIME Azcapotzalco, Instituto Politécnico Nacional, Ciudad de México 02250, MexicoSEPI, ESIME Azcapotzalco, Instituto Politécnico Nacional, Ciudad de México 02250, MexicoSEPI, ESIME Azcapotzalco, Instituto Politécnico Nacional, Ciudad de México 02250, MexicoSEPI, ESIME Azcapotzalco, Instituto Politécnico Nacional, Ciudad de México 02250, MexicoSEPI, ESIME Zacatenco, Instituto Politécnico Nacional, Ciudad de México 07738, MexicoSEPI, ESIME Azcapotzalco, Instituto Politécnico Nacional, Ciudad de México 02250, MexicoSEPI, ESIME Azcapotzalco, Instituto Politécnico Nacional, Ciudad de México 02250, MexicoSEPI, ESIME Azcapotzalco, Instituto Politécnico Nacional, Ciudad de México 02250, MexicoCIIDIR-Oaxaca, Instituto Politécnico Nacional, Oaxaca 71230, MexicoThe objective of this paper is to estimate the unmeasurable variables of a multistable chaotic system using a Luenberger-like observer. First, the observability of the chaotic system is analyzed. Next, a Lipschitz constant is determined on the attractor of this system. Then, the methodology proposed by Raghavan and the result proposed by Thau are used to try to find an observer. Both attempts are unsuccessful. In spite of this, a Luenberger-like observer can still be used based on a proposed gain. The performance of this observer is tested by numerical simulation showing the convergence to zero of the estimation error. Finally, the chaotic system and its observer are implemented using 32-bit microcontrollers. The experimental results confirm good agreement between the responses of the implemented and simulated observers.http://dx.doi.org/10.1155/2020/9531431 |
| spellingShingle | J. Humberto Pérez-Cruz Jacobo Marcos Allende Peña Christian Nwachioma Jose de Jesus Rubio Jaime Pacheco Jesus Alberto Meda-Campaña David Ávila-González Olivia Guevara Galindo Ignacio Adrian Romero Salvador Isidro Belmonte Jiménez A Luenberger-Like Observer for Multistable Kapitaniak Chaotic System Complexity |
| title | A Luenberger-Like Observer for Multistable Kapitaniak Chaotic System |
| title_full | A Luenberger-Like Observer for Multistable Kapitaniak Chaotic System |
| title_fullStr | A Luenberger-Like Observer for Multistable Kapitaniak Chaotic System |
| title_full_unstemmed | A Luenberger-Like Observer for Multistable Kapitaniak Chaotic System |
| title_short | A Luenberger-Like Observer for Multistable Kapitaniak Chaotic System |
| title_sort | luenberger like observer for multistable kapitaniak chaotic system |
| url | http://dx.doi.org/10.1155/2020/9531431 |
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