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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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2020, Vol.2020 (2020), p.1-12
Main Authors: Belmonte Jiménez, Salvador Isidro, Adrian Romero, Ignacio, Ávila-González, David, Meda-Campaña, Jesús Alberto, Pacheco, Jaime, Rubio, José de Jesús, Nwachioma, Christian, Allende Peña, Jacobo Marcos, Pérez-Cruz, J. Humberto, Guevara Galindo, Olivia
Format: Article
Language:English
Subjects:
Chaos theory
Computer simulation
Eigenvalues
Equilibrium
Microcontrollers
Numerical analysis
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Summary: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.
ISSN:1076-2787
1099-0526
DOI:10.1155/2020/9531431