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A Luenberger-Like Observer for Multistable Kapitaniak Chaotic System

Author

Listed:
  • 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

Abstract

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.

Suggested Citation

  • 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 A, 2020. "A Luenberger-Like Observer for Multistable Kapitaniak Chaotic System," Complexity, Hindawi, vol. 2020, pages 1-12, July.
    • Handle: RePEc:hin:complx:9531431
    DOI: 10.1155/2020/9531431
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    Cited by:

    1. Nwachioma, Christian & Pérez-Cruz, J. Humberto, 2021. "Analysis of a new chaotic system, electronic realization and use in navigation of differential drive mobile robot," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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