Advertisement

Synchronization of Nonlinear Fractional-Order Systems by Means of PI\(^{r\alpha }\) Reduced Order Observer

  • Rafael Martínez-GuerraEmail author
  • Claudia Alejandra Pérez-Pinacho
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

The main contribution in this chapter is the synthesis of a new fractional-reduced-order observer for the synchronization problem in partially known nonlinear fractional-order systems, we propose a PI\(^{r \alpha }\) reduced-order observer for estimating the unknown state variables based on Fractional Algebraic Observability (FAO) property (a system’s copy is not necessary). This novel observer presents some advantages, for example, the norm of the estimation error, the time of convergence, and the performance of the PI\(^{r\alpha }\) reduced-order observer can be improved by the correct choice of the gains.

References

  1. 1.
    A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier B.V., 2006.CrossRefGoogle Scholar
  2. 2.
    R. Caponetto, G. Dongola, L. Fortuna and I. Petrás, Fractional order systems modeling and control applications, World Scientific, 2010.Google Scholar
  3. 3.
    A. Fradkov, Cybernetical physics: from control of chaos to Quantum control, Berlin: Springer, 2007.Google Scholar
  4. 4.
    C. Li and G. Chen, Chaos and hyperchaos in fractional-order Rössler equations, Physica A, vol. 341, pp. 55–61, 2004.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Rafael Martínez-Guerra
    • 1
    Email author
  • Claudia Alejandra Pérez-Pinacho
    • 1
  1. 1.Automatic ControlCINVESTAV-IPNMexico CityMexico

Personalised recommendations