International Journal of Theoretical Physics

, Volume 45, Issue 11, pp 2084–2092 | Cite as

Supersymmetric Free-Damped Oscillators: Adaptive Observer Estimation of the Riccati Parameter

  • V. Ibarra-Junquera
  • H. C. Rosu
  • O. Cornejo-Pérez


A supersymmetric class of free damped oscillators with three parameters has been obtained in 1998 by Rosu and Reyes through the factorization of the Newton equation. The supplementary parameter is the integration constant of the general Riccati solution. The estimation of the latter parameter is performed here by employing the recent adaptive observer scheme of Besançon et al., but applied in a nonstandard form in which a time-varying quantity containing the unknown Riccati parameter is estimated first. Results of computer simulations are presented to illustrate the good feasibility of this approach for a case in which the estimation is not easily accomplished by other means.


three-parameter free-damped oscillator adaptive observer Riccati parameter 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Besançon, G., Zhang, O., and Hammouri, H. (2004). High gain observer based state and parameter estimation in nonlinear systems, paper 204 in the 6th Int. Fed. Aut. Ctrl. Symposium, Stuttgart Symposium on Nonlinear Control Systems, available at
  2. Gauthier, J. P., Hammouri, H., and Othaman, S. (1992). IEEE Transactions of Automatic Control 37, 875.MATHCrossRefGoogle Scholar
  3. Khalil, H. K. (1992). Nonlinear Systems, Prentice-Hall, Inc.Google Scholar
  4. Marino, R. (1990). IEEE Transactions of Automatic Control 35, 1054.MATHMathSciNetCrossRefGoogle Scholar
  5. Marino, R. and Tomei, P. (1995). IEEE Transactions of Automatic Control 40, 1300.MATHMathSciNetCrossRefGoogle Scholar
  6. Rosu, H. C. and Espinoza, P. B. (2001). Physical Review E 63, 037603 .CrossRefADSGoogle Scholar
  7. Rosu, H. C. and Reyes, M. A. (1998). Physical Review E 57, 4850.CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. Ibarra-Junquera
    • 1
  • H. C. Rosu
    • 2
  • O. Cornejo-Pérez
    • 2
  1. 1.Faculty of Chemical SciencesUniversity of ColimaCoquimatlánMexico
  2. 2.Potosinian Institute of Science and Technology (IPICyT)San Luis PotosíMexico

Personalised recommendations