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The Journal of the Astronautical Sciences

, Volume 57, Issue 1–2, pp 261–273 | Cite as

Generalized Bilinear System Identification

  • Jer-Nan Juang
Article

Abstract

A novel method is presented for identification of a bilinear system generalized to include higher-order input coupling terms. It derives from an existing method for identification of a continuous-time bilinear system. The method first generates a set of pulse responses from a constant input over a sample period for identification of the state matrix, the output matrix, and the direct transmission matrix. The method then produces another set of pulse responses with the same constant input over varying sample periods for identification of the input matrix and the coefficient matrices associated with the coupling terms between the state and the inputs. A simple example is given to illustrate the concept of the identification method.

Keywords

Input Matrix Output Matrix State Matrix Pulse Response Constant Input 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Bruni, C, Dipillo, G., and Koch, G. “On the Mathematical Models of Bilinear Systems,” Ricerche Di Automatica, Vol. 2, No. 1, 1971, pp. 11–26.Google Scholar
  2. [2]
    Bruni, C, Dipillo, G., and Koch, G. “Bilinear Systems: An Appealing Class of Nearly Linear Systems in Theory and Application,” IEEE Transactions on Automatic Control, AC-19, 1974, pp. 334-348.Google Scholar
  3. [3]
    Mohler, R. R. and Kolodziej, W. J. “An Overview of Bilinear System Theory and Applications,” IEEE Transactions on Systems, Man and Cybernetics, SMC-10, 1980, pp. 683-688.Google Scholar
  4. [4]
    Mohler, R.R. Nonlinear Systems: Applications to Bilinear Control, Vol. 2, Prentice-Hall, New Jersey, 1991.Google Scholar
  5. [5]
    Elliott, D.L. “Bilinear Systems,” in Encyclopedia of Electrical Engineering, Vol. II John Webster (ed.), John Wiley and Sons, New York, 1999, pp. 308–323.Google Scholar
  6. [6]
    Rugh, W.J. Nonlinear System Theory: The Volterra/Wiener Approach, The Johns Hopkins University Press, Baltimore, 1981.MATHGoogle Scholar
  7. [7]
    Heinrich, R., Neel, B. G., and Rapoport, T. T. “Mathematical Models of Protein Kinase Signal Transduction,” Molecular Cell, Vol. 9, No. 5, 2002, pp. 957–970.CrossRefGoogle Scholar
  8. [8]
    Sontag, E. D. and Chaves, E. “Exact computation of Amplification for a Class of Nonlinear Systems Arising from Cellular Signaling Pathways,” Automatica, Vol. 42, No. 11, 2006, pp. 1987–1992.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    Juang, J.-N. Applied System Identification, Prentice Hall, New Jersey, 1994.MATHGoogle Scholar
  10. [10]
    Juang, J.-N. and Phan, M. Q. Identification and Control of Mechanical Systems, Cambridge University Press, New York, 2001.CrossRefGoogle Scholar
  11. [11]
    Juang, J.-N. “Continuous-Time Bilinear System Identification,” Nonlinear Dynamics, Kluwer Academic Publishers, Special Issue, Vol. 39, Nos. 1–2, (January I–II2005), pp. 79–94.MathSciNetMATHCrossRefGoogle Scholar
  12. [12]
    Sontag, E. D., Wang, Y, and Megretski, A. “Input Classes for Identification of Bilinear Systems,” IEEE Transactions on Automatic Control, 54, 2009, pp. 195–207.MathSciNetCrossRefGoogle Scholar
  13. [13]
    Rangarathan, V, Jha, A. N., and Rajamani, V. S. “Recursive Estimation Algorithms for Bilinear and Nonlinear Systems Using a Polynomial Approach,” International Journal of Control, Vol. 44, No. 2, 1986, pp. 419–426.CrossRefGoogle Scholar
  14. [14]
    Brewer, J. “Bilinear Equations in Ecology,” in Systems and Control Encyclopedia: Theory, Technology, Applications, Madan G. Singh (Ed.), Pergamon Press, Oxford, Volume 1, 1987, pp. 414–417.Google Scholar
  15. [15]
    Aganovic, Z. and Gajic, Z. “The Successive Approximation Procedure for Finite-Time Optimal Control of Bilinear System,” IEEE Transactions on Automatic Control, Vol. 42, 1994, pp. 1932–1935.MathSciNetCrossRefGoogle Scholar

Copyright information

© Amarican Astronautical Society, Inc 2009

Authors and Affiliations

  • Jer-Nan Juang
    • 1
    • 2
    • 3
    • 4
    • 5
  1. 1.National Applied Research LaboratoriesTaipeiTaiwan
  2. 2.National Chung-Hsing UniversityTai-ChungTaiwan
  3. 3.Texas A&M University
  4. 4.National Taiwan UniversityTaipeiTaiwan
  5. 5.National Cheng-Kung UniversityTainanTaiwan

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