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Picard Discretization of Nonlinear Systems: Symbolic or Numeric Implementation?

  • J. Rodríguez-Millán
  • A. Patete
  • C. González
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4739)

Abstract

In this paper we report the numeric implementation of previously proposed symbolic non-standard discretization methods for nonlinear dynamical control systems. We discuss the advantages and disadvantages of both symbolic and numeric implementations, and illustrate them through their applications to case studies.

Keywords

Linear control systems nonlinear control systems symbolic discretization numeric integration hybrid computation 

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References

  1. 1.
    Oppenheim, A., Willsky, A., Hamid, S.: Signals and Systems, 2nd edn. Prentice-Hall, Englewood-Cliffs (1997)Google Scholar
  2. 2.
    Isermann, R.: Digital Control Systems, Fundamentals, Deterministic Control, vol. 1. Springer, Berlin (1989)Google Scholar
  3. 3.
    Rodríguez-Millán, J.: Sistemas Dinámicos (E-book), Universidad de Los Andes, Mérida (to appear, 2007)Google Scholar
  4. 4.
    Coddington, E., Levinson, N.: Theory of Ordinary Differential Equations. Tata McGraw-Hill Publishing Co, New Delhi (1977)Google Scholar
  5. 5.
    Rodríguez-Millán, J., González, C.: Three Mathematica Supported Proposals for the Discretization of Nonlinear Control Systems, Nonlinear Analysis 63, e617-628 (2005), Available online at http://www.sciencedirect.com
  6. 6.
    Rodríguez-Millán, J., González, C., Patete, A.: Analysis, Synthesis and Mimetization of Nonlinear Dynamical Control Systems Using Mathematica. In: Quesada-Arencibia, A., Moreno-Díaz, j.R., Rodríguez, J. (eds.) Cast and Tools for Robotics, Vehicular and Communication Systems, Eurocast 2005 - Extended Abstracts. IUCTC Universidad de Las Palmas de Gran Canarias, Las Palmas, pp. 316–320 (2005)Google Scholar
  7. 7.
    Rodríguez-Millán, J., González, C., Patete, A.: Improved Non-standard Discretization Methods for Nonlinear Dynamical Control Systems. In: Moreno Díaz, R., Pichler, F., Quesada Arencibia, A. (eds.) EUROCAST 2005. LNCS, vol. 3643, Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Wolfram, S.: The Mathematica Book, 5th edn. Wolfram Media, USA (2003)Google Scholar
  9. 9.
    Patete, A.: Discretization of Nonlinear Systems, Case Study: A Cascade of Two Tanks, Universidad de Los Andes, Postgrado de Control y Automatización, Mérida (2007)Google Scholar
  10. 10.
    Patete, A.: Discretization of Nonlinear Systems, Case Study: Two Pendulum Mounted on a Chariot, Universidad de Los Andes, Postgrado de Control y Automatización, Mérida (2007)Google Scholar
  11. 11.
    Patete, A., Discretization of Nonlinear Systems, Case Study: The Centrifugal Pendulum, Universidad de Los Andes, Postgrado de Control y Automatización, Mérida (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • J. Rodríguez-Millán
    • 1
  • A. Patete
    • 2
  • C. González
    • 3
  1. 1.Universidad de Los Andes - Facultad de Ingeniería - Dept. Sistemas de Control, Apartado 11 - La Hechicera, Mérida 5101-AVenezuela
  2. 2.Tokyo Denki University, Advanced Science and Technology, Ishisaka, Hatoyama, Hiki-gun, Saitama 350-0394Japan
  3. 3.Universidad Carlos III, Dept. de Sistemas y Automática, Laboratorio de Robótica, Av. De la Universidad 30, Leganés, Madrid 28911Spain

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