Skip to main content
SpringerLink
Log in

Optimal control of linear time-varying systems via Fourier series

  • Technical Note
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

The optimal control of linear time-varying systems with quadratic cost functional is obtained by Fourier series approximation. The properties of Fourier series are first briefly presented and the operational matrix of backward integration together with the product operational matrix are utilized to reduce the optimal control problem to a set of simultaneous linear algebraic equations. An illustrative example is included to demonstrate the validity and applicability of the technique.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chen, C. F., andHsiao, C. H.,Design of Piecewise Constant Gains for Optimal Control via Walsh Functions, IEEE Transactions on Automatic Control, Vol. AC-20, pp. 596–603, 1975.

    Google Scholar 

  2. Chen, W. L., andShih, Y. P.,Analysis and Optimal Control of Time-Varying Linear Systems via Walsh Functions, International Journal of Control, Vol. 27, pp. 917–932, 1978.

    Google Scholar 

  3. Hsu, N. S., andCheng, B.,Analysis and Optimal Control of Time-Varying Linear Systems via Block-Pulse Functions, International Journal of Control, Vol. 33, pp. 1107–1122, 1981.

    Google Scholar 

  4. Hwang, C., andShih, Y. P.,Optimal Control of Delay Systems via Block-Pulse Functions, Journal of Optimization Theory and Applications, Vol. 45, pp. 101–112, 1985.

    Google Scholar 

  5. Clement, P. R.,Laguerre Functions in Signal Analysis and Parameter Identification, Journal of the Franklin Institute, Vol. 313, pp. 85–95, 1982.

    Google Scholar 

  6. Hwang, C., andShih, Y. P.,Laguerre Series Direct Method for Variational Problems, Journal of Optimization Theory and Applications, Vol. 39, pp. 143–149, 1983.

    Google Scholar 

  7. Hwang, C., andChen, M. Y.,Analysis and Optimal Control of Time-Varying Linear Systems via Shifted Legendre Polynomials, International Journal of Control, Vol. 41, pp. 1317–1330, 1985.

    Google Scholar 

  8. Wang, M. L., andChang, R. Y.,Optimal Control of Lumped-Parameter Systems via Shifted Legendre Polynomial Approximation, Journal of Optimization Theory and Applications, Vol. 45, pp. 313–324, 1985.

    Google Scholar 

  9. Paraskevopoulos, P. N.,Chebyshev Series Approach to System Identification Analysis and Optimal Control, Journal of the Franklin Institute, Vol. 316, pp. 135–157, 1983.

    Google Scholar 

  10. Chou, J. H., andHorng, I. R.,Application of Chebyshev Polynomials to the Optimal Control of Time-Varying Linear Systems, International Journal of Control, Vol. 41, pp. 135–144, 1985.

    Google Scholar 

  11. Mouroutsos, S. G., andSparis, P. D.,Taylor Series Approach to System Identification, Analysis, and Optimal Control, Journal of the Franklin Institute, Vol. 319, pp. 359–371, 1985.

    Google Scholar 

  12. Razzaghi, M., andRazzaghi, M.,Taylor Series Direct Method for Variational Problems, Journal of the Franklin Institute, Vol. 325, pp. 125–131, 1988.

    Google Scholar 

  13. Paraskevopoulos, P. N., Sparis, P. D., andMouroutsos, S. G.,The Fourier Series Operational Matrix of Integration, International Journal of Systems Science, Vol. 16, pp. 171–176, 1985.

    Google Scholar 

  14. Razzaghi, M., andRazzaghi, M.,Fourier Series Direct Method for Variational Problems, International Journal of Control, Vol. 48, pp. 887–895, 1988.

    Google Scholar 

  15. Kleinman, D. L., Fortmann, T., andAthans, M.,On the Design of Linear Systems with Piecewise-Constant Feedback Gains, IEEE Transactions on Automatic Control, Vol. AC-13, pp. 354–361, 1968.

    Google Scholar 

  16. Kalman, R. E., andEnglar, T. S.,A User's Manual for the Automatic Synthesis Program (Program C), NASA Contractor Report No. CR–475, 1966.

  17. Razzaghi, M.,A Computational Solution for a Matrix Riccati Differential Equation, Numerische Mathematik, Vol. 32, pp. 271–279, 1979.

    Google Scholar 

  18. Razzaghi, M.,A Computational Solution for the Matrix Riccati Equation Using Laplace Transforms, International Journal of Computer Mathematics, Vol. 11, pp. 297–304, 1982.

    Google Scholar 

  19. Bellman, R.,Introduction to Matrix Analysis, McGraw-Hill, New York, New York, 1970.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi

    M. Razzaghi (Professor)

Authors
  1. M. Razzaghi
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by D. G. Luenberger

Rights and permissions

Reprints and permissions

About this article

Cite this article

Razzaghi, M. Optimal control of linear time-varying systems via Fourier series. J Optim Theory Appl 65, 375–384 (1990). https://doi.org/10.1007/BF01102353

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01102353

Key Words

Search

Navigation