Skip to main content
SpringerLink
Log in

A computational solution for a Matrix Riccati differential equation

  • Published:
Numerische Mathematik Aims and scope Submit manuscript

Summary

This paper is concerned with the solution of the finite time Riccati equation. The solution to the Riccati equation is given in terms of the partition of the transition matrix. Matrix differential equations for the partition of the transition matrix are derived and are solved using computational methods. Examples illustrating the method are presented and the computational algorithms are given.

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. Breakwell, J.V., Ho, Y.C.: On the Conjugate Point Condition for the Control Problem. Int. J. Eng. Sci.2, 565–579 (1964)

    Article  Google Scholar 

  2. Frazer, R.A., Duncan, W.J., Collar, A.R.: Elementary Matrices. Cambridge University Press 1938

  3. Friedland, B.: On Solution of the Riccati Equation in Optimization Problem. IEEE Trans. on Automatic Control, pp. 303–304, 1967

  4. Kalman, R.E.: Contribution to the Theory of Optimal Control. Bol. Soc. Mat. Mexicana5, 102–119 (1960)

    Google Scholar 

  5. Kalman, R.E., Englar, T.S.: A User's Manual for the Automatic Synthesis Program (Program C). NASA CR-475, 1966

  6. Kleinman, D.L.: On the Linear Regulator Problem and the Matrix Riccati Equation, M.I.T. Report ESL-R271, 1966

  7. Lee, I.: Optimal Trajectories, Guidance and Conjugate Points. Information and Control8, 589–606 (1965)

    Article  Google Scholar 

  8. Macfarlane, A.K.: An Eigenvector Solution of the Optimal Linear Regulator Problem. J. of Electronics and Control14, 643–654 (1963)

    Google Scholar 

  9. Razzaghi, M.: Solution of the matrix Riccati Equation in Optimal Control. (To appear in J. of Information Sciences)

  10. Razzaghi, M., Jamshidi, M.: On the Jacobi Conditions for Control Problems with Input Delay. Proc. IEE122, 1313–1315 (1975)

    Google Scholar 

  11. Shubert, H.A.: An Analytic Solution for an Algebraic Matrix Riccati Equation. IEEE. Trans. On Automatic Control AC-19, 255–256 (1974)

    Article  Google Scholar 

  12. Vidyasgar, M.: A Novel Method of Evaluatinge Al in Closed Form. IEEE Trans. AC-15, 600–601 (1970)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Science and Computer, Tehran Polytechnic, Tehran, Iran

    M. Razzaghi

Authors
  1. M. Razzaghi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Razzaghi, M. A computational solution for a Matrix Riccati differential equation. Numer. Math. 32, 271–279 (1979). https://doi.org/10.1007/BF01397001

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01397001

Subject Classifications

Search

Navigation