Skip to main content
SpringerLink
Log in

To the Synthesis of Optimal Control Systems

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

The linear-quadratic optimal control problem subject to linear terminal constraints is considered. An optimal feedback control that is linear in the state variables is constructed.

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. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1983; Gordon and Breach, New York, 1986).

    Google Scholar 

  2. A. A. Fel’dbaum, Foundations of the Theory of Optimal Automatic Systems (Nauka, Moscow, 1966) [in Russian].

    Google Scholar 

  3. R. Kalman, “On the general theory of control systems,” in Proc. of the First Int. Congress on Automatic Control, London, 1960, pp. 481–493.

    Google Scholar 

  4. A. M. Letov, Mathematical Theory of Control Processes (Nauka, Moscow, 1981) [in Russian].

    Google Scholar 

  5. H. Kvakernaak and R. Sivan, Linear Optimal Control Systems (Wiley, New York, 1972; Mir, Moscow, 1977).

    Google Scholar 

  6. A. B. Kurzhanskii, “On the synthesis of controls based on actually available data,” Vestn. Mosk. Gos. Univ., Ser. 15, Vychisl. Mat. Kibern. Special Issue, 114–122 (2005).

    Google Scholar 

  7. R. Gabasov, F. M. Kirillova, and E. I. Poyasok, “Optimal Control of a Dynamic System with Multiple Uncertainty in the Initial State as Based on Imperfect Measurements of Input and Output Signals,” Comput. Math. Math. Phys. 52, 992–1008 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  8. L. Grüne and J. Pannek, Nonlinear Model Predictive Control: Theory and Algorithms, 2nd ed. (Springer, Cham, Switzerland, 2017).

    Book  MATH  Google Scholar 

  9. R. Gabasov and F. M. Kirillova, The Qualitative Theory of Optimal Processes (Nauka, Moscow, 1971; Dekker, New York, 1976).

    MATH  Google Scholar 

  10. B. Sh. Mordukhovich, “Existence of optimal controls,” in Itogi Nauki Tekh., Ser.: Modern Problems of Mathematics (VINITI, Moscow, 1976), Vol. 6, pp. 207–271.

    Google Scholar 

  11. R. Gabasov and F. M. Kirillova, Foundations of Dynamic Programming (Belarus. Gos. Univ., Minsk, 1975) [in Russian].

    MATH  Google Scholar 

  12. A. I. Kalinin and L. I. Lavrinovich, “Application of the perturbation method for the minimization of an integral quadratic functional on the trajectories of a quasilinear system,” J. Comput. Syst. Sci. Int. 53, 149–158 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  13. N. N. Krasovskii, Theory of Motion Control (Nauka, Moscow, 1968) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Belarussian State University, Minsk, 220030, Belarus

    A. I. Kalinin

Authors
  1. A. I. Kalinin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. I. Kalinin.

Additional information

Original Russian Text © A.I. Kalinin, 2018, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2018, Vol. 58, No. 3, pp. 397–402.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kalinin, A.I. To the Synthesis of Optimal Control Systems. Comput. Math. and Math. Phys. 58, 378–383 (2018). https://doi.org/10.1134/S0965542518030065

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542518030065

Keywords

Search

Navigation