Skip to main content
Log in

Optimization of linear discrete systems in the integral logarithmic index

  • Linear Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

The problem of designing a linear discrete system by the criterion of differential entropy per time unit of the stabilized variable in the steady-state mode was formulated and resolved. Independence of the optimal controller of the spectral composition of perturbation was established. In the class of stabilizing feedbacks, a full family of optimal controllers was constructed for the plant with a transfer function fixed in control.

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

Access this article

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. Bonjorno Jabr, H. and Youla, D., Modern Wiener-Hopf Design of Optimal Controllers. Part 1: The Single Input Case, IEEE Trans. Automat. Control, 1976, vol. 21, pp. 3–148.

    Article  Google Scholar 

  2. Vidyasagar, M., Control System Synthesis: A Factorization Approach, Cambridge: MIT Press, 1985.

    MATH  Google Scholar 

  3. Rozanov, Yu.A., Statsionarnye sluchainye protsessy (Stationary Random Processes), Moscow: Nauka, 1990.

    Google Scholar 

  4. Tsypkin, Ya.Z., Sliding Approximation and Principle of Absorption, Dokl. Ross. Akad. Nauk, 1997, vol. 357, no. 6, pp. 750–752.

    MathSciNet  Google Scholar 

  5. Bunich, A.L., Degenerate Linear-Quadratic Problem of Discrete Plant Control under Uncertainty, Autom. Remote Control, 2011, vol. 72, no. 11, pp. 2351–2363.

    Article  MATH  MathSciNet  Google Scholar 

  6. Zhou, K., Doyle, J.C., and Glover, K., Robust and Optimal Control, Upper Saddle River: Prentice Hall, 1996.

    MATH  Google Scholar 

  7. Emel’yanov, S.V. and Korovin, S.K., Novye tipy obratnoi svyazi. Upravlenie pri neopredelennosti (New Types of Feedback. Control under Uncertainty), Moscow: Nauka, 1997.

    Google Scholar 

  8. Matveev, A.S. and Yakubovich, V.A., Nonconvex Problems of Global Optinmization in the Control Theory, in Itogi Nauki Tekhn., Ser. Sovr. Mat. Prilozhen. Thematical Reviews, Moscow: VINITI, 1998, vol. 60, pp. 128–175.

    Google Scholar 

  9. Kolmogorov, A.N., Information Transmission Theory in Teoriya informatsii i teoriya algoritmov (Information Theory and Theory of Algorithms), Moscow: Nauka, 1987.

    MATH  Google Scholar 

  10. Hoffman, K., Banach Spaces of Analytic Functions, Englewood Cliffs: Prentice Hall, 1962. Translated under the title Banakhovy prostranstva analiticheskikh funktsii’, Moscow: Inostrannaya Literatura, 1963.

    MATH  Google Scholar 

  11. Vladimirov, I.G., Kurdykov, A.P., and Semyonov, A.V., Asymptotics of Anisotropic Norms of Stationary Linear Systems, Autom. Remote Control, 1999, vol. 60, no. 3, part 1, pp. 359–366.

    MATH  Google Scholar 

  12. Denisenko, V., PID-controllers: Problems of Implementation. Part 2, Sovrem. Tekhnol. Avtomatiz., 2008, no. 1, pp. 86–99.

    Google Scholar 

  13. Viswanadham, N. and Vidyasagar, M., Algebraic Design Techniques for Reliable Stabilization, IEEE Trans. Automat. Control, 1982, vol. 27, no. 5, pp. 1085–1095.

    Article  MATH  MathSciNet  Google Scholar 

  14. Yakubovich, V.A., Optimization and Invariance of Linear Stationary Control Systems, Autom. Remote Control, 1984, vol. 45, no. 8, part 1, pp. 963–999.

    MATH  MathSciNet  Google Scholar 

  15. Hayman, W.K., Meromorphic Functions, Oxford: Clarendon Press, 1964. Translated under the title Meromorfnye funktsii, Moscow: Mir, 1966.

    MATH  Google Scholar 

  16. Tsypkin, Ya.Z., Optimality in the Problems and Methods of the Modern Control Theory, Vestn. Akad. Nauk USSR, 1982, no. 9, pp. 116–121.

    Google Scholar 

  17. Evgrafov, M.A., Analiticheskie funktsii (Analytical Functions), Moscow: Nauka, 1968.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. L. Bunich.

Additional information

Original Russian Text © A.L. Bunich, 2014, published in Avtomatika i Telemekhanika, 2014, No. 12, pp. 3–12.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bunich, A.L. Optimization of linear discrete systems in the integral logarithmic index. Autom Remote Control 75, 2091–2098 (2014). https://doi.org/10.1134/S0005117914120017

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117914120017

Keywords

Navigation