Skip to main content

Algorithms for the Synthesis of Optimal Linear-Quadratic Stationary Controllers

  • Conference paper
  • First Online:

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1323))

Abstract

Algorithms for the synthesis of optimal linear-quadratic stationary controllers in adaptive control systems for technological objects are presented. To construct the control system, the state parameter space method was used. To determine the optimal control of the problem under consideration in various situations, it is proposed to use the solutions of the algebraic Riccati equation. The given computational schemes made it possible to effectively solve the problems of parametric synthesis of optimal controllers in control systems for industrial technological processes.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M.: 10th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions - ICSCCW-2019, p. 970, Springer Science and Business Media LLC (2020). https://doi.org/10.1007/978-3-030-35249-3

  2. Krasovskogo, A.A., Nauka, M.: Automatic Control Theory Handbook (1987). (in Russian)

    Google Scholar 

  3. Averyanov, V.K., Sidorenko, G.I., Tolmachev, V.N., Shapovalo, A.A.: Methodology of synthesis of algorithms for optimal control of adaptive power supply systems with wind power plants. In: IOP Conference Series: Materials Science and Engineering (2019). https://doi.org/10.1088/1757-899X/666/1/012031

  4. Egupov, N.D., Pupkov, K.A.: Methods of classical and modern theory of automatic control, vol. 5, Textbook, Baumana (2004). (in Russian)

    Google Scholar 

  5. Antonov, V., Terexov, V., Tyukin, I.: Adaptive control in technical systems, Tutorial, Sankt-Peterburg (in Russian). (2001)

    Google Scholar 

  6. Fomin, V.N., Fradkov, A.L., Yakubovich, V.A.: Adaptive management of dynamic objects, The Science (1981). (in Russian)

    Google Scholar 

  7. Igamberdiyev, H.Z., Sevinov, J.U., Zaripov, O.O.: Regular methods and algorithms for the synthesis of adaptive control systems with tunable models, TashGTU (2014). (in Russian)

    Google Scholar 

  8. Igamberdiev, H.Z., Sevinov, J.U.: Algorithms for regular synthesis of adaptive systems management of technological objects based on the concepts of identification approach. J. Chem. Tech. Cont. Manag. 6, 42–50 (2019)

    Google Scholar 

  9. Briand, D.O., Anderson, J.B.: Moore. In: Optimal Control Linear Quadratic Methods, p. 380, Prentice-Hall, Inc., USA, Canberra (1989). ISBN 0-13-638651-2

    Google Scholar 

  10. Barabanov, A.E.: Using the method of least squares in design of adaptive optimal control for a linear dynamic process. Autom. Remote Control 44(12), 1574–1581 (1983)

    MATH  Google Scholar 

  11. Igamberdiev, H.Z., Yusupov, E.A., Sotvoldiev, H.I., Azamxonov, B.S.: Sustainable algorithms for the synthesis of a suboptimal dynamic object management system. In: Advance Intelligence System Computing, pp. 902–907, Springer Science and Business Media LLC (2020)

    Google Scholar 

  12. Loan, N.T., Shon, X.X.: On the solution of an ill-posed problem of optimal linear filtering with correlated noise. Autom. Telemechanics 4, 58–73 (1983)

    MathSciNet  Google Scholar 

  13. Yusupbekov, N.R., Igamberdiev, H.Z., Mamirov. U.F.: Algorithms of sustainable estimation of unknown input signals in control systems. J. Mult. Val. Logic Soft Comp. 33(1-2), 1–10 (2019). https://www.oldcitypublishing.com/pdf/9291

  14. Mallaev, A.R., Xusanov, S.N., Sevinov, J.U.: Algorithms of nonparametric synthesis of discrete one-dimensional controllers. Int. J. Adv. Sci. Tech. 29(5), 1045–1050 (2020)

    Google Scholar 

  15. Sevinov, J.U., Zaripov, O.O., Zaripova, S.O.: The algorithm of adaptive estimation in the synthesis of the dynamic objects control systems. Int. J. Adv. Sci. Tech. 29(5), 1096–1100 (2020). http://sersc.org/journals/index.php/IJAST/article/view/7887

  16. Francis, B.: The optimal linear-quadratic time invariant regulator with cheap control. IEEE Trans. Autom. Control (1979)

    Google Scholar 

  17. Francis, B.: Perfect regulation and feedforward control of linear multivariable systems. In: IEEE Conference Decision Control including the 16th Symposium on Adaptive Processes and a Special Symposium on Fuzzy Set Theory and Applications (1977)

    Google Scholar 

  18. Igamberdiyev, H.Z., Yusupbekov, A.N., Zaripov, O.O., Sevinov, J.U.: Algorithms of adaptive identification of uncertain operated objects in dynamical models. Procedia Comput. Sci. 120, 854–861 (2017). https://doi.org/10.1016/j.procs.2017.11.318

    Article  Google Scholar 

  19. Igamberdiev, H.Z., Sevinov, J.U., Yusupbekov, A.N.: Regular algorithms for identifying the parameters of an object and a controller in a closed-loop control system. J. Chem. Tech. Cont. Manag. 6, 50–54 (2017)

    Google Scholar 

  20. Zaripov, O.O., Shukurova, O.P., Sevinov, J.U.: Algorithms for identification of linear dynamic control objects based on the pseudo-concept concept. Inter. J. Psy. Rehab. 24(3), 261–267 (2020). https://doi.org/10.37200/IJPR/V24I3/PR200778

    Article  Google Scholar 

  21. Igamberdiev, H.Z., Boeva, O.H., Sevinov, J.U.: Sustainable algorithms for selecting feedback in dynamic object management systems. J. Adv. Res. Dyn. Control Syst. 12(07), 2162–2166 (2020). https://doi.org/10.5373/JARDCS/V12SP7/20202337

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. U. Sevinov .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Sevinov, J.U., Mallaev, A.R., Xusanov, S.N. (2021). Algorithms for the Synthesis of Optimal Linear-Quadratic Stationary Controllers. In: Aliev, R.A., Yusupbekov, N.R., Kacprzyk, J., Pedrycz, W., Sadikoglu, F.M. (eds) 11th World Conference “Intelligent System for Industrial Automation” (WCIS-2020). WCIS 2020. Advances in Intelligent Systems and Computing, vol 1323. Springer, Cham. https://doi.org/10.1007/978-3-030-68004-6_9

Download citation

Publish with us

Policies and ethics