C&SA | Contents

Volume 61 >>> № 2 MARCH — APRIL 2025

-->

UDC 519.71

K.R. Aidazade¹, S.Z. Guliyev²

¹ Institute of Control Systems, National Academy of Sciences of Azerbaijan; Azerbaijan University of Architecture and Construction, Baku, Azerbaijan

kamil.aydazade@gmail.com

² Institute of Control Systems, National Academy of Sciences of Azerbaijan; Azerbaijan State University of Oil and Industry, Baku, Azerbaijan

azcopal@gmail.com

SYNTHESIS OF ZONAL CONTROLS USING INFORMATION
ABOUT THE HISTORY OF THE OBJECT’S STATE

Abstract. In the article, we propose an approach to feedback control for nonlinear objects with lumped parameters, which involves dividing the entire set of the object’s potential phase states into a finite number of subsets or zones. In this approach, the synthesized controls are based not on the measured phase state values directly, but rather on the zonal values of the parameters corresponding to the zone associated with the current and past object’s measured states. We have derived necessary optimality conditions for zonal values of feedback control parameters, as well as conducted computational experiments on various test problems, which confirmed the efficiency of the proposed approach to controlling nonlinear dynamic objects.

Keywords: feedback control, zonal parameters, gradient of functional, time lag, nonlinear dynamic objects.

full text

REFERENCES

1. Bellman R.E., Glicksberg I., Gross O.A. Some aspects of the mathematical theory of control processes. Rand Corporation: Santa Monica, California, 1958. 263 p.

2. Lions J.L. Optimal control of systems governed by partial differential equations. Berlin; Heidelberg: Springer-Verlag, 1971. 396 p.

3. Kuntsevich V.M., Chikrii A.A. controlled processes: methods of investigation and applications. Cybernetics and Systems Analysis. 2003. Vol. 39, N 4. P. 477–487. https://doi.org/10.1023/ .

4. Ray W.H. Advanced process control. New York: McGraw-Hill, 1981. 376 p.

5. Bryson A.E. Applied linear optimal control: Examples and algorithms. Cambridge: Cambridge University Press, 2002. 362 p. https://doi.org/10.1115/ .

6. Ermoliev Yu.M., Gulenko V.P., Tsarenko T.I. Finite-difference method in optimal control problems [in Russian]. Kyiv: Naukova Dumka, 1978. 164 p.

7. Deineka V.S., Sergienko I.V. Optimal control of heterogeneous distributed systems [in Russian]. Kyiv: Nauk. Dumka, 2003. 506 p.

8. Deineka V.S., Sergienko I.V. Analysis of multicomponent distributed systems and optimal control [in Russian]. Kyiv: Nauk. Dumka, 2007. 703 p.

9. Pshenichny B.N. Convex analysis and extremal problems [in Russian]. Moscow: Nauka, 1980. 320 p.
10. Bryson A.E., Ho Y.-C. Applied optimal control: Optimization, estimation and control. New-York: Routledge, 1975. 496 p. https://doi.org/10.1201/ .

11. Butkovsky A.G. Theory of optimal control of systems with distributed parameters [in Russian]. Moscow: Nauka, 1965. 475 p.

12. Emelianov S.V. Automatic control systems with variable structure [in Russian]. Moscow: Nauka, 1967. 336 p.

13. Polyak B.T., Khlebnikov M.V., Rapoport L.B. Mathematical Theory of Automatic Control [in Russian]. Moscow: Lenand, 2019. 500 p.

14. Mordukhovich B.Sh. Approximation methods in optimization and control problems [in Russian]. Moscow: Nauka, 1988. 360 p.

15. Polyak R.A. Introduction to continuous optimization. SOIA. 2021. Vol.172. Cham: Springer, 2021. XVI, 541 p. https://doi.org/10.1007/ .

16. Zgurovsky M.Z., Pankratova N.D. Systems analysis: problems, methodology, applications [in Russian]. Kyiv: Nauk. Dumka, 2005. 745 p.

17. Sergienko I.V., Deineka V.S. Optimal control of distributed systems with conjugation conditions. NOIA. 2005. Vol. 75. New York: Springer, 2005. XVI, 383 p. https://doi.org/10.1007/ .

18. Sirazetdinov T.K. Optimization of systems with distributed parameters [in Russian]. Moscow: Nauka, 1977. 470 p.

19. Feldbaum A.A., Butkovsky A.G. Methods of the Theory of Automatic Control [in Russian]. Moscow: Nauka, 1971. 743 p.

20. Lee H.-G. Linearization of nonlinear control systems. Singapore: Springer, 2022. XIII, 589 p. https://doi.org/10.1007/ .

21. Guliyev S.Z. Synthesis of zonal controls of nonlinear systems under discrete observations. Automatic Control and Computer Sciences. 2011. Vol. 45, Iss. 6. P. 338–345. https://doi.org/ .

22. Guliyev S.Z. Synthesis of control in nonlinear systems with different types of feedback and strategies of control. Journal of Automation and Information Sciences. 2013. Vol. 45, Iss. 7. P. 74–86. https://doi.org/10.1615/ .

23. Aida-zade K.R., Guliyev S.Z. Zonal control synthesis for nonlinear systems under nonlinear output feedback. Journal of Automation and Information Sciences. 2015. Vol. 47, Iss. 1. P. 51–66. https://doi.org/10.1615/ .

24. Shor N.Z. Algorithms of sequential and non-smooth optimization: Collection of selected works [in Russian]. Chisinau: Eureka, 2012. 270 p.

25. Stetsyuk P.I. Ellipsoid methods and r –algorithms [in Russian]. Chisinau: Eureka, 2014. 488 p.

UDC 519.71

SYNTHESIS OF ZONAL CONTROLS USING INFORMATION ABOUT THE HISTORY OF THE OBJECT’S STATE

REFERENCES

SYNTHESIS OF ZONAL CONTROLS USING INFORMATION
ABOUT THE HISTORY OF THE OBJECT’S STATE