Abstract
The authors consider the problem of synthesis of power control of the sources moving according to the given rules along certain trajectories when the bar is heated. The current values of the controls are determined depending on bar’s temperature at the points of measurement. Formulas for the components of the gradient of the objective functional are obtained with respect to the feedback parameters and coordinates of the measurement points, which are used to numerically solve the test problem using first-order numerical optimization methods. The results of computer experiments are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J.-L. Lions, Controle Optimal de Systèmes Gouvernés par des Équations aux Dérivées Partielles, Dunod Ganthier-Villars, Paris (1969).
A. G. Butkovsky, Methods of Control of Distributed Parameter Systems [in Russian], Nauka, Moscow (1984).
V. S. Deineka and I. V. Sergienko, Optimal Control of Inhomogeneous Distributed Systems [in Russian], Naukova Dumka, Kyiv (2003).
V. I. Utkin, Sliding Conditions in Optimization and Control Problems [in Russian], Nauka, Moscow (1981).
W. H. Ray, Advanced Process Control, McGraw-Hill Book Company (1980).
A. I. Egorov, Fundamentals of the Control Theory [in Russian], Fizmatlit, Moscow (2004).
A. G. Butkovskii and L. M. Pustylnikov, Theory of Mobile Control of Distributed Parameter Systems [in Russian], Nauka, Moscow (1980).
T. K. Sirazetdinov, Optimization of Distributed Parameter Systems [in Russian], Nauka, Moscow (1977).
I. V. Sergienko and V. S. Deineka, Optimal Control of Distributed Systems with Conjugation Conditions, Kluwer Acad. Publ., New York (2005).
B. T. Polyak, M. V. Khlebnikov, and L. B. Rapoport, Mathematical Theory of Automatic Control [in Russian], LENAND, Moscow (2019).
J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes at application, Vol. 1, Paris (1968).
F. P. Vasil’ev, Optimization Methods [in Russian], Faktorial Press, Moscow (2002).
S. Z. Guliyev, “Synthesis of zonal controls for a problem of heating with delay under nonseparated boundary conditions,” Cybern. Syst. Analysis, Vol. 54, No. 1, 110–121 (2018).
K. R. Aida-zade and V. M. Abdullaev, “On an approach to designing control of the distributed-parameter processes,” Autom. and Remote Control, Vol. 73, No. 9, 1443–1455 (2012).
A. M. Nakhushev, Loaded Equations and their Application [in Russian], Nauka, Moscow (2012).
A. A. Alikhanov, A. M. Berezgov, and M. X. Shkhanukov-Lafishev, “Boundary value problems for certain classes of loaded differential equations and solving them by finite difference methods,” Comp. Math. Math. Phys., Vol. 48, No. 9, 1581–1590 (2008).
V. M. Abdullaev and K. R. Aida-zade, “Numerical method of solution to loaded nonlocal boundary value problems for ordinary differential equations,” Comp. Math. Math. Phys., Vol. 54, No. 7, 1096–1109 (2014).
V. M. Abdullayev and K. R. Aida-zade, “Finite-difference methods for solving loaded parabolic equations,” Comp. Math. Math. Phys., Vol. 56, No. 1, 93–105 (2016).
K. R. Aida-zade and A. G. Bagirov, “On the problem of spacing of oil wells and control of their production rates,” Autom. and Remote Control, Vol. 67, No. 1, 44–53 (2006).
A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1989).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Kibernetyka ta Systemnyi Analiz, No. 4, July–August, 2021, pp. 104–117.
Rights and permissions
About this article
Cite this article
Aida-zade, K.R., Bagirov, A.H. & Hashimov, V.A. Feedback Control of the Power of Moving Sources in Bar Heating. Cybern Syst Anal 57, 592–604 (2021). https://doi.org/10.1007/s10559-021-00384-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10559-021-00384-4