Abstract
The article proposes an approach to solving the problem of synthesis of motion and power control of lumped sources with optimization of the locations of the points of the measurements. For specificity, the problem of feedback control of moving heat sources during rod heating is considered. The power and speed of point-wise sources are assigned depending on the state of the processes at the measurement points. The formulas for the gradient components of the objective functional, allowing for the numerical solution of the problem using of the first-order optimization methods are obtained.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Antipin, A.S., Khoroshilova, E.V.: Feedback synthesis for a terminal control problem. Comput. Math. and Math. Phys. 58, 1903–1918 (2018)
Butkovskiy, A.G.: Methods of control of systems with distributed parameters. Nauka, Moscow (1984).(In Russian)
Deineka, V.S., Sergienko, I.V.: Optimal control of non-homogeneous distributed systems. Naukova Dumka, Kiev (2003).(In Russian)
Utkin, V.I.: Sliding Modes in Control and Optimization. Springer, Heidelberg (1992). https://doi.org/10.1007/978-3-642-84379-2
Ray W.H.: Advanced process control. McGraw-Hill Book Company (2002)
Yegorov, A.I.: Bases of the control theory. Fizmatlit, Moscow (2004).(In Russian)
Butkovskiy, A.G., Pustylnikov, L.M.: The theory of mobile control of systems with distributed parameters. Nauka, Moscow (1980).(In Russian)
Sirazetdinov, T.K.: Optimization of systems with distributed parameters. Nauka, Moscow (1977).(In Russian)
Sergienko, I.V., Deineka, V.S.: Optimal control of distributed systems with conjugation conditions. Kluwer Acad. Publ, New York (2005)
Polyak, B.T., Khlebnikov, M.V., Rapoport, L.B.: Mathematical theory of automatic control. LENAND, Moscow (2019)
Vasilyev, F.P.: Optimization methods, 824. Faktorial Press, Moscow (2002).(In Russian)
Guliyev, S.Z.: Synthesis of zonal controls for a problem of heating with delay under non-separated boundary conditions. Cybern. Syst. Analysis. 54(1), 110–121 (2018)
Aida-zade, K.R., Abdullaev, V.M.: On an approach to designing control of the distributed-parameter processes. Autom. Remote Control 73(9), 1443–1455 (2012)
Aida-zade, K.R., Hashimov, V.A., Bagirov, A.H.: On a problem of synthesis of control of power of the moving sources on heating of a rod. Proc. Inst. Math. Mech. ANAS 47(1), 183–196 (2021)
Nakhushev, A.M.: Loaded equations and their application. Nauka, Moscow (2012)
Alikhanov, A.A., Berezgov, A.M., Shkhanukov-Lafishev, M.X.: Boundary value problems for certain classes of loaded differential equations and solving them by finite difference methods. Comp. Math. Math. Phys. 48(9), 1581–1590 (2008)
Abdullaev, V.M., Aida-zade, K.R.: Numerical method of solution to loaded nonlocal boundary value problems for ordinary differential equations. Comp. Math. Math. Phys. 54(7), 1096–1109 (2014)
Abdullayev, V.M., Aida-zade, K.R.: Finite-difference methods for solving loaded parabolic equations. Comp. Math. Math. Phys. 56(1), 93–105 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Aida-zade, K.R., Hashimov, V. (2021). Synthesis of Power and Movement Control of Heating Sources of the Rod. In: Olenev, N.N., Evtushenko, Y.G., Jaćimović, M., Khachay, M., Malkova, V. (eds) Advances in Optimization and Applications. OPTIMA 2021. Communications in Computer and Information Science, vol 1514. Springer, Cham. https://doi.org/10.1007/978-3-030-92711-0_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-92711-0_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-92710-3
Online ISBN: 978-3-030-92711-0
eBook Packages: Computer ScienceComputer Science (R0)