Classical Continuous Constraint Boundary Optimal Control Vector Problem for Triple Nonlinear Parabolic System
DOI:
https://doi.org/10.23851/mjs.v34i2.1272Keywords:
Classical Constraints Boundary Optimal Triple Control, Nonlinear Triple Parabolic Boundary Value Problem, Necessary and Sufficient Optimality ConditionsAbstract
In this paper, our purpose is to study the classical continuous constraints boundary optimal triple control vector problem dominating nonlinear triple parabolic boundary value problem. The existence theorem for a classical continuous triple optimal control vector CCCBOTCV is stated and proved under suitable assumptions. The mathematical formulation of the adjoint triple boundary value problem associated with the nonlinear triple parabolic boundary value problem is discovered. The Fréchet derivative of the Hamiltonian is derived. Under proper assumptions, both theorems are granted; the necessary conditions for optimality and the sufficient conditions for optimality of the classical continuous constraints boundary optimal triple control vector problem are stated and proven.
Received: 08/12/2022
Revised: 08/01/2023
Accepted: 31/01/2023
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M.G. Cojocaru, A.S. Jaber, " Optimal Control of a Vaccinating Game Toward Increasing Overall Coverage," J. appl. math. phys., Vol.6, pp. 754-769, 2018.
E. Staffetti E, X. Li,Y. Matsuno, M. Soler, "Optimal Control Techniques in Aircraft Guidance and Control,," Int. J. Aerosp. Eng. 2 pages, 2019.
I. Syahrini, R. Masabar, A. Aliasuddin, S. Munzir, Y. Hazim, "The Application of Optimal Control Through Fiscal Policy on Indonesian Economy," J. Asian Finance Econ. Bus. Vol.8, No. 3, pp. 0741-0750, 2021.
G. Rigatos, M. Abbaszadeh, "Nonlinear Optimal Control for Multi-DOF Robotic Manipulators with Flexible Joints," Optim. Control Appl. Methods, Vol.42, no. 6,pp. 1708-1733, 2021.
D. Derome D, H. Razali, A. Fazlizan, A. Jedi, K.P. Roberts. Determination of Optimal Time -Average Wind Speed Data in the Southern Part of Malaysia. Baghdad Sci. J. Vol.19, no.5, pp.1111-1122, 2022.
P. Lin, W.Wang, "Optimal Control Problems for Some Ordinary Differential Equations with Behavior of Blowup or Quenching,," Math. Control Relat. Fields.Vol.8, no. 4, pp. 809-828, 2018.
A. Manzoni, A. Quarteroni, S. Salsa, Optimal Control of Partial Differential Equations: Analysis, Approximation, and Applications (Applied Mathematical Sciences, 207). 1st edition. New York: Spriger; 2021, p. 515.
Y. Wang, X. Luo, S. Li, "Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling Zone," Adv.Math. Phys, Vol. 2015, Article ID 585967, 10 pages,2015.
Sh. Du • Z. Cai, Adaptive Finite Element Method for Dirichlet Boundary Control of Elliptic Partial Differential Equations,," J. Sci. Comput. ,vol.89,no36, pp.1-25, 2021.
I. Aksikas, J. J. Winkin, and D. Dochain, "Optimal LQ-feedback control for a Class of First-Order Hyperbolic Distributed Parameter Systems," ESAIM- Control, Optim. and Calc. Var., Vol. 14, no. 04, pp. 897-908, 2008.
J. A. Ali Al-Hawasy, A. A. H. Naeif," The Continuous Classical Boundary Optimal Control of a Couple Nonlinear Parabolic Partial Differential Equations,," Special Issus: 1st Scientific International Conference, College of Science, Al-Nahrain University, Part I, pp.123-136, 21-22/11/2017.
J. A. Ali Al-Hawasy, S. J. M. Al-Qaisi,"The Continuous Classical Boundary Optimal Control of a Couple Nonlinear Elliptic Partial Differential Equations with State Constraints," Al-Mustansiriyah Journal of Science. Vol. 30, Issue 1,pp.143-151, 2019.
J. A. Ali Al-Hawasy, "The Continuous Classical Boundary Optimal Control of Couple Nonlinear Hyperbolic Boundary Value Problem with Equality and Inequality Constraints," Baghdad Sci. J. Vol.16, no.4, pp.1064-1074, Supplement 2019.
J. A. Ali Al-Hawasy, N. A. Th. Al-Ajeeli,"The Continuous Classical Boundary Optimal Control of Triple Nonlinear Elliptic Partial Differential Equations with State Constraints,," Iraqi Journal of Science, Vol. 62, No. 9, pp. 3020-3030, 2021.
L. H Ali J. A. Al-Hawasy," Boundary Optimal Control for Triple Nonlinear Hyperbolic Boundary Value Problem with State Constraints,," Iraqi Journal of Science, Vol 62, No 6, pp. 2009-2021, 2021.
J. Al-Hawasy , Y. H. Rashid "Classical Continuous Boundary Optimal Control Vector Problem for Triple Nonlinear Parabolic System," Al-Mustansiriyah Journal of Science. Vol. 34, No. 1.
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