Main Article Content
This paper aims to study the quaternary classical continuous optimal control problem consisting of the quaternary nonlinear parabolic boundary value problem, the cost function, and the equality and inequality constraints on the state and the control. Under appropriate hypotheses, it is demonstrated that the quaternary classical continuous optimal control ruling by the quaternary nonlinear parabolic boundary value problem has a quaternary classical continuous optimal control vector that satisfies the equality constraint and inequality state and control constraint. Moreover, mathematical formulation of the quaternary adjoint equations related to the quaternary state equations is discovered, and then the weak form of the quaternary adjoint equations is obtained. Lastly, both the necessary conditions for optimality and sufficient conditions for optimality of the proposed problem are stated and proved. The derivation for the Fréchet derivative of the Hamiltonian is attained.
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Ameen, AT; Ismael, AJ. A Detection of Wheat Damping off and Root Rot Disease Pathogenic Fungi and it Bio Control by Pseudomonas Fluorescens. Baghdad Science Journal. 2017,14,1, 22-31.
Syahrini, I.; Masabar, R.; Aliasuddin, A.; Munzir, S.; Hazim, Y. The Application of Optimal Control through Fiscal Policy on Indonesian Economy. The Journal of Asian Finance, Economics and Business. 2021, 8, 3, 0741-0750.
Rigatos, G.; Abbaszadeh, M. Nonlinear optimal control for multi-DOF robotic manipulators with flexible joints. Optim. Control Appl. Methods. 2021, 42,6, 1708-1733.
Staffetti E; Li X; Matsuno Y; Soler M. Optimal Control Techniques in Aircraft Guidance
and Control International Journal of Aerospace Engineering. 2019.
Warga, J. Optimal Control of Differential and Functional Equations.; Academic Press: New York and London, 1972. ISBN: 9781483259192.
Lions, J.L. Optimal Control of Systems Governed by Partial Differential Equations; Spriger-Verlag: New York, 1972.
Chryssoverghi, I.; Al-Hawasy, J. The Continuous Classical Optimal Control Problem of
Semi Linear Parabolic Equations (CCOCP). J. of Kerbala University.2010, 8, 3.
Brett, C.; Dedner, A.; Elliott, C. Optimal Control of Elliptic PDEs at Points. IMA Journal
of Numerical Analysis. 2015, 36, 3, 1 - 34.
Al-Hawasy, J. The Continuous Classical Optimal Control of a Nonlinear Hyperbolic
Equation (CCOCP). Al-Mustansiriyah Journal of Science. 2008, 19, 8, 96 - 110.
Al-Hawasy, J.; Kadhem, G.M. The Continuous Classical Optimal Control for Coupled Nonlinear Parabolic Partial Differential Equations with Equality and Inequality Constraints. J. of Al-Nahrain University. 2016, 19, 1, 173 - 186.
Al-Rawdhanee, E.H.; The Continuous Classical Optimal Control of a couple Non-Linear
Elliptic Partial Differential Equations. M.Sc. thesis, Baghdad-Iraq: Al-Mustansiriyah
Al-Hawasy, J. The Continuous Classical Optimal Control of a Couple Nonlinear Hyperbolic Partial Differential Equations with Equality and Inequality Constraints. Iraqi Journal of Science. 2016, 57, 2C, 1528 - 1538.
Al-Hawasy, J.; Jaber, M.A.K. The Continuous Classical Optimal Control governing by
Triple Linear Parabolic Boundary Value Problem. Ibn Al Haitham Jour. for Pure & Appl.
Sci. 2020, 33, 1, 129 - 142.
Al-Hawasy, J.; Jasim, D.A. The Continuous Classical Optimal Control Problems for
Triple Nonlinear Elliptic Partial Differential Equations. Ibn Al-Haitham Jour. for Pure &
Appl. Sci. 2020, 33, 3, 101 - 112.
Al-Hawasy, J.A.; Ali, L.H. Boundary Optimal Control For Triple Nonlinear Hyperbolic
Boundary Value Problem With State Constraints. Iraqi Journal of Science. 2021, 62, 6,
Al-Anbaki, W.A. The Classical Continuous Optimal Control for Quaternary Nonlinear
Parabolic Boundary Value Problem. MSc. thesis, Mustansiriyah University, College of
Sciences, Department of Mathematics, Baghdad, Iraq. 2022.