The Optimal Classical Continuous Control Quaternary Vector of Quaternary Nonlinear Hyperbolic Boundary Value Problem
Main Article Content
Abstract
This work is concerned with studying the optimal classical continuous control quaternary vector problem. It is consisted of; the quaternary nonlinear hyperbolic boundary value problem and the cost functional. At first, the weak form of the quaternary nonlinear hyperbolic boundary value problem is obtained. Then under suitable hypotheses, the existence theorem of a unique state quaternary vector solution for the weak form where the classical continuous control quaternary vector is considered known is stated and demonstrated by employing the method of Galerkin and the compactness theorem. In addition, the continuity operator between the state quaternary vector solution of the weak form and the corresponding classical continuous control quaternary vector is demonstrated in three different infinite dimensional spaces (Hilbert spaces). Furthermore, with suitable hypotheses, the existence theorem of an optimal classical continuous control quaternary vector dominated by the weak form of the quaternary nonlinear hyperbolic boundary value problem is stated and demonstrated.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
licenseTermsPublication Dates
References
Grigorenko, N.; Grigorieva, Ѐ. V.; Roi, P. K.; Khailov, E.N. Optimal Control Problems
for a Mathematical Model of the Treatment of Psoriasis, Computational Mathematics and
Modeling. 2019, 304, 352-363.
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. Optimal Control Applications and Methods. 2021,6,1708-
Kahina, L.; Spiteri, P.; Demim, F.; Mohamed, A. ; Nemra, A.; Messine, F. Application
Optimal Control for a Problem Aircraft Flight, Journal of Engineering Science and
Technology Review. 2018, 11, 156-164.
Bors, D. ; Walczak, S. Optimal Control Elliptic Systems with Distributed and Boundary
Controls . Nonlinear Analysis. 2005, 63,5-7,1367-1376.
Al-Hawasy, J. “The Continuous Classical Optimal Control Problem of a Nonlinear
Hyperbolic Partial Differential Equations (CCOCP)”, Al-Mustansiriyah Journal of
Science. 2008, 19, 3, 96-110,.
Chryssoverghi I., Al-Hawasy J. The Continuous Classical Optimal Control Problem of
Semi Linear Parabolic Equations (CCOCP), Journal of Karbala University. 2010,8,3.
Al-Hawasy J., and Al-Rawdhanee E. H, The Continuous Classical Optimal Control
of a Couple of Non-linear Elliptic Equation”, Mathematical Theory and Modeling.
,4,14.
Al-Hawasy J. The Continuous Classical Optimal Control of a Coupled Nonlinear
Hyperbolic Partial Differential Equations with Equality and Inequality Constraints, Iraqi
Journal of Science. 2016,57, 2C, 1528-1538.