The Optimal Classical Continuous Control Quaternary Vector of Quaternary Nonlinear Hyperbolic Boundary Value Problem

Main Article Content

jamil Amir Al-Hawasy
Mayeada Abd Alsatar Hassan

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

How to Cite
[1]
Al-Hawasy, jamil A. and Abd Alsatar Hassan, M. 2022. The Optimal Classical Continuous Control Quaternary Vector of Quaternary Nonlinear Hyperbolic Boundary Value Problem. Ibn AL-Haitham Journal For Pure and Applied Sciences. 35, 3 (Jul. 2022), 161–174. DOI:https://doi.org/10.30526/35.3.2833.
Section
Mathematics

Publication 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.