Constraints Optimal Classical Continuous Control Vector Problem for Quaternary Nonlinear Hyperbolic System

Authors

Jamil Amir Al-Hawasy Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq.
Mayeada Abd Alsatar Hassan Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq.

DOI:

https://doi.org/10.30526/36.2.2992

Keywords:

Necessary Conditions, Sufficient Conditions, Nonlinear Hyperbolic System, Quaternary Optimal Classical Continuous Control vector.

Abstract

This paper is concerned with the quaternary nonlinear hyperbolic boundary value problem (QNLHBVP) studding constraints quaternary optimal classical continuous control vector (CQOCCCV), the cost function (CF), and the equality and inequality quaternary state and control constraints vector (EIQSCCV). The existence of a CQOCCCV dominating by the QNLHBVP is stated and demonstrated using the Aubin compactness theorem (ACTH) under appropriate hypotheses (HYPs). Furthermore, mathematical formulation of the quaternary adjoint equations (QAEs) related to the quaternary state equations (QSE) are discovere so as its weak form (WF) . The directional derivative (DD) of the Hamiltonian (Ham) is calculated. The necessary and sufficient conditions for optimality (NCSO) theorems for the proposed problem are stated and proved.

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