The Continuous Classical Boundary Optimal Control of Couple Nonlinear Hyperbolic Boundary Value Problem with Equality and Inequality Constraints

Authors

Jamil A. Ali Al-Hawasy, Department of Mathematics, College of Science, Al-Mustansiriyah University, Baghdad, IraqFollow

Abstract

The paper is concerned with the state and proof of the existence theorem of a unique solution (state vector) of couple nonlinear hyperbolic equations (CNLHEQS) via the Galerkin method (GM) with the Aubin theorem. When the continuous classical boundary control vector (CCBCV) is known, the theorem of existence a CCBOCV with equality and inequality state vector constraints (EIESVC) is stated and proved, the existence theorem of a unique solution of the adjoint couple equations (ADCEQS) associated with the state equations is studied. The Frcéhet derivative derivation of the "Hamiltonian" is obtained. Finally the necessary theorem (necessary conditions "NCs") and the sufficient theorem (sufficient conditions" SCs") for optimality of the state constrained problem are stated and proved.

Keywords

Classical boundary optimal control, Nonlinear hyperbolic, Necessary, Sufficient conditions

Article Type

Supplemental Issue

How to Cite this Article

Al-Hawasy, Jamil A. Ali (2019) "The Continuous Classical Boundary Optimal Control of Couple Nonlinear Hyperbolic Boundary Value Problem with Equality and Inequality Constraints," Baghdad Science Journal: Vol. 16: Iss. 4, Article 33.
DOI: https://doi.org/10.21123/bsj.2019.16.4(Suppl.).1064