The Optimal Control Problem for Triple Nonlinear Parabolic Boundary Value Problem with State Vector Constraints

Jamil A. Ali  Al-Hawasy; Thekaa M.   Rasheed

doi:10.24996/ijs.2022.63.5.27

Authors

Jamil A. Ali Al-Hawasy Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
Thekaa M. Rasheed Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2022.63.5.27

Keywords:

Classical Continuous Optimal Control, Nonlinear Triple Parabolic Boundary Value Problem, Fréchet Derivative, Necessary and Sufficient Optimality Conditions

Abstract

In this paper, the classical continuous triple optimal control problem (CCTOCP) for the triple nonlinear parabolic boundary value problem (TNLPBVP) with state vector constraints (SVCs) is studied. The solvability theorem for the classical continuous triple optimal control vector CCTOCV with the SVCs is stated and proved. This is done under suitable conditions. The mathematical formulation of the adjoint triple boundary value problem (ATHBVP) associated with TNLPBVP is discovered. The Fréchet derivative of the Hamiltonian" is derived. Under suitable conditions, theorems of necessary and sufficient conditions for the optimality of the TNLPBVP with the SVCs are stated and proved.