The Classical Continuous Mixed Optimal Control of Couple Nonlinear Parabolic Partial Differential Equations with State Constraints

Jamil A Ali  Al-Hawasy; Ghufran M  Kadhem; Ahmed Abdul Hasan  Naeif

doi:10.24996/ijs.2021.62.12.24

Authors

Jamil A Ali Al-Hawasy Mathematics Dept., College of Science, Mustansiriyah University, Iraq https://orcid.org/0000-0002-7225-8030
Ghufran M Kadhem Babylonian Directorate of Education
Ahmed Abdul Hasan Naeif Babylonian Directorate of Education

DOI:

https://doi.org/10.24996/ijs.2021.62.12.24

Keywords:

Mixed Classical Optimal Control, Frechet Derivative, Necessary and Sufficient Conditions for Optimality

Abstract

In this work, the classical continuous mixed optimal control vector (CCMOPCV) problem of couple nonlinear partial differential equations of parabolic (CNLPPDEs) type with state constraints (STCO) is studied. The existence and uniqueness theorem (EXUNTh) of the state vector solution (SVES) of the CNLPPDEs for a given CCMCV is demonstrated via the method of Galerkin (MGA). The EXUNTh of the CCMOPCV ruled with the CNLPPDEs is proved. The Frechet derivative (FÉDE) is obtained. Finally, both the necessary and the sufficient theorem conditions for optimality (NOPC and SOPC) of the CCMOPCV with state constraints (STCOs) are proved through using the Kuhn-Tucker-Lagrange (KUTULA) multipliers theorem (KUTULATH).