Boundary Optimal Control for Triple Nonlinear Hyperbolic Boundary Value Problem with State Constraints

  • Lamyaa H Ali Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
  • Jamil A. Al-Hawasy Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
Keywords: Boundary optimal control vector, necessary condition, sufficient condition, directional derivative

Abstract

The paper is concerned with the state and proof of the solvability theorem of unique state vector solution (SVS) of triple nonlinear hyperbolic boundary value problem (TNLHBVP), via utilizing the Galerkin method (GAM) with the Aubin theorem (AUTH), when the boundary control vector (BCV) is known. Solvability theorem of a boundary optimal control vector (BOCV) with equality and inequality state vector constraints (EINESVC) is proved. We studied the solvability theorem of a unique solution for the adjoint triple boundary value problem (ATHBVP) associated with TNLHBVP. The directional derivation (DRD) of the "Hamiltonian"(DRDH) is deduced. Finally, the necessary theorem (necessary conditions "NCOs") and the sufficient theorem (sufficient conditions" SCOs"), together denoted as NSCOs, for the optimality (OP) of the state constrained problem (SCP) are stated and proved.

Published
2021-07-01
How to Cite
Ali, L. H., & Al-Hawasy, J. A. (2021). Boundary Optimal Control for Triple Nonlinear Hyperbolic Boundary Value Problem with State Constraints. Iraqi Journal of Science, 62(6), 2009-2021. https://doi.org/10.24996/ijs.2021.62.6.27
Section
Mathematics