Solvability for classical continuous boundary optimal control problem dominating by triple hyperbolic equations

Abstract

Abstract This work concerns with the study of the continuous classical boundary optimal control problem (CCBUOCP) dominating by triple linear hyperbolic (TLH) partial differential equations(TLHPDEQS). The existing theorem for a unique state vector solution(SVES) for the TLH boundary value problem (TLHBVP) as well as for its adjoint triple linear equations (ATLEQ) is proved using the method of Galerkin (MG) when the continuous classical boundary control vector (CCBUCV) is known. The existing theorem of a continuous classical boundary optimal control vector (CCBUOCV) dominating by the TLHBVP is proved. The directional derivative (DIDE) for the cost functional (CFu) is derived. Finally the theorem for necessity conditions for optimality (THNCO) of the problem is proved.