Continues Classical Quaternary Boundary Optimal Control Problem of Quaternary Linear Hyperbolic System - Fadhel , Mahmood A.; Al-Hawasy, Jamil A. Ali (Communications in Mathematics and Applications, 2025)
This work concerns with the study of the continuous classical quaternary boundary optimal control problem or for brief quaternary boundary optimal control problem (QBOCP) controlling by quaternary linear hyperbolic system (QLHS). The existence theorem for a unique quaternary state vector solution (QSVS) for the QLHS as well as for its quaternary adjoint linear system (QALS) is proved via the method of Galerkin (MG) with given continuous boundary control quaternary vector (CBCQV). The existence theorem of a continuous boundary optimal control quaternary vector (CBOCQV) controlling by the QLHS is demonstrated. The directional derivative (DDV) for the objective functional (OF) is derived. Lastly, the necessity conditions for optimality (NCO) of the problem is studied.
Keywords: Quaternary boundary optimal control; Quaternary linear hyperbolic system; Quaternary adjoint linear system; Directional derivative; Necessity conditions