  This paper studies the linear-quadratic (LQ) optimal control problem of a
class of systems governed by the first-order hyperbolic partial differential
equations (PDEs) with final state constraints. The main contribution is to
present the solvability condition and the corresponding explicit optimal
controller by using the Lagrange multiplier method and the technique of solving
forward and backward partial differential equations (FBPDEs). In particular,
the result is reduced to the case with zero-valued final state constraints.
Several numerical examples are provided to demonstrate the performance of the
designed optimal controller.
