Bang-bang theorem for a coupled ODE-PDE control system (Q2314444)

This paper solves an optimal control problem for a system of one dimensional hyperbolic conservation laws which is controlled through the boundary condition, depending on the state of a nonlinear control system. It is proved that the system admits a solution within the set of admissible controls and it is also shown that there always exist almost optimal bang-bang controls whose values are extremal points of the set of admissible controls.