Abstract:
Research considered investigates the optimal control problem which is constrained by a hyperbolic
conservation law (HCL). We carried out a comparative study of the solutions of the
optimal control problem subject to each one of the two di erent types of hyperbolic relaxation
systems [64, 92]. The objective was to employ the adjoint-based optimization to minimize the
cost functional of a matching type between the optimal solution and the target solution. Numerical
tests were then carried out and promising results obtained. Finally, an extension was
made to the adjoint-based optimization approach to apply second-order schemes for the optimal
control problem in which also good numerical results were observed.
