Adjoint-based optimization for optimal control problems governed by nonlinear hyperbolic conservation laws

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 different 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.