Numerical method for optimal control problems governed by nonlinear hyperbolic systems of PDEs

Abstract

We develop a numerical method for the solution to linear adjoint equations arising, for example, in optimization problems governed by hyperbolic systems of nonlinear conservation and balance laws in one space dimension. Formally, the solution requires one to numerically solve the hyperbolic system forward in time and a corresponding linear adjoint system backward in time. Numerical results for the control problem constrained by either the Euler equations of gas dynamics or isothermal gas dynamics equations are presented. Both smooth and discontinuous prescribed terminal states are considered.