Optimal Control of the Propagation of a Graph in Inhomogeneous Media
Klaus Deckelnick, Charles M. Elliott, Vanessa Styles · SIAM Journal on Control and Optimization · 2009
We study an optimal control problem for viscosity solutions of a Hamilton–Jacobi equation describing the propagation of a one-dimensional graph with the control being the speed function. The existence of an optimal control is proved together with an approximate controllability result in the $H^{-1}$-norm. We prove convergence of a discrete optimal control problem based on a monotone finite difference scheme and describe some numerical results.