Numerical Methods for the Optimal Control of Scalar Conservation Laws
Provides numerical methods for optimal control of hyperbolic PDEs, relevant for applications in traffic flow, gas dynamics, etc., but the results are incremental and domain-specific.
The paper develops continuous and discretized relaxation schemes for optimal control of scalar conservation laws, demonstrating convergence results for higher-order discretizations and numerical tracking of nonsmooth desired states.
We are interested in a class of numerical schemes for the optimization of nonlinear hyperbolic partial differential equations. We present continuous and discretized relaxation schemes for scalar, one-- conservation laws. We present numerical results on tracking type problems with nonsmooth desired states and convergence results for higher--order spatial and temporal discretization schemes.