Boundary Control Design for Traffic With Nonlinear Dynamics

We address a problem of boundary control for a nonlinear scalar conservation law. Namely, this article is devoted to the boundary control of a Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) with triangular flux function evolving along a single road. The target state is a time- and space-dependent trajectory. The boundary control law is constructed using the analytical solution of the Hamilton–Jacobi (H–J) equation, which is an integral form of the LWR PDE. We design a feedback controller and illustrate its performance on a numerical example using the Godunov scheme.