Boundary Control Design for Traffic with Nonlinear Dynamics
Abstract
We address a problem of boundary control for a nonlinear scalar conservation law. Namely, this paper is devoted to the boundary control of an LWR 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 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.
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