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-...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2022-03, Vol.67 (3), p.1301-1313
Main Authors: Tumash, Liudmila, Canudas-de-Wit, Carlos, Monache, Maria Laura Delle
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary control
Boundary control problem
Computational modeling
Conservation laws
Control systems design
Control theory
Electric shock
Exact solutions
Feedback control
Hamilton–Jacobi formulation
LWR model
Mathematical model
Mathematics
Nonlinear control
Nonlinear dynamics
Optimal control
Optimization and Control
Partial differential equations
Roads
Traffic control
Trajectory
Trajectory control
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Summary: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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2021.3069394