Boundary Control Design for Traffic With Nonlinear Dynamics

• 成果类型: Article
• 署名作者: Tumash, Liudmila; Canudas-de-Wit, Carlos; Delle Monache, Maria Laura
• 署名单位: Inria; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3069394
• 发表日期: 2022
• 页码: 1301-1313
• 关键词: Electric shock; Mathematical model; trajectory; Boundary conditions; roads; computational modeling; optimal control; Boundary control problem; Hamilton-Jacobi formulation; LWR model; Partial differential equations; Traffic control

摘要

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.