TY - JOUR

T1 - Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks

AU - Li, Yanning

AU - Canepa, Edward S.

AU - Claudel, Christian

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2014/3

Y1 - 2014/3

N2 - This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.

AB - This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.

UR - http://hdl.handle.net/10754/594249

UR - http://ieeexplore.ieee.org/document/6730649/

UR - http://www.scopus.com/inward/record.url?scp=84930248983&partnerID=8YFLogxK

U2 - 10.1109/tcns.2014.2304152

DO - 10.1109/tcns.2014.2304152

M3 - Article

SN - 2325-5870

VL - 1

SP - 28

EP - 39

JO - IEEE Transactions on Control of Network Systems

JF - IEEE Transactions on Control of Network Systems

IS - 1

ER -