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

Handle URI:
http://hdl.handle.net/10754/594249
Title:
Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks
Authors:
Li, Yanning; Canepa, Edward S. ( 0000-0002-5779-2059 ) ; Claudel, Christian
Abstract:
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.
KAUST Department:
Mechanical Engineering Program; Electrical Engineering Program
Citation:
Li Y, Canepa E, Claudel C (2014) Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks. IEEE Trans Control Netw Syst 1: 28–39. Available: http://dx.doi.org/10.1109/tcns.2014.2304152.
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
IEEE Transactions on Control of Network Systems
Issue Date:
Mar-2014
DOI:
10.1109/tcns.2014.2304152
Type:
Article
ISSN:
2325-5870
Appears in Collections:
Articles; Electrical Engineering Program; Mechanical Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorLi, Yanningen
dc.contributor.authorCanepa, Edward S.en
dc.contributor.authorClaudel, Christianen
dc.date.accessioned2016-01-19T14:44:20Zen
dc.date.available2016-01-19T14:44:20Zen
dc.date.issued2014-03en
dc.identifier.citationLi Y, Canepa E, Claudel C (2014) Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks. IEEE Trans Control Netw Syst 1: 28–39. Available: http://dx.doi.org/10.1109/tcns.2014.2304152.en
dc.identifier.issn2325-5870en
dc.identifier.doi10.1109/tcns.2014.2304152en
dc.identifier.urihttp://hdl.handle.net/10754/594249en
dc.description.abstractThis 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.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.subjectDistributed parameter systemsen
dc.subjectinteger programmingen
dc.subjectlinear programmingen
dc.subjectnetworksen
dc.subjectoptimal controlen
dc.subjectquadratic programmingen
dc.subjecttraffic controlen
dc.titleOptimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networksen
dc.typeArticleen
dc.contributor.departmentMechanical Engineering Programen
dc.contributor.departmentElectrical Engineering Programen
dc.identifier.journalIEEE Transactions on Control of Network Systemsen
kaust.authorLi, Yanningen
kaust.authorCanepa, Edward S.en
kaust.authorClaudel, Christian G.en
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