Solutions to estimation problems for scalar hamilton-jacobi equations using linear programming

Handle URI:
http://hdl.handle.net/10754/563304
Title:
Solutions to estimation problems for scalar hamilton-jacobi equations using linear programming
Authors:
Claudel, Christian G. ( 0000-0003-0702-6548 ) ; Chamoin, Timothee; Bayen, Alexandre M.
Abstract:
This brief presents new convex formulations for solving estimation problems in systems modeled by scalar Hamilton-Jacobi (HJ) equations. Using a semi-analytic formula, we show that the constraints resulting from a HJ equation are convex, and can be written as a set of linear inequalities. We use this fact to pose various (and seemingly unrelated) estimation problems related to traffic flow-engineering as a set of linear programs. In particular, we solve data assimilation and data reconciliation problems for estimating the state of a system when the model and measurement constraints are incompatible. We also solve traffic estimation problems, such as travel time estimation or density estimation. For all these problems, a numerical implementation is performed using experimental data from the Mobile Century experiment. In the context of reproducible research, the code and data used to compute the results presented in this brief have been posted online and are accessible to regenerate the results. © 2013 IEEE.
KAUST Department:
Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Distributed Sensing Systems Laboratory (DSS)
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
IEEE Transactions on Control Systems Technology
Issue Date:
Jan-2014
DOI:
10.1109/TCST.2013.2238940
Type:
Article
ISSN:
10636536
Appears in Collections:
Articles; Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorClaudel, Christian G.en
dc.contributor.authorChamoin, Timotheeen
dc.contributor.authorBayen, Alexandre M.en
dc.date.accessioned2015-08-03T11:45:17Zen
dc.date.available2015-08-03T11:45:17Zen
dc.date.issued2014-01en
dc.identifier.issn10636536en
dc.identifier.doi10.1109/TCST.2013.2238940en
dc.identifier.urihttp://hdl.handle.net/10754/563304en
dc.description.abstractThis brief presents new convex formulations for solving estimation problems in systems modeled by scalar Hamilton-Jacobi (HJ) equations. Using a semi-analytic formula, we show that the constraints resulting from a HJ equation are convex, and can be written as a set of linear inequalities. We use this fact to pose various (and seemingly unrelated) estimation problems related to traffic flow-engineering as a set of linear programs. In particular, we solve data assimilation and data reconciliation problems for estimating the state of a system when the model and measurement constraints are incompatible. We also solve traffic estimation problems, such as travel time estimation or density estimation. For all these problems, a numerical implementation is performed using experimental data from the Mobile Century experiment. In the context of reproducible research, the code and data used to compute the results presented in this brief have been posted online and are accessible to regenerate the results. © 2013 IEEE.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.subjectLinear programmingen
dc.subjectState estimationen
dc.titleSolutions to estimation problems for scalar hamilton-jacobi equations using linear programmingen
dc.typeArticleen
dc.contributor.departmentElectrical Engineering Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentDistributed Sensing Systems Laboratory (DSS)en
dc.identifier.journalIEEE Transactions on Control Systems Technologyen
dc.contributor.institutionDepartment of Applied Mathematics, Ecole Polytechnique, Paris, Franceen
dc.contributor.institutionDepartment of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, United Statesen
kaust.authorClaudel, Christian G.en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.