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dc.contributor.authorClaudel, Christian G.
dc.contributor.authorChamoin, Timothee
dc.contributor.authorBayen, Alexandre M.
dc.date.accessioned2015-08-03T11:45:17Z
dc.date.available2015-08-03T11:45:17Z
dc.date.issued2014-01
dc.identifier.citationClaudel, C. G., Chamoin, T., & Bayen, A. M. (2014). Solutions to Estimation Problems for Scalar Hamilton–Jacobi Equations Using Linear Programming. IEEE Transactions on Control Systems Technology, 22(1), 273–280. doi:10.1109/tcst.2013.2238940
dc.identifier.issn10636536
dc.identifier.doi10.1109/TCST.2013.2238940
dc.identifier.urihttp://hdl.handle.net/10754/563304
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.
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)
dc.subjectLinear programming
dc.subjectState estimation
dc.titleSolutions to estimation problems for scalar hamilton-jacobi equations using linear programming
dc.typeArticle
dc.contributor.departmentElectrical Engineering Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentDistributed Sensing Systems Laboratory (DSS)
dc.identifier.journalIEEE Transactions on Control Systems Technology
dc.contributor.institutionDepartment of Applied Mathematics, Ecole Polytechnique, Paris, France
dc.contributor.institutionDepartment of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, United States
kaust.personClaudel, Christian G.


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