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Solutions to estimation problems for scalar hamilton-jacobi equations using linear programming
Solutions to estimation problems for scalar hamilton-jacobi equations using linear programming
Type
Article
Authors
Claudel, Christian G.
Chamoin, Timothee
Bayen, Alexandre M.
KAUST Department
Electrical Engineering Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Distributed Sensing Systems Laboratory (DSS)
Date
2014-01
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.
Citation
Claudel, 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
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Journal
IEEE Transactions on Control Systems Technology
DOI
10.1109/TCST.2013.2238940
Permanent link to this record
http://hdl.handle.net/10754/563304
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Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Electrical and Computer Engineering Program
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