Viability theory
Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations
SIAM Journal on Control and Optimization
Convex Optimization
Data Assimilation: The Ensemble Kalman Filter
Data Assimilation: The Ensemble Kalman Filter
Dirichlet Problems for some Hamilton-Jacobi Equations with Inequality Constraints
SIAM Journal on Control and Optimization
Minimal error certificates for detection of faulty sensors using convex optimization
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
IEEE Transactions on Information Theory
A framework for privacy and security analysis of probe-based traffic information systems
Proceedings of the 2nd ACM international conference on High confidence networked systems
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This article proposes a new method for data assimilation and data reconciliation problems applicable to systems modeled by conservation laws. The problem is solved directly in the equivalent format of a Hamilton-Jacobi partial differential equation, for which the solution is fully characterized by a Lax-Hopf formula. Using properties of the solution, we prove that when the data of the problem is prescribed in piecewise affine form, the resulting constraints which consist of the partial differential equation in data assimilation and reconciliation problems are convex, and can be instantiated explicitly. This property enables us to identify a class of data assimilation and data reconciliation problems that can be formulated using convex programs in standard form. We illustrate the capabilities of the method for reconstruction of highway traffic flow using experimental data generated from the Mobile Century experiment.