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Hofleitner A.,University of California at Berkeley | Claudel C.,Electrical Engineering and Mechanical Engineering | Bayen A.,University of California at Berkeley
Proceedings of the American Control Conference | Year: 2012

This article presents a method for reconstructing downstream boundary conditions to a HamiltonJacobi partial differential equation for which initial and upstream boundary conditions are prescribed as piecewise affine functions and an internal condition is prescribed as an affine function. Based on viability theory, we reconstruct the downstream boundary condition such that the solution of the Hamilton-Jacobi equation with the prescribed initial and upstream conditions and reconstructed downstream boundary condition satisfies the internal value condition. This work has important applications for estimation in flow networks with unknown capacity reductions. It is applied to urban traffic, to reconstruct signal timings and temporary capacity reductions at intersections, using Lagrangian sensing such as GPS devices onboard vehicles. © 2012 AACC American Automatic Control Council). Source


Hofleitner A.,University of California at Berkeley | Claudel C.,Electrical Engineering and Mechanical Engineering | Bayen A.M.,University of California at Berkeley
Proceedings of the IEEE Conference on Decision and Control | Year: 2012

This article presents a method for deriving the probability distribution of the solution to a Hamilton-Jacobi partial differential equation for which the value conditions are random. The derivations lead to analytical or semi-analytical expressions of the probability distribution function at any point in the domain in which the solution is defined. The characterization of the distribution of the solution at any point is a first step towards the estimation of the parameters defining the random value conditions. This work has important applications for estimation in flow networks in which value conditions are noisy. In particular, we illustrate our derivations on a road segment with random capacity reductions. © 2012 IEEE. Source

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