Title :
Reconstruction of boundary conditions from internal conditions using viability theory
Author :
Hofleitner, A. ; Claudel, Christian ; Bayen, A.
Author_Institution :
Electr. Eng. & Comput. Sci., UC Berkeley, Berkeley, CA, USA
Abstract :
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.
Keywords :
affine transforms; initial value problems; partial differential equations; piecewise linear techniques; road traffic control; GPS devices onboard vehicles; Hamilton Jacobi partial differential equation; Lagrangian sensing; boundary conditions; downstream boundary condition reconstruction; flow network estimation; initial boundary conditions; internal conditions; internal value condition; piecewise affine functions; signal timing reconstruction; temporary capacity reductions; urban traffic; viability theory; Boundary conditions; Context; Equations; Mathematical model; Sensors; Trajectory; Vehicles;
Conference_Titel :
American Control Conference (ACC), 2012
Conference_Location :
Montreal, QC
Print_ISBN :
978-1-4577-1095-7
Electronic_ISBN :
0743-1619
DOI :
10.1109/ACC.2012.6314947
