TY - GEN
T1 - Reconstruction of boundary conditions from internal conditions using viability theory
AU - Hofleitner, Aude
AU - Claudel, Christian G.
AU - Bayen, Alexandre M.
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2012/6
Y1 - 2012/6
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/575806
UR - http://ieeexplore.ieee.org/document/6314947/
U2 - 10.1109/acc.2012.6314947
DO - 10.1109/acc.2012.6314947
M3 - Conference contribution
SN - 9781457710957
BT - 2012 American Control Conference (ACC)
PB - Institute of Electrical and Electronics Engineers (IEEE)
ER -