Reconstruction of boundary conditions from internal conditions using viability theory
Type
Conference PaperKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionDistributed Sensing Systems Laboratory (DSS)
Electrical Engineering Program
Mechanical Engineering Program
Physical Science and Engineering (PSE) Division
Date
2012-06Permanent link to this record
http://hdl.handle.net/10754/575806
Metadata
Show full item recordAbstract
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.Conference/Event name
American Control Conference (ACC), 2012ISBN
9781457710957ae974a485f413a2113503eed53cd6c53
10.1109/acc.2012.6314947