Computation and control of solutions to the Burgers equation using viability theory

This paper presents a new approach which links the solution to the Burgers tracking problem to the concept of capture basin used in viability theory. This link enables the proof of the existence and uniqueness of the solution of the Burgers tracking problem. The Burgers tracking problem is linked to the Frankowska solutions of the Burgers equation. These results are easily extended to any first order hyperbolic partial differential equation (PDE) written in conservation law form, which is illustrated with the famous Lighthit-Whitham-Richards (LWR) PDE, known in highway traffic theory. The implications of these results on the control of the inviscid Burgers PDK are finally listed.