Skip to Main content Skip to Navigation
Journal articles

Regularity and Lyapunov stabilization of weak entropy solutions to scalar conservation laws

Abstract : We consider the problem of Lyapunov boundary stabilization of the weak entropy solution to a scalar conservation law with strictly convex flux in one dimension of space, around a uniform equilibrium. We show that for a specific class of boundary conditions, the solution to the initial-boundary value problem for an initial condition with bounded variations can be approximated arbitrarily closely in the L1 norm by a piecewise smooth solution with finitely many discontinuities. The constructive method we present designs explicit boundary conditions in this class, which guarantee Lyapunov stability of the weak entropy solution to the initial-boundary value problem. We show how the greedy control, obtained by maximizing the decrease of the natural Lyapunov function, may fail to asymptotically stabilize and a brute force control generates unbounded variation of traces. We then design a stabilizing control, which avoid oscillations, and propose a nonlocal technique (depending on time and the whole initial datum) which optimizes the convergence time. Controllers performance is illustrated on numerical benchmarks using the Godunov scheme.
Complete list of metadata

Cited literature [19 references]  Display  Hide  Download
Contributor : Maria Laura Delle Monache Connect in order to contact the contributor
Submitted on : Thursday, February 4, 2016 - 6:06:05 PM
Last modification on : Friday, August 9, 2019 - 3:24:28 PM
Long-term archiving on: : Saturday, November 12, 2016 - 10:00:10 AM


Files produced by the author(s)


  • HAL Id : hal-01267722, version 1



Sébastien Blandin, Xavier Litrico, Maria Laura Delle Monache, Benedetto Piccoli, Alexandre Bayen. Regularity and Lyapunov stabilization of weak entropy solutions to scalar conservation laws. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2017, 62 (4), pp.1620-1635. ⟨hal-01267722⟩



Record views


Files downloads