LaxHopf based incorporation of internal boundary conditions into Hamilton-Jacobi equation. Part II: Computational methods

Christian Claudel, Alexandre M. Bayen

Research output: Contribution to journalArticlepeer-review

77 Scopus citations

Abstract

This article presents a new method for explicitly computing solutions to a HamiltonJacobi partial differential equation for which initial, boundary and internal conditions are prescribed as piecewise affine functions. Based on viability theory, a LaxHopf formula is used to construct analytical solutions for the individual contribution of each affine condition to the solution of the problem. The results are assembled into a LaxHopf algorithm which can be used to compute the solution to the partial differential equation at any arbitrary time at no other cost than evaluating a semi-analytical expression numerically. The method being semi-analytical, it performs at machine accuracy (compared to the discretization error inherent to finite difference schemes). The performance of the method is assessed with benchmark analytical examples. The running time of the algorithm is compared with the running time of a Godunov scheme.

Original languageEnglish (US)
Article number5461008
Pages (from-to)1158-1174
Number of pages17
JournalIEEE Transactions on Automatic Control
Volume55
Issue number5
DOIs
StatePublished - May 1 2010

Keywords

  • Hamilton-Jacobi (HJ)
  • Initial conditions (ICs)
  • Lax-Hopf formula
  • Partial differential equation (PDE)
  • Piecewise affine (PWA)
  • Terminal conditions (TCs)

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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