Equivalent formulation and numerical analysis of a fire confinement problem

Alberto Bressan, Tao Wang

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We consider a class of variational problems for differential inclusions, related to the control of wild fires. The area burned by the fire at time t > 0 is modelled as the reachable set for a differential inclusion x ε F(x), starting from an initial set R0. To block the fire, a barrier can be constructed progressively in time. For each t > 0, the portion of the wall constructed within time t is described by a rectifiable set γ(t) ⊂ ℝ2. In this paper we show that the search for blocking strategies and for optimal strategies can be reduced to a problem involving one single admissible rectifiable set Γ ⊂ ℝ2, rather than the multifunction t → γ(t) ⊂ ℝ2. Relying on this result, we then develop a numerical algorithm for the computation of optimal strategies, minimizing the total area burned by the fire.

Original languageEnglish (US)
Pages (from-to)974-1001
Number of pages28
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume16
Issue number4
DOIs
StatePublished - Oct 2010

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics

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