Volume 16, Number 4, October-December 2010
|Page(s)||974 - 1001|
|Published online||11 August 2009|
Equivalent formulation and numerical analysis of a fire confinement problem
Department of Mathematics, Penn State University
University Park, Pa. 16802, USA. email@example.com; firstname.lastname@example.org
Revised: 26 April 2009
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 ∈ 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) ⊂ . 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 ⊂ , rather than the multifunction t γ(t) ⊂ . Relying on this result, we then develop a numerical algorithm for the computation of optimal strategies, minimizing the total area burned by the fire.
Mathematics Subject Classification: 49Q20 / 34A60 / 49J24 / 93B03
Key words: Dynamic blocking problem / differential inclusion / constrained minimum time problem
© EDP Sciences, SMAI, 2009
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