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Equivalent formulation and numerical analysis of a fire confinement problem
Published online by Cambridge University Press: 11 August 2009
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 $\dot x$∈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) ⊂$\mathbb{R}^2$
. 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⊂$\mathbb{R}^2$
,
rather than the multifunction t$\mapsto$
γ(t) ⊂$\mathbb{R}^2$
.
Relying on this result, we then develop
a numerical algorithm for the computation of
optimal strategies, minimizing the total area burned by the fire.
- Type
- Research Article
- Information
- ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 4 , October 2010 , pp. 974 - 1001
- Copyright
- © EDP Sciences, SMAI, 2009
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