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Equivalent formulation and numerical analysis of a fire confinement problem
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- Journal:
- ESAIM: Control, Optimisation and Calculus of Variations / Volume 16 / Issue 4 / October 2010
- Published online by Cambridge University Press:
- 11 August 2009, pp. 974-1001
- Print publication:
- October 2010
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- Article
- Export citation
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We consider a class of variationalproblems for differential inclusions, related to thecontrol of wild fires. The area burned by the fire at time t> 0is modelled as the reachable set fora differential inclusion $\dot x$
∈F(x), starting froman initial set R 0. To block the fire, a barrier can be constructedprogressively in time. For each t> 0, the portion of the wall constructedwithin time t is described by a rectifiable setγ(t) ⊂ $\mathbb{R}^2$ 
. In this paperwe show that the searchfor blocking strategies and for optimal strategies can be reduced toa 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 developa numerical algorithm for the computation ofoptimal strategies, minimizing the total area burned by the fire.
