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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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