Equivalent formulation and numerical analysis of a fire confinement problem
ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 974-1001.

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 ˙ 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) 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 2 , rather than the multifunction t γ(t) 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.

DOI : 10.1051/cocv/2009033
Classification : 49Q20, 34A60, 49J24, 93B03
Mots clés : dynamic blocking problem, differential inclusion, constrained minimum time problem
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Bressan, Alberto; Wang, Tao. Equivalent formulation and numerical analysis of a fire confinement problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 974-1001. doi : 10.1051/cocv/2009033. http://www.numdam.org/articles/10.1051/cocv/2009033/

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