Equivalent formulation and numerical analysis of a fire confinement problem
ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 4, p. 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 $\stackrel{˙}{x}$ 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) ${ℝ}^{2}$. 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 ${ℝ}^{2}$, rather than the multifunction t $↦$ γ(t) ${ℝ}^{2}$. Relying on this result, we then develop a numerical algorithm for the computation of optimal strategies, minimizing the total area burned by the fire.

DOI : https://doi.org/10.1051/cocv/2009033
Classification:  49Q20,  34A60,  49J24,  93B03
Keywords: dynamic blocking problem, differential inclusion, constrained minimum time problem
@article{COCV_2010__16_4_974_0,
author = {Bressan, Alberto and Wang, Tao},
title = {Equivalent formulation and numerical analysis of a fire confinement problem},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {16},
number = {4},
year = {2010},
pages = {974-1001},
doi = {10.1051/cocv/2009033},
zbl = {pre05821905},
mrnumber = {2744158},
language = {en},
url = {http://www.numdam.org/item/COCV_2010__16_4_974_0}
}

Bressan, Alberto; Wang, Tao. Equivalent formulation and numerical analysis of a fire confinement problem. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 4, pp. 974-1001. doi : 10.1051/cocv/2009033. http://www.numdam.org/item/COCV_2010__16_4_974_0/

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