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Existence of optimal strategies for a fire confinement problem
Author(s) -
Bressan Alberto,
De Lellis Camillo
Publication year - 2009
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20271
Subject(s) - differential inclusion , mathematics , block (permutation group theory) , set (abstract data type) , differential (mechanical device) , class (philosophy) , mathematical optimization , value (mathematics) , combinatorics , computer science , engineering , artificial intelligence , statistics , programming language , aerospace engineering
Abstract We consider a class of variational problems for differential inclusions related to the control of forest fires. The area burned by the fire at time t > 0 is modeled as the reachable set for a differential inclusion ẋ ∈ F ( x ) starting from an initial set R 0 . To block the fire, a barrier can be constructed progressively in time at a given speed. In this paper we prove the existence of an optimal strategy, which minimizes the value of the area destroyed by the fire plus the cost of constructing the barrier. © 2008 Wiley Periodicals, Inc.