This paper introduces a new class of variational problems for differential inclusions, motivated by the control of forest fires. The area burned by the fire at time t > 0 is modelled as the reachable set for a differential inclusion (x) over dot is an element of F(x), starting from an initial set R-0. To block the fire, a wall can be constructed progressively in time, at a given speed. In this paper, we study the possibility of constructing a wall which completely encircles the fire. Moreover, we derive necessary conditions for an optimal strategy, which minimizes the total area burned by the fire. (C) 2007 Elsevier Inc. All rights reserved.
