For more information about this meeting, contact Becky Halpenny.
|Title:||"Mathematical Control and Dynamic Blocking Problems"|
|Seminar:||Ph.D. Thesis Defense|
|Speaker:||Tao Wang, Adviser: Alberto Bressan, Penn State|
|We focus on a new class of optimization problems, originally motivated by models of confinement of wild fires. The burned region is described by the reachable set for a differential inclusion. To block its spreading, we assume that barriers can be constructed in real time. In mathematical terms, a barrier is a one-dimensional rectifiable set, which cannot be crossed by trajectories of the differential inclusion.
As a preliminary step, we show that the search for blocking strategies and for optimal strategies can be reduced to a problem involving one single admissible rectifiable set, rather than a time-dependent multifunction.
Regarding the blocking strategy in the half plane, we prove that the fire can be entirely enclosed by the wall in finite time, if and only if the construction speed is strictly greater than the fire propagation speed.
Meanwhile, relying on a classification of blocking arcs, we derive local and global necessary conditions for an optimal strategy, which minimizes the value of burned region plus the cost of wall construction. Moreover, we derive optimality conditions for the strategies containing a type of arcs which can slow down the fire advancement, and also necessary conditions satisfied at the initial point.
At last, we study optimization problem in the isotropic case where the initial region is initially a disc, and the fire outspreads with unit speed in all directions. Among all barriers consisting of a single closed curve, we further prove that the optimal strategy is axisymmetric, and consists of an arc of circumference and two arcs of logarithmic spirals.|
Room Reservation Information
|Date:||05 / 19 / 2011|
|Time:||10:00am - 12:00pm|