TY - CHAP

T1 - Dynamic blocking problems for a model of fire propagation

AU - Bressan, Alberto

N1 - Funding Information:
This work was partially supported by NSF through grant DMS 1108702 “Problems of Nonlinear Control”.

PY - 2013

Y1 - 2013

N2 - This paper contains a survey of recent work on a class of dynamic blocking problems. The basic model consists of a differential inclusion describing the growth of a set in the plane. To restrain its expansion, it is assumed that barriers can be constructed, in real time. Here the issues of major interest are: (i) whether the growth of the set can be eventually blocked, and (ii) what is the optimal location of the barriers, minimizing a cost criterion. After introducing the basic definitions and concepts, the paper reviews various results on the existence or non-existence of blocking strategies. A theorem on the existence of an optimal strategy is then recalled, together with various necessary conditions for optimality. Sufficient conditions for optimality and a numerical algorithm for the computation of optimal barriers are also discussed, together with several open problems.

AB - This paper contains a survey of recent work on a class of dynamic blocking problems. The basic model consists of a differential inclusion describing the growth of a set in the plane. To restrain its expansion, it is assumed that barriers can be constructed, in real time. Here the issues of major interest are: (i) whether the growth of the set can be eventually blocked, and (ii) what is the optimal location of the barriers, minimizing a cost criterion. After introducing the basic definitions and concepts, the paper reviews various results on the existence or non-existence of blocking strategies. A theorem on the existence of an optimal strategy is then recalled, together with various necessary conditions for optimality. Sufficient conditions for optimality and a numerical algorithm for the computation of optimal barriers are also discussed, together with several open problems.

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U2 - 10.1007/978-1-4614-5389-5_2

DO - 10.1007/978-1-4614-5389-5_2

M3 - Chapter

AN - SCOPUS:84874318798

SN - 9781461453888

T3 - Fields Institute Communications

SP - 11

EP - 40

BT - Advances in Applied Mathematics, Modeling, and Computational Science

A2 - Melnik, Roderick

ER -