DMCA
Global Optimality Conditions for a Dynamic Blocking Problem (2010)
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BibTeX
@MISC{Bressan10globaloptimality,
author = {Alberto Bressan and Tao Wang},
title = {Global Optimality Conditions for a Dynamic Blocking Problem},
year = {2010}
}
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Abstract
The paper is concerned with a class of optimal blocking problems in the plane. We consider a time dependent set R(t) ⊂ IR 2, described as the reachable set for a differential inclusion. To restrict its growth, a barrier can be constructed, in real time. This is a one-dimensional rectifiable set which blocks the trajectories of the differential inclusion. In this paper we introduce a definition of “regular strategy”, based on a careful classification of blocking arcs. Moreover, we derive local and global necessary conditions for an optimal strategy, which minimizes the value of the region ∪t≥0R(t) plus the cost of constructing the barrier. We show that a Lagrange multiplier, corresponding to the constraint on the construction speed, can be interpreted as the “instantaneous value of time”. This value, which we compute by two separate formulas, remains constant when free arcs are constructed and is monotone decreasing otherwise. 1
Keyphrases
global optimality condition dynamic blocking problem differential inclusion careful classification regular strategy instantaneous value reachable set free arc one-dimensional rectifiable set construction speed lagrange multiplier global necessary condition optimal strategy separate formula real time
