# Global optimality conditions for a dynamic blocking problem

ESAIM: Control, Optimisation and Calculus of Variations (2012)

- Volume: 18, Issue: 1, page 124-156
- ISSN: 1292-8119

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topBressan, Alberto, and Wang, Tao. "Global optimality conditions for a dynamic blocking problem." ESAIM: Control, Optimisation and Calculus of Variations 18.1 (2012): 124-156. <http://eudml.org/doc/221891>.

@article{Bressan2012,

abstract = {The paper is concerned with a class of optimal blocking problems in the plane. We
consider a time dependent set R(t) ⊂ ℝ2,
described as the reachable set for a differential inclusion. To restrict its growth, a
barrier Γ 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 total value of the burned region 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. },

author = {Bressan, Alberto, Wang, Tao},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Dynamic blocking problem; optimality conditions; differential inclusion with obstacles; dynamic blocking problem},

language = {eng},

month = {2},

number = {1},

pages = {124-156},

publisher = {EDP Sciences},

title = {Global optimality conditions for a dynamic blocking problem},

url = {http://eudml.org/doc/221891},

volume = {18},

year = {2012},

}

TY - JOUR

AU - Bressan, Alberto

AU - Wang, Tao

TI - Global optimality conditions for a dynamic blocking problem

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2012/2//

PB - EDP Sciences

VL - 18

IS - 1

SP - 124

EP - 156

AB - The paper is concerned with a class of optimal blocking problems in the plane. We
consider a time dependent set R(t) ⊂ ℝ2,
described as the reachable set for a differential inclusion. To restrict its growth, a
barrier Γ 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 total value of the burned region 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.

LA - eng

KW - Dynamic blocking problem; optimality conditions; differential inclusion with obstacles; dynamic blocking problem

UR - http://eudml.org/doc/221891

ER -

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