# Infinite time regular synthesis

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 3, page 381-405
- ISSN: 1292-8119

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topPiccoli, B.. "Infinite time regular synthesis." ESAIM: Control, Optimisation and Calculus of Variations 3 (2010): 381-405. <http://eudml.org/doc/197353>.

@article{Piccoli2010,

abstract = {
In this paper we provide a new sufficiency theorem for regular syntheses. The concept of regular synthesis is discussed in [12], where
a sufficiency theorem for finite time syntheses is proved.
There are interesting examples of optimal syntheses that are very regular, but whose trajectories have time domains not necessarily
bounded. The regularity assumptions of the main theorem in [12] are verified by every piecewise smooth feedback control generating
extremal trajectories that reach the target in finite time with a finite number of switchings. In the case of this paper the situation is
even more complicate, since we admit both trajectories with finite and infinite time.
We use weak differentiability assumptions on the synthesis and weak continuity assumptions on the associated value function.
},

author = {Piccoli, B.},

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

keywords = {Optimal control; Bolza problems; regular synthesis. ; Pontryagin principle; open-loop optimization; nonlinear; Hamiltonian formalism},

language = {eng},

month = {3},

pages = {381-405},

publisher = {EDP Sciences},

title = {Infinite time regular synthesis},

url = {http://eudml.org/doc/197353},

volume = {3},

year = {2010},

}

TY - JOUR

AU - Piccoli, B.

TI - Infinite time regular synthesis

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 3

SP - 381

EP - 405

AB -
In this paper we provide a new sufficiency theorem for regular syntheses. The concept of regular synthesis is discussed in [12], where
a sufficiency theorem for finite time syntheses is proved.
There are interesting examples of optimal syntheses that are very regular, but whose trajectories have time domains not necessarily
bounded. The regularity assumptions of the main theorem in [12] are verified by every piecewise smooth feedback control generating
extremal trajectories that reach the target in finite time with a finite number of switchings. In the case of this paper the situation is
even more complicate, since we admit both trajectories with finite and infinite time.
We use weak differentiability assumptions on the synthesis and weak continuity assumptions on the associated value function.

LA - eng

KW - Optimal control; Bolza problems; regular synthesis. ; Pontryagin principle; open-loop optimization; nonlinear; Hamiltonian formalism

UR - http://eudml.org/doc/197353

ER -

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