Infinite time regular synthesis

Piccoli, 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 -