Approximation of control problems involving ordinary and impulsive controls

Fabio Camilli; Maurizio Falcone

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

  • Volume: 4, page 159-176
  • ISSN: 1292-8119

Abstract

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In this paper we study an approximation scheme for a class of control problems involving an ordinary control v, an impulsive control u and its derivative u ˙ . Adopting a space-time reparametrization of the problem which adds one variable to the state space we overcome some difficulties connected to the presence of u ˙ . We construct an approximation scheme for that augmented system, prove that it converges to the value function of the augmented problem and establish an error estimates in L∞ for this approximation. Moreover, a characterization of the limit of the discrete optimal controls is given showing that it converges (in a suitable sense) to an optimal control for the continuous problem.

How to cite

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Camilli, Fabio, and Falcone, Maurizio. "Approximation of control problems involving ordinary and impulsive controls." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 159-176. <http://eudml.org/doc/197369>.

@article{Camilli2010,
abstract = { In this paper we study an approximation scheme for a class of control problems involving an ordinary control v, an impulsive control u and its derivative $\dot u$. Adopting a space-time reparametrization of the problem which adds one variable to the state space we overcome some difficulties connected to the presence of $\dot u$. We construct an approximation scheme for that augmented system, prove that it converges to the value function of the augmented problem and establish an error estimates in L∞ for this approximation. Moreover, a characterization of the limit of the discrete optimal controls is given showing that it converges (in a suitable sense) to an optimal control for the continuous problem. },
author = {Camilli, Fabio, Falcone, Maurizio},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Impulsive control; approximation scheme; dynamic programming; viscosity solution; dynamic programming; impulsive controls},
language = {eng},
month = {3},
pages = {159-176},
publisher = {EDP Sciences},
title = {Approximation of control problems involving ordinary and impulsive controls},
url = {http://eudml.org/doc/197369},
volume = {4},
year = {2010},
}

TY - JOUR
AU - Camilli, Fabio
AU - Falcone, Maurizio
TI - Approximation of control problems involving ordinary and impulsive controls
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 4
SP - 159
EP - 176
AB - In this paper we study an approximation scheme for a class of control problems involving an ordinary control v, an impulsive control u and its derivative $\dot u$. Adopting a space-time reparametrization of the problem which adds one variable to the state space we overcome some difficulties connected to the presence of $\dot u$. We construct an approximation scheme for that augmented system, prove that it converges to the value function of the augmented problem and establish an error estimates in L∞ for this approximation. Moreover, a characterization of the limit of the discrete optimal controls is given showing that it converges (in a suitable sense) to an optimal control for the continuous problem.
LA - eng
KW - Impulsive control; approximation scheme; dynamic programming; viscosity solution; dynamic programming; impulsive controls
UR - http://eudml.org/doc/197369
ER -

References

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