# 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

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topCamilli, 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 -

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