Optimal impulsive control of delay systems

Florent Delmotte; Erik I. Verriest; Magnus Egerstedt

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 14, Issue: 4, page 767-779
  • ISSN: 1292-8119

Abstract

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In this paper, we solve an optimal control problem using the calculus of variation. The system under consideration is a switched autonomous delay system that undergoes jumps at the switching times. The control variables are the instants when the switches occur, and a set of scalars which determine the jump amplitudes. Optimality conditions involving analytic expressions for the partial derivatives of a given cost function with respect to the control variables are derived using the calculus of variation. A locally optimal impulsive control strategy can then be found using a numerical gradient descent algorithm.

How to cite

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Delmotte, Florent, Verriest, Erik I., and Egerstedt, Magnus. "Optimal impulsive control of delay systems." ESAIM: Control, Optimisation and Calculus of Variations 14.4 (2008): 767-779. <http://eudml.org/doc/250312>.

@article{Delmotte2008,
abstract = { In this paper, we solve an optimal control problem using the calculus of variation. The system under consideration is a switched autonomous delay system that undergoes jumps at the switching times. The control variables are the instants when the switches occur, and a set of scalars which determine the jump amplitudes. Optimality conditions involving analytic expressions for the partial derivatives of a given cost function with respect to the control variables are derived using the calculus of variation. A locally optimal impulsive control strategy can then be found using a numerical gradient descent algorithm. },
author = {Delmotte, Florent, Verriest, Erik I., Egerstedt, Magnus},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Optimal control; impulse control; switched systems; delay systems; calculus of variation.; optimal control; impulse control; calculus of variation},
language = {eng},
month = {1},
number = {4},
pages = {767-779},
publisher = {EDP Sciences},
title = {Optimal impulsive control of delay systems},
url = {http://eudml.org/doc/250312},
volume = {14},
year = {2008},
}

TY - JOUR
AU - Delmotte, Florent
AU - Verriest, Erik I.
AU - Egerstedt, Magnus
TI - Optimal impulsive control of delay systems
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2008/1//
PB - EDP Sciences
VL - 14
IS - 4
SP - 767
EP - 779
AB - In this paper, we solve an optimal control problem using the calculus of variation. The system under consideration is a switched autonomous delay system that undergoes jumps at the switching times. The control variables are the instants when the switches occur, and a set of scalars which determine the jump amplitudes. Optimality conditions involving analytic expressions for the partial derivatives of a given cost function with respect to the control variables are derived using the calculus of variation. A locally optimal impulsive control strategy can then be found using a numerical gradient descent algorithm.
LA - eng
KW - Optimal control; impulse control; switched systems; delay systems; calculus of variation.; optimal control; impulse control; calculus of variation
UR - http://eudml.org/doc/250312
ER -

References

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