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Optimal impulsive control of delay systems

Published online by Cambridge University Press:  30 January 2008

Florent Delmotte ,
Erik I. Verriest  and
Magnus Egerstedt
Florent Delmotte
Affiliation:
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30302, USA; florent@ece.gatech.edu; erik.verriest@ece.gatech.edu; magnus@ece.gatech.edu
Erik I. Verriest
Affiliation:
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30302, USA; florent@ece.gatech.edu; erik.verriest@ece.gatech.edu; magnus@ece.gatech.edu
Magnus Egerstedt
Affiliation:
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30302, USA; florent@ece.gatech.edu; erik.verriest@ece.gatech.edu; magnus@ece.gatech.edu
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Abstract

In this paper, we solve an optimal control problem using thecalculus of variation. The system under consideration is aswitched autonomous delay system that undergoes jumps at theswitching times. The control variables are the instants when theswitches occur, and a set of scalars which determine the jumpamplitudes. Optimality conditions involving analytic expressionsfor the partial derivatives of a given cost function with respectto the control variables are derived using the calculus ofvariation. A locally optimal impulsive control strategy can thenbe found using a numerical gradient descent algorithm.

Keywords

Optimal controlimpulsecontrolswitched systemsdelay systemscalculus of variation.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 14 , Issue 4 , October 2008 , pp. 767 - 779
Copyright
© EDP Sciences, SMAI, 2008

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