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.
Mots-clés : optimal control, impulse control, switched systems, delay systems, calculus of variation
@article{COCV_2008__14_4_767_0,
author = {Delmotte, Florent and Verriest, Erik I. and Egerstedt, Magnus},
title = {Optimal impulsive control of delay systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {767--779},
publisher = {EDP-Sciences},
volume = {14},
number = {4},
year = {2008},
doi = {10.1051/cocv:2008009},
mrnumber = {2451795},
zbl = {1148.49017},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv:2008009/}
}
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 PY - 2008 SP - 767 EP - 779 VL - 14 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2008009/ DO - 10.1051/cocv:2008009 LA - en ID - COCV_2008__14_4_767_0 ER -
%0 Journal Article %A Delmotte, Florent %A Verriest, Erik I. %A Egerstedt, Magnus %T Optimal impulsive control of delay systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2008 %P 767-779 %V 14 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2008009/ %R 10.1051/cocv:2008009 %G en %F COCV_2008__14_4_767_0
Delmotte, Florent; Verriest, Erik I.; Egerstedt, Magnus. Optimal impulsive control of delay systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 4, pp. 767-779. doi : 10.1051/cocv:2008009. http://archive.numdam.org/articles/10.1051/cocv:2008009/
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