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.

Keywords: 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}, zbl = {1148.49017}, mrnumber = {2451795}, language = {en}, url = {http://www.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://www.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://www.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, Volume 14 (2008) no. 4, pp. 767-779. doi : 10.1051/cocv:2008009. http://www.numdam.org/articles/10.1051/cocv:2008009/

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