Geodesic
Optimal impulsive control of delay systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 4, pp. 767-779

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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.

DOI : 10.1051/cocv:2008009
Classification : 49K15, 49K25
Keywords: optimal control, impulse control, switched systems, delay systems, calculus of variation 
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     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://geodesic.mathdoc.fr/articles/10.1051/cocv:2008009/}
}
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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

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