Geodesic
A maximum principle for smooth optimal impulsive control problems with multipoint state constraints
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 6, pp. 981-997

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A nonlinear optimal impulsive control problem with trajectories of bounded variation subject to intermediate state constraints at a finite number on nonfixed instants of time is considered. Features of this problem are discussed from the viewpoint of the extension of the classical optimal control problem with the corresponding state constraints. A necessary optimality condition is formulated in the form of a smooth maximum principle; thorough comments are given, a short proof is presented, and examples are discussed. 
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     author = {V. A. Dykhta and O. N. Samsonyuk},
     title = {A~maximum principle for smooth optimal impulsive control problems with multipoint state constraints},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {981--997},
     publisher = {mathdoc},
     volume = {49},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_6_a4/}
}
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V. A. Dykhta; O. N. Samsonyuk. A maximum principle for smooth optimal impulsive control problems with multipoint state constraints. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 6, pp. 981-997. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_6_a4/