Geodesic
Necessary Optimality Conditions for a~Class of Optimal Control Problems with Discontinuous Integrand
Informatics and Automation, Optimal control, Tome 262 (2008), pp. 222-239

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a nonlinear optimal control problem with an integral functional in which the integrand contains the characteristic function of a given closed subset of the phase space. Using an approximation method, we prove necessary optimality conditions in the form of the Pontryagin maximum principle without any a priori assumptions about the behavior of an optimal trajectory. 
@article{TRSPY_2008_262_a16,
     author = {A. I. Smirnov},
     title = {Necessary {Optimality} {Conditions} for {a~Class} of {Optimal} {Control} {Problems} with {Discontinuous} {Integrand}},
     journal = {Informatics and Automation},
     pages = {222--239},
     publisher = {mathdoc},
     volume = {262},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2008_262_a16/}
}
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A. I. Smirnov. Necessary Optimality Conditions for a~Class of Optimal Control Problems with Discontinuous Integrand. Informatics and Automation, Optimal control, Tome 262 (2008), pp. 222-239. http://geodesic.mathdoc.fr/item/TRSPY_2008_262_a16/