Geodesic
Mix of controls and the Pontryagin maximum principle
Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 4, pp. 5-20

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In this paper, necessary conditions for a minimum (the Pontryagin maximum principle) for an optimal control problem are proved on the basis of the concept of a mix, which enables one to reduce the study of the original problem to some approximation thereof, which is linear in the control. The study of the latter problem proves more simple. 
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     author = {E. R. Avakov and G. G. Magaril-Il'yaev},
     title = {Mix of controls and the {Pontryagin} maximum principle},
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E. R. Avakov; G. G. Magaril-Il'yaev. Mix of controls and the Pontryagin maximum principle. Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 4, pp. 5-20. http://geodesic.mathdoc.fr/item/FPM_2014_19_4_a0/