Geodesic
Existence theorems on optimizing functions for optimal systems with distributed parameters
Izvestiya. Mathematics , Tome 4 (1970) no. 3, pp. 697-719

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Existence theorems on optimal controls for systems with distributed parameters and with trajectories given by a general operator of the form $u_p(t,\omega,v)$ are proved. A set of quasiregular functionals is chosen as a criterion of optimality of the process. Such a choice essentially exhausts the cases which are practically interesting in applications. 
@article{IM2_1970_4_3_a11,
     author = {V. I. Plotnikov},
     title = {Existence theorems on optimizing functions for optimal systems with distributed parameters},
     journal = {Izvestiya. Mathematics },
     pages = {697--719},
     publisher = {mathdoc},
     volume = {4},
     number = {3},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_3_a11/}
}
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V. I. Plotnikov. Existence theorems on optimizing functions for optimal systems with distributed parameters. Izvestiya. Mathematics , Tome 4 (1970) no. 3, pp. 697-719. http://geodesic.mathdoc.fr/item/IM2_1970_4_3_a11/