Geodesic
Optimal synthesis in an infinite-dimensional space
Informatics and Automation, Differential equations and topology. II, Tome 271 (2010), pp. 40-58

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For a class of optimal control problems and Hamiltonian systems generated by these problems in the space $l_2$, we prove the existence of extremals with a countable number of switchings on a finite time interval. The optimal synthesis that we construct in the space $l_2$ forms a fiber bundle with piecewise smooth two-dimensional fibers consisting of extremals with a countable number of switchings over an infinite-dimensional basis of singular extremals. 
@article{TRSPY_2010_271_a4,
     author = {V. F. Borisov and M. I. Zelikin and L. A. Manita},
     title = {Optimal synthesis in an infinite-dimensional space},
     journal = {Informatics and Automation},
     pages = {40--58},
     publisher = {mathdoc},
     volume = {271},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2010_271_a4/}
}
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V. F. Borisov; M. I. Zelikin; L. A. Manita. Optimal synthesis in an infinite-dimensional space. Informatics and Automation, Differential equations and topology. II, Tome 271 (2010), pp. 40-58. http://geodesic.mathdoc.fr/item/TRSPY_2010_271_a4/