We consider a problem of maximization of the distance traveled by a material point in the presence of a nonlinear friction under a bounded thrust and fuel expenditure. Using the maximum principle we obtain the form of optimal control and establish conditions under which it contains a singular subarc. This problem seems to be the simplest one having a mechanical sense in which singular subarcs appear in a nontrivial way.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1148,
author = {Andrei Dmitruk and Ivan Samylovskiy},
title = {A simple trolley-like model in the presence of a nonlinear friction and a bounded fuel expenditure},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {33},
year = {2013},
pages = {135-147},
zbl = {1297.49030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1148}
}
Andrei Dmitruk; Ivan Samylovskiy. A simple trolley-like model in the presence of a nonlinear friction and a bounded fuel expenditure. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 33 (2013) pp. 135-147. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1148/
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