# A simple trolley-like model in the presence of a nonlinear friction and a bounded fuel expenditure

Andrei Dmitruk; Ivan Samylovskiy

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2013)

- Volume: 33, Issue: 2, page 135-147
- ISSN: 1509-9407

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topAndrei Dmitruk, and 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 33.2 (2013): 135-147. <http://eudml.org/doc/270640>.

@article{AndreiDmitruk2013,

abstract = {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.},

author = {Andrei Dmitruk, Ivan Samylovskiy},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {optimal control problem; Pontryagin Maximum Principle; extremals; singular arcs; Pontryagin's maximum principle},

language = {eng},

number = {2},

pages = {135-147},

title = {A simple trolley-like model in the presence of a nonlinear friction and a bounded fuel expenditure},

url = {http://eudml.org/doc/270640},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Andrei Dmitruk

AU - Ivan Samylovskiy

TI - A simple trolley-like model in the presence of a nonlinear friction and a bounded fuel expenditure

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2013

VL - 33

IS - 2

SP - 135

EP - 147

AB - 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.

LA - eng

KW - optimal control problem; Pontryagin Maximum Principle; extremals; singular arcs; Pontryagin's maximum principle

UR - http://eudml.org/doc/270640

ER -

## References

top- [1] R.H. Goddard, A method on reaching extreme altitudes Smitsonian Miscellaneous Collection 71 (1919) 82 pages
- [2] J.F. Bonnans, P. Martinon and E. Trelat, Singular arcs in the generalized Goddard's Problem, JOTA 139 (2008) 439-461. doi: 10.1007/s10957-008-9387-1 Zbl1159.49027
- [3] P. Martinon, F. Bonnans, J. Laurent-Varin and E. Trelat, Numerical study of optimal trajectories with singular arcs for an Ariane 5 launcher, J. Guidance, Control, and Dynamics 32 (2009) 51-55. doi: 10.2514/1.37387
- [4] C. Ponssard, K. Graichen, N. Petit and J. Laurent-Varin, Ascent optimization for a heavy space launcher, Proceedings of the European Control Conference 2009, Budapest, Hungary (2009) 3033-3038.

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