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

Abstract

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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.

How to cite

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Andrei 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

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  1. [1] R.H. Goddard, A method on reaching extreme altitudes Smitsonian Miscellaneous Collection 71 (1919) 82 pages 
  2. [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. [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. [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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