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Category:Path-constrained arcs: Difference between revisions

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Whenever a path constraint is active, i.e., it holds <math>c_i(x(t)) = 0 \; \forall \; t \in [t^\text{start}, t^\text{end}] \subseteq [0, t_f]</math>, and no continuous control <math>u(\cdot)</math> can be determined to compensate for the changes in <math>x(\cdot)</math>, naturally <math>\alpha(\cdot)</math> needs to do so by taking values in the interior of its feasible domain. An illustrating example has been given in <bibref>Sager2009</bibref>, where velocity limitations for the energy-optimal operation of New York subway trains are taken into account. The optimal integer solution does only exist in the limit case of infinite switching (Zeno behavior), or when a tolerance is given.  
Whenever a path constraint is active, i.e., it holds <math>c_i(x(t)) = 0 \; \forall \; t \in [t^\text{start}, t^\text{end}] \subseteq [0, t_f]</math>, and no continuous control <math>u(\cdot)</math> can be determined to compensate for the changes in <math>x(\cdot)</math>, naturally <math>\alpha(\cdot)</math> needs to do so by taking values in the interior of its feasible domain. An illustrating example has been given in <bib id="Sager2009" />, where velocity limitations for the energy-optimal operation of New York subway trains are taken into account. The optimal integer solution does only exist in the limit case of infinite switching (Zeno behavior), or when a tolerance is given.  


== References ==
== References ==

Revision as of 17:54, 20 January 2016

Whenever a path constraint is active, i.e., it holds ci(x(t))=0∀t∈[tstart,tend]⊆[0,tf], and no continuous control u(⋅) can be determined to compensate for the changes in x(⋅), naturally α(⋅) needs to do so by taking values in the interior of its feasible domain. An illustrating example has been given in [Sager2009]Author: Sager, S.; Reinelt, G.; Bock, H.G.
Journal: Mathematical Programming
Number: 1
Pages: 109--149
Title: Direct Methods With Maximal Lower Bound for Mixed-Integer Optimal Control Problems
Url: http://mathopt.de/PUBLICATIONS/Sager2009.pdf
Volume: 118
Year: 2009
Link to Google Scholar
, where velocity limitations for the energy-optimal operation of New York subway trains are taken into account. The optimal integer solution does only exist in the limit case of infinite switching (Zeno behavior), or when a tolerance is given.

References

<bibreferences/>