Difference between revisions of "Category:Path-constrained arcs"
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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 < | + | 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 19:54, 20 January 2016
Whenever a path constraint is active, i.e., it holds ![c_i(x(t)) = 0 \; \forall \; t \in [t^\text{start}, t^\text{end}] \subseteq [0, t_f]](https://mintoc.de/images/math/b/2/a/b2ae1f8d2da30f32c01f209278698096.png)
, and no continuous control 
can be determined to compensate for the changes in 
, naturally 
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
, 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/>
Pages in category "Path-constrained arcs"
The following 10 pages are in this category, out of 10 total.
