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 < | 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 == | ||
< | <biblist /> | ||
[[Category:Solution characterization]] | [[Category:Solution characterization]] | ||
Latest revision as of 10:10, 23 January 2016
Whenever a path constraint is active, i.e., it holds , 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
| [Sager2009] | Sager, S.; Reinelt, G.; Bock, H.G. (2009): Direct Methods With Maximal Lower Bound for Mixed-Integer Optimal Control Problems. Mathematical Programming, 118, 109--149 | |
Pages in category "Path-constrained arcs"
The following 11 pages are in this category, out of 11 total.