View source for Category:Path-constrained arcs

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. 

== References ==
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[[Category:Solution characterization]]