Category:Path-constrained arcs

Whenever a path constraint is active, i.e., it holds ${\displaystyle c_i(x(t))=0\mathrm{\forall }t\in [t^{\text{start}},t^{\text{end}}]\subseteq [0,t_f]}$, and no continuous control ${\displaystyle u(\cdot )}$ can be determined to compensate for the changes in ${\displaystyle x(\cdot )}$, naturally ${\displaystyle \alpha (\cdot )}$ 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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