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
Title: Direct Methods With Maximal Lower Bound for Mixed-Integer Optimal Control Problems
, 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.
|[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|