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The full discretization is usually done at fixed collocation points. If the optimal profiles experience discontinuities, oscillations are introduced in the system (see left side of the figure). The OptControlCentre can move the positions of the time elements within certain (user given) bounds. The positions of the collocation points become part of the optimization problem as they are treated as optimization parameters. Results are sometimes astonishing, the oscillations around the discontinuities become much smaller. The drawback, however, is that the optimization problem itself becomes much more nonlinear and thus takes longer to solve.
The approach for moving the time elements is the following: The fixed positions of the collocation points are calculated and given as starting guesses. Margins are defined in which the points can move to both sides. The maximum margin is 49% of the length of a time element to prevent two points overlapping and thus follow to a collapse of the problem due to division by zero.
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