Abstract

Multiple shooting is an indirect solution method for complicated optimal control problems. It yields precise numerical solutions. The rate of convergence is usually quadratic due to the underlying Newton type method. However, it was recently noticed that if the general necessary conditions of optimal control are applied to state constrained problem formulations from aerospace engineering the method decelerates often to a slow linear rate of convergence. We identify the culprit, namely the appearance of a quadratic control component in the optimal control problem and certain boundary and/or interior point conditions. Finally we provide a reformulation of these boundary and/or interior point conditions in order to avoid this situation.

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