Abstract
The sensitivity analysis for state constrained optimal control problems [7, 8] is illustrated by a practically relevant problem: the optimal control of a container crane based on a model developed in [12]. The container crane is subject to a state constraint on the vertical velocity. The multiple shooting method is used to determine a highly precise nominal solution which is still lacking in the literature. Second order sufficient conditions are checked by showing that an associated Riccati equation has a bounded solution. Sensitivity differentials of optimal solutions are computed with respect to perturbations in the swing angle and velocity. This allows for a fast computation of real-time approximations of perturbed optimal solutions.
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Augustin, D., Maurer, H. (2001). Sensitivity Analysis and Real-Time Control of a Container Crane under State Constraints. In: Grötschel, M., Krumke, S.O., Rambau, J. (eds) Online Optimization of Large Scale Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04331-8_4
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DOI: https://doi.org/10.1007/978-3-662-04331-8_4
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