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Sensitivity Analysis and Real-Time Control of a Container Crane under State Constraints

In: Online Optimization of Large Scale Systems

Author

Listed:
  • Dirk Augustin

    (Westfälische Wilhelms-Universität Münster, Institut für Numerische Mathematik)

  • Helmut Maurer

    (Westfälische Wilhelms-Universität Münster, Institut für Numerische Mathematik)

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.

Suggested Citation

  • Dirk Augustin & Helmut Maurer, 2001. "Sensitivity Analysis and Real-Time Control of a Container Crane under State Constraints," Springer Books, in: Martin Grötschel & Sven O. Krumke & Jörg Rambau (ed.), Online Optimization of Large Scale Systems, pages 69-82, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04331-8_4
    DOI: 10.1007/978-3-662-04331-8_4
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