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Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems Using Boundary Value Methods

In: Online Optimization of Large Scale Systems

Author

Listed:
  • Helmut Maurer

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

  • Dirk Augustin

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

Abstract

Parametric nonlinear control problems subject to mixed control-state constraints and pure state constraints are investigated. Parameters are introduced to model perturbations of the control system and may appear in all system data. We review conditions under which the optimal solutions are differentiable functions of the parameter. In the theoretical part, these conditions are related to regularity conditions and to second order sufficient conditions. On the numerical side, the conditions are connected to shooting methods for solving the boundary value problems that characterize the optimal solution. We discuss methods for computing the sensitivity differentials of the optimal solutions with respect to parameters. The calculated sensitivity differentials can be used to construct real-time approximations of the perturbed solutions via first order Taylor expansions. Two numerical case studies are discussed in detail to illustrate the numerical methods for mixed control-state constraints and for pure state constraints.

Suggested Citation

  • Helmut Maurer & Dirk Augustin, 2001. "Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems Using Boundary Value Methods," Springer Books, in: Martin Grötschel & Sven O. Krumke & Jörg Rambau (ed.), Online Optimization of Large Scale Systems, pages 17-55, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04331-8_2
    DOI: 10.1007/978-3-662-04331-8_2
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