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Parametric Sensitivity Analysis of Perturbed PDE Optimal Control Problems with State and Control Constraints

  • C. Büskens
  • R. Griesse
Article

Abstract

We study parametric optimal control problems governed by a system of time-dependent partial differential equations (PDE) and subject to additional control and state constraints. An approach is presented to compute the optimal control functions and the so-called sensitivity differentials of the optimal solution with respect to perturbations. This information plays an important role in the analysis of optimal solutions as well as in real-time optimal control.

The method of lines is used to transform the perturbed PDE system into a large system of ordinary differential equations. A subsequent discretization then transcribes parametric ODE optimal control problems into perturbed nonlinear programming problems (NLP), which can be solved efficiently by SQP methods.

Second-order sufficient conditions can be checked numerically and we propose to apply an NLP-based approach for the robust computation of the sensitivity differentials of the optimal solutions with respect to the perturbation parameters. The numerical method is illustrated by the optimal control and sensitivity analysis of the Burgers equation.

Key Words

Perturbed optimal control problems control-state constraints nonlinear programming methods partial differential equations parametric sensitivity analysis 

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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • C. Büskens
    • 1
  • R. Griesse
    • 2
  1. 1.Center for Technical MathematicsUniversität BremenBremenGermany
  2. 2.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria

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