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

C. Büskens and R. Griesse
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C. Büskens: Universität Bremen
R. Griesse: Austrian Academy of Sciences

Journal of Optimization Theory and Applications, 2006, vol. 131, issue 1, No 2, 17-35

Abstract: 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.

Keywords: Perturbed optimal control problems; control-state constraints; nonlinear programming methods; partial differential equations; parametric sensitivity analysis (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10957-006-9122-8

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