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Solution differentiability for parametric nonlinear control problems with inequality constraints

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System Modelling and Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 197))

Abstract

This paper considers parametric nonlinear control problems subject to mixed control-state constraints. The data perturbations are modeled by a parameter p of a Banach space. Using recent second-order sufficient conditions (SSC) it is shown that the optimal solution and the adjoint multipliers are differentiable functions of the parameter. The proof blends numerical shooting techniques for solving the associated boundary value problem with theoretical methods for obtaining SSC. In a first step, a differentiable family of extremals for the underlying parametric boundary value problem is constructed by assuming the regularity of the shooting matrix. Optimality of this family of extremals can be established in a second step when SSC are imposed.

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Author information

Authors and Affiliations

  1. Institut für Numerische und instrumentelle Mathematik, Westfälische Wilhelms-Universität Münster, Einsteinstrasse 62, 48149, Münster, Germany

    Helmut Maurer & Hans Josef Pesch

  2. Mathematisches Institut, Technische Universität München, Arcisstrasse 21, 80333, München, Germany

    Helmut Maurer & Hans Josef Pesch

Authors
  1. Helmut Maurer
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  2. Hans Josef Pesch
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Jacques Henry Jean-Pierre Yvon

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© 1994 Springer-Verlag

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Maurer, H., Pesch, H.J. (1994). Solution differentiability for parametric nonlinear control problems with inequality constraints. In: Henry, J., Yvon, JP. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035492

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  • DOI: https://doi.org/10.1007/BFb0035492

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19893-2

  • Online ISBN: 978-3-540-39337-5

  • eBook Packages: Springer Book Archive

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