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Asymptotic expansions for singularly perturbed differential matrix riccati equations with applications to linear — Quadratic optimization problems

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Asymptotic Analysis II —

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 985))

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Abstract

A general optimization problem with quadratic cost for linear systems leads to the study of a singularly perturbed matrix Riccati differential equations if the dynamics is described by a singularly perturbed system. A similar singularly perturbed Riccati equation arises in the cheap control problems. These problems motivate the asymptotic expansions obtained in the paper.

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References

  1. P.V. Kokotovic,R.E. O’Malley Jr.,P. Sannuti, 1976, Singular perturbations and order reduction in control theory.An overview, Automatica,vol. 12,123–132.

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Authors and Affiliations

  1. Facultatea de matematicĂ, Universitatea din Bucureşti, R-70109, Bucureşti, Romania

    V. DrĂgan

Authors
  1. V. DrĂgan
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F. Verhulst

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© 1983 Springer-Verlag

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DrĂgan, V. (1983). Asymptotic expansions for singularly perturbed differential matrix riccati equations with applications to linear — Quadratic optimization problems. In: Verhulst, F. (eds) Asymptotic Analysis II —. Lecture Notes in Mathematics, vol 985. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062377

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  • DOI: https://doi.org/10.1007/BFb0062377

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12286-9

  • Online ISBN: 978-3-540-39612-3

  • eBook Packages: Springer Book Archive

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