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Design criteria for uncertain models with structured and unstructured uncertainties

  • Part I Identification For Robust Control
  • Conference paper
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Robustness in identification and control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 245))

Abstract

This paper introduces and solves a weighted game-type cost criterion for estimation and control purposes that allows for a general class of uncertainties in the model or data. Both structured and unstructured uncertainties are allowed, including some special cases that have been used in the literature. The optimal solution is shown to satisfy an orthogonality condition similar to least-squares designs, except that the weighting matrices need to be modified in a certain optimal manner. One particular application in the context of state regulation for uncertain state-space models is considered. It is shown that in this case, the solution leads to a control law with design equations that are similar in nature to LQR designs. The gain matrix, however, as well as the Riccati variable, turn out to be state-dependent in a certain way. Further applications of these game-type formulations to image processing, estimation, and communications are discussed in [1–3].

This material was based on work supported in part by the National Science Foundation under Award No. CCR-9732376. The work of V. H. Nascimento was also supported by a fellowship from CNPq - Brazil, while on leave from Escola Politécnica da Universidade de São Paulo.

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Author information

Authors and Affiliations

  1. Adaptive and Nonlinear Systems Laboratory, Electrical Engineering Department, University of California, 90024, Los Angeles, CA

    Ali H. Sayed & Vitor H. Nascimento

Authors
  1. Ali H. Sayed
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  2. Vitor H. Nascimento
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Editor information

A. Garulli (Assistant Professor)A. Tesi (Assistant Professor)

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© 1999 Springer-Verlag London Limited

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Sayed, A.H., Nascimento, V.H. (1999). Design criteria for uncertain models with structured and unstructured uncertainties. In: Garulli, A., Tesi, A. (eds) Robustness in identification and control. Lecture Notes in Control and Information Sciences, vol 245. Springer, London. https://doi.org/10.1007/BFb0109867

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  • DOI: https://doi.org/10.1007/BFb0109867

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-179-5

  • Online ISBN: 978-1-84628-538-7

  • eBook Packages: Springer Book Archive

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