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Computational Complexity Issues in Robust Control

Encyclopedia of Systems and Control

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Abstract

Robust control theory has introduced several new and challenging problems for researchers. Some of these problems have been solved by innovative approaches and led to the development of new and efficient algorithms. However, some of the other problems in robust control theory had attracted significant amount of research, but none of the proposed algorithms were efficient, namely, had execution time bounded by a polynomial of the “problem size.” Several important problems in robust control theory are either of decision type or of computation/approximation type, and one would like to have an algorithm which can be used to answer all or most of the possible cases and can be executed on a classical computer in reasonable amount of time. There is a branch of theoretical computer science, called theory of computation, which can be used to study the difficulty of problems in robust control theory. In the following, classical computer system, algorithm, efficient algorithm, unsolvability, tractability, NP-hardness, and NP-completeness will be introduced in a more rigorous fashion, with applications to problems from robust control theory.

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Authors and Affiliations

  1. Fatih University, Istanbul, Turkey

    Onur Toker

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  1. Onur Toker
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Correspondence to Onur Toker .

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Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

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© 2014 Springer-Verlag London

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Toker, O. (2014). Computational Complexity Issues in Robust Control. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_130-2

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_130-2

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  • Online ISBN: 978-1-4471-5102-9

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Chapter history

  1. Latest

    Computational Complexity in Robustness Analysis and Design
    Published:
    10 August 2020

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_130-3

  2. Computational Complexity Issues in Robust Control
    Published:
    07 March 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_130-2

  3. Original

    Computational Complexity Issues in Robust Control
    Published:
    12 February 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_130-1

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