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Limits of the Robustness Paradigm

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Randomized Algorithms for Analysis and Control of Uncertain Systems

Part of the book series: Communications and Control Engineering ((CCE))

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Abstract

This chapter discusses the limits of the classical robustness paradigm and set the motivation and ground for the probabilistic approach to analysis and design. In particular, it introduces the notions of complexity, decidability, conservatism and discontinuity problems, with specific emphasis on NP-hard problems arising in the context of control systems, illustrated by several examples.

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Notes

  1. 1.

    The notation O(⋅) means the following: for functions f,g:ℝ+→ℝ+, we write f(n)=O(g(n)) if there exist positive numbers n 0 and c such that f(n)≤cg(n) for all n≥n 0.

  2. 2.

    The frequently used terminology “curse of dimensionality” has been coined by Bellman in 1957 in his classical book on dynamic programming [49].

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Authors and Affiliations

  1. CNR - IEIIT, Politecnico di Torino, Turin, Italy

    Roberto Tempo & Fabrizio Dabbene

  2. Dip. Automatica e Informatica, Politecnico di Torino, Turin, Italy

    Giuseppe Calafiore

Authors
  1. Roberto Tempo
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  2. Giuseppe Calafiore
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  3. Fabrizio Dabbene
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Tempo, R., Calafiore, G., Dabbene, F. (2013). Limits of the Robustness Paradigm. In: Randomized Algorithms for Analysis and Control of Uncertain Systems. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-4610-0_5

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  • DOI: https://doi.org/10.1007/978-1-4471-4610-0_5

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-4609-4

  • Online ISBN: 978-1-4471-4610-0

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