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Discrete-State Abstractions of Nonlinear Systems Using Multi-resolution Quantizer

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Hybrid Systems: Computation and Control (HSCC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5469))

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Abstract

This paper proposes a design method for discrete abstractions of nonlinear systems using multi-resolution quantizer, which is capable of handling state dependent approximation precision requirements. To this aim, we extend the notion of quantizer embedding, which has been proposed by the authors’ previous works as a transformation from continuous-state systems to discrete-state systems, to a multi-resolution setting. Then, we propose a computational method that analyzes how a locally generated quantization error is propagated through the state space. Based on this method, we present an algorithm that generates a multi-resolution quantizer with a specified error precision by finite refinements. Discrete abstractions produced by the proposed method exhibit non-uniform distribution of discrete states and inputs.

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Author information

Authors and Affiliations

  1. Tokyo Institute of Technology, ĹŚokayama 2-12-1, Meguro, Tokyo, Japan

    Yuichi Tazaki & Jun-ichi Imura

Authors
  1. Yuichi Tazaki
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  2. Jun-ichi Imura
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of California, 4531E Boelter Hall, CA 90095, Los Angeles, USA

    Rupak Majumdar

  2. Department of Electrical Engineering, University of California, 66-147F Engineering, IV Building, CA 90095-1594, Los Angeles, USA

    Paulo Tabuada

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Tazaki, Y., Imura, Ji. (2009). Discrete-State Abstractions of Nonlinear Systems Using Multi-resolution Quantizer. In: Majumdar, R., Tabuada, P. (eds) Hybrid Systems: Computation and Control. HSCC 2009. Lecture Notes in Computer Science, vol 5469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00602-9_25

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  • DOI: https://doi.org/10.1007/978-3-642-00602-9_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00601-2

  • Online ISBN: 978-3-642-00602-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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