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Model Equations: Restoration of Equivalent Characteristics

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Extracting Knowledge From Time Series

Part of the book series: Springer Series in Synergetics ((SSSYN))

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Abstract

In the case called “grey box” in Sect. 5.2, a researcher has partial knowledge about the structure of model equations \({{\mathbf{x}}_{n + 1}} = {\mathbf{f}}({{\mathbf{x}}_n},{\mathbf{c}})\) or \({{{\mathrm{d}}{\mathbf{x}}} \mathord{\left/ {\vphantom {{{\mathrm{d}}{\mathbf{x}}} {{\mathrm{d}}t}}} \right. \kern-\nulldelimiterspace} {{\mathrm{d}}t}} = {\mathbf{f}}({\mathbf{x}},{\mathbf{c}})\). More concretely, some components of the function f are unknown. Then, the problem gets more complicated, than just parameter estimation discussed in Chap. 8, and more interesting from a practical viewpoint.

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Authors and Affiliations

  1. Saratov State University, Astrakhanskaya Street 83, 410012, Saratov, Russia

    Prof. Boris P. Bezruchko

  2. Russian Academy of Science, V.A. Kotel’nikov Institute of RadioEngineering and Electronics, Saratov Branch, Zelyonaya Str. 38, 410019, Saratov, Russia

    Dr. Dmitry A. Smirnov

Authors
  1. Prof. Boris P. Bezruchko
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  2. Dr. Dmitry A. Smirnov
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Correspondence to Boris P. Bezruchko .

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Bezruchko, B.P., Smirnov, D.A. (2010). Model Equations: Restoration of Equivalent Characteristics. In: Extracting Knowledge From Time Series. Springer Series in Synergetics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12601-7_9

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  • DOI: https://doi.org/10.1007/978-3-642-12601-7_9

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