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Information entropy and state observation of a dynamical system

  • Section IV Information Theoretic Approach
  • Conference paper
  • First Online:
Uncertainty in Knowledge-Based Systems (IPMU 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 286))

Abstract

An hereditary linear "observation operator" ℓ gives at instant t an image y(t) of the state x of a dynamical differential linear system whose initial state is known only through a probability distribution with information entropy Hx(to). The information entropy Hy(t) of the probability distribution of y(t) is equal to Hx(to) plus a "dynamical gain fo information entropy" and an "observational gain of information entropy". The dynamical gain involves the trace of the evolution matrix of the system. The observational gain involves ℓ and the fundamental matrix of the system. Special cases are presented, one involving a "generalized Laplace transform with matrix argument".

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References

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Author information

Authors and Affiliations

  1. Université Paris-Nord, 2, rue de Vouillé, F-75015, Paris

    Robert Vallée

Authors
  1. Robert Vallée
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Editor information

B. Bouchon R. R. Yager

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© 1987 Springer-Verlag Berlin Heidelberg

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Vallée, R. (1987). Information entropy and state observation of a dynamical system. In: Bouchon, B., Yager, R.R. (eds) Uncertainty in Knowledge-Based Systems. IPMU 1986. Lecture Notes in Computer Science, vol 286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18579-8_38

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  • DOI: https://doi.org/10.1007/3-540-18579-8_38

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18579-6

  • Online ISBN: 978-3-540-48020-4

  • eBook Packages: Springer Book Archive

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