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Estimation of Controllable Initial Fuzzy States of Linear Time-Invariant Dynamical Systems

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Mathematical Modelling and Scientific Computation (ICMMSC 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 283))

Abstract

In this paper, we consider linear time-invariant dynamical systems with fuzzy initial condition. Dynamics of such systems is given by linear time-invariant fuzzy differential equations. First, we discuss the evolution of solution to such fuzzy differential dynamical systems and also establish the existence and uniqueness of the solution. We then provide an estimate of initial fuzzy state that can be controlled to a predefined target fuzzy state, that is, given any two crisp states x0, x1 in ℝn, and a fuzzy state X1 around x1, we compute a fuzzy state X0 around x0 so that X0 is fuzzy-controllable to X1. In a special case, when the plant matrix has non-negative entries, the fuzzy state X0 is fuzzy-controllable to X1 with the crisp control that steers x0 to x1. Examples are given to substantiate the results obtained.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram, 695547, India

    Bhaskar Dubey & Raju K. George

Authors
  1. Bhaskar Dubey
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  2. Raju K. George
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Gandhigram Rural University, 624302, Gandhigram, Tamil Nadu, India

    P. Balasubramaniam

  2. Department of Mathematics, Gandhigram Rural Institute - Deemed University, 624302, Gandhigram, Tamil Nadu, India

    R. Uthayakumar

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© 2012 Springer-Verlag Berlin Heidelberg

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Dubey, B., George, R.K. (2012). Estimation of Controllable Initial Fuzzy States of Linear Time-Invariant Dynamical Systems. In: Balasubramaniam, P., Uthayakumar, R. (eds) Mathematical Modelling and Scientific Computation. ICMMSC 2012. Communications in Computer and Information Science, vol 283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28926-2_34

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  • DOI: https://doi.org/10.1007/978-3-642-28926-2_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28925-5

  • Online ISBN: 978-3-642-28926-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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