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Qualitative theory and computational aspects of large scale dynamic nonlinear systems — A review and some open questions

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Modelling and Adaptive Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 105))

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Abstract

Deterministic nonlinear large scale dynamical systems are considered as the interconnection of subsystems described by n-ports having nonlinear memoryless and/or memory-type characteristics.

Statements and conditions are given in terms of interconnection and subsystem characteristics. The particular questions considered, mostly in the time domain, are :

the uniqueness of the solution,

the qualitative properties of the solution,

the uniqueness of the computed solution,

the convergence of the computations,

the complexity of the computations in terms of the complexity of the systems and the computing machines and

the choice of the time step in large systems.

Furthermore, the role of the choice of the state variables, the role of the qualitative properties of the subsystem characteristics, the choice of the nonlinear models in large systems and the controversial role of asymptotic results in guessing the complexity of computations are discussed.

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Authors and Affiliations

  1. Computer and Automation Institute, Hungarian Academy of Sciences, Uri-u 49, H-1014, Budapest

    T. Roska

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  1. T. Roska
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Christopher Ian Byrnes Alexander B. Kurzhanski

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© 1988 Springer-Verlag

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Roska, T. (1988). Qualitative theory and computational aspects of large scale dynamic nonlinear systems — A review and some open questions. In: Byrnes, C.I., Kurzhanski, A.B. (eds) Modelling and Adaptive Control. Lecture Notes in Control and Information Sciences, vol 105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043194

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  • DOI: https://doi.org/10.1007/BFb0043194

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19019-6

  • Online ISBN: 978-3-540-38904-0

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