Abstract
It is well known that many dynamical systems exhibit hysteresis behaviour in one way or another. Usually this is connected to some memory mechanism present within the system. Within a mathematical model, such a mechanism either can be built in explicitly, or it can be an implicit consequence of the model equations. The former approach has been pursued by Krasnoselskii and several collaborators: They define an operator W, which maps a scalar input function \(x = x(t)\) to a scalar output function \(y = y(t)\)
by a three-step procedure which formalizes the intuitive content of figure 1.
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References
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© 1988 Birkhäuser Verlag Basel
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Brokate, M. (1988). Optimal Control of ODE Systems with Hysteresis Nonlinearities. In: Hoffmann, KH., Zowe, J., Hiriart-Urruty, JB., Lemarechal, C. (eds) Trends in Mathematical Optimization. International Series of Numerical Mathematics/Internationale Schriftenreihe zur Numerischen Mathematik/Série internationale d’Analyse numérique, vol 84. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9297-1_2
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DOI: https://doi.org/10.1007/978-3-0348-9297-1_2
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