Geodesic
Inverse rate-dependent Prandtl-Ishlinskii operators and applications
Applications of Mathematics, Tome 68 (2023) no. 6, pp. 713-726

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In the past years, we observed an increased interest in rate-dependent hysteresis models to characterize complex time-dependent nonlinearities in smart actuators. A natural way to include rate-dependence to the Prandtl-Ishlinskii model is to consider it as a linear combination of play operators whose thresholds are functions of time. In this work, we propose the extension of the class of rate-dependent Prandtl-Ishlinskii operators to the case of a whole continuum of play operators with time-dependent thresholds. We prove the existence of an analytical inversion formula, and illustrate its applicability in the study of error bounds for inverse compensation.
DOI : 10.21136/AM.2023.0231-22
Classification : 47J40, 74N30
Keywords: hysteresis; Prandtl-Ishlinskii operator; inverse rate-dependent Prandtl-Ishlinskii operator 
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Al Janaideh, Mohammad; Krejčí, Pavel; Monteiro, Giselle Antunes. Inverse rate-dependent Prandtl-Ishlinskii operators and applications. Applications of Mathematics, Tome 68 (2023) no. 6, pp. 713-726. doi: 10.21136/AM.2023.0231-22

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