Applications of Mathematics, first online, pp. 1-14

Inverse rate-dependent Prandtl-Ishlinskii operators and applications

Mohammad Al Janaideh, Pavel Krejčí, Giselle Antunes Monteiro

Received September 27, 2022.   Published online February 9, 2023.

Abstract:  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.
Keywords:  hysteresis; Prandtl-Ishlinskii operator; inverse rate-dependent Prandtl-Ishlinskii operator
Classification MSC:  74N30, 47J40

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Affiliations:   Mohammad Al Janaideh, Department of Mechanical Engineering, Memorial University, St. John's, Newfoundland A1B 3X5, Canada, e-mail:; Pavel Krejčí, Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 166 29 Praha 6, Czech Republic, e-mail:; Giselle Antunes Monteiro (corresponding author), Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic, e-mail:

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