On Cauchy problem and stability of inversion-free feedforward control of piecewise monotonic Krasnoselskii-Pokrovskii hysteresis

Jana Kopfova; Michael Ruderman

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arXiv · 2603.03891

On Cauchy problem and stability of inversion-free feedforward control of piecewise monotonic Krasnoselskii-Pokrovskii hysteresis

Jana Kopfova·Michael Ruderman

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Abstract

We consider the non-homogeneous first-order differential equation with hysteresis described by the Krasnoselskii-Pokrovskii rate-independent hysteresis operator. Existence and uniqueness of solutions as well as the boundedness of solution in response to a bounded input are proved. The global stability of the equation is also investigated. Periodic solutions and their stability are studied in addition. The differential equation under analysis constitutes the so-called inversion-free feedforward control, which was proposed for mitigating arbitrary rate-independent hysteresis effects in the actuated systems. The experimentally identified non-smooth and non-strictly monotonic hysteresis of a magnetic shape memory alloy (MSMA) actuator serves as the case study. The performed analysis is settled in a series of theorems which are illustrated by numerical examples.

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Jana Kopfova, Michael Ruderman. 2026-03-04. On Cauchy problem and stability of inversion-free feedforward control of piecewise monotonic Krasnoselskii-Pokrovskii hysteresis. https://arxiv.org/abs/2603.03891

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