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arXiv · 2608.17791

Optimal W-infinity Control of Prandtl-Ishlinskii Hysteresis Model via Weak Derivatives

Daniel Neri Cardoso·Petrus Emmanuel Oliveira Gomes Brant Abreu·Guilherme Vianna Raffo
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Abstract

This work proposes a novel robust optimal W-infinity controller for dynamic systems with Prandtl-Ishlinskii hysteresis. By utilizing weighted Sobolev spaces Wm,p,Gamma, the approach uses weak derivatives to rigorously handle the non-differentiable, input non-affine nature of hysteresis. This formulation recasts the Prandtl-Ishlinskii operator as a bounded uncertainty multiplying the input rate, enabling robust optimal controller design via linear matrix inequalities, while guaranteeing W3,2,Gamma-stability with a W-infinity-gain bound. A numerical study on a piezoelectric actuator model validates its effectiveness, demonstrating asymptotic tracking and the attenuation of both hysteresis and external disturbances through a straightforward implementation.

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Daniel Neri Cardoso, Petrus Emmanuel Oliveira Gomes Brant Abreu, Guilherme Vianna Raffo. 2026-08-18. Optimal W-infinity Control of Prandtl-Ishlinskii Hysteresis Model via Weak Derivatives. https://arxiv.org/abs/2608.17791

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