基于弱导数的Prandtl-Ishlinskii迟滞模型的最优W-无穷控制
Optimal W-infinity Control of Prandtl-Ishlinskii Hysteresis Model via Weak Derivatives
AI总结：
本研究针对含Prandtl-Ishlinskii迟滞的动态系统，利用加权Sobolev空间与弱导数设计鲁棒最优W-无穷控制器，通过线性矩阵不等式实现控制器设计，经压电致动器模型验证可实现渐近跟踪并衰减迟滞与外部扰动。
AI中文摘要：
本研究针对含Prandtl-Ishlinskii迟滞的动态系统，提出一种新型鲁棒最优W-无穷控制器。通过利用加权Sobolev空间Wm,p,Γ，该方法采用弱导数严格处理迟滞的不可微、输入非仿射特性。此公式将Prandtl-Ishlinskii算子重构为乘于输入变化率的有界不确定性，可通过线性矩阵不等式实现鲁棒最优控制器设计，同时保证W3,2,Γ稳定性及W-无穷增益界。针对压电致动器模型的数值研究验证了该方法的有效性，其通过简单实现即可实现渐近跟踪，同时衰减迟滞与外部扰动。
英文摘要：
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.
