Precision Tracking for Nonminimum Phase LPTV Systems via a Lifted Time Stable Inversion

• 成果类型: Article
• 署名作者: Zhu, Shaoqin; Ji, Xiaoqiang; Longman, Richard W.; Xu, Yangsheng
• 署名单位: The Chinese University of Hong Kong, Shenzhen; Shenzhen Institute of Artificial Intelligence & Robotics for Society; Columbia University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3550382
• 发表日期: 2025
• 页码: 6096-6103
• 关键词: Linear systems; Time-varying systems; Matrix decomposition; Filtering theory; Feedforward systems; vectors; Artificial intelligence; training; reviews; regulation; Feedforward control; linear periodic time-varying systems; nonminimum phase; stable inversion

摘要

Feedforward control demonstrates the capacity of precision tracking in applications, typically necessitating the solution of the inverse model. For nonminimum phase systems with unstable internal dynamics, the inverse model yields unbounded inputs, impeding the implementation of the feedforward control method. Existing stable inversion leverages noncausal input and initial state transition to achieve exact tracking with an infinite time preview of the output. However, a limited preview window results in tracking errors, and the existence of the optimal transition relies on the invertibility of the Grammian matrix. Recently, a novel stable inversion based on lifting time systems has been introduced. It enables finite-time precision tracking without an infinite preview window and exhibits significant application potential, though confined to linear time-invariant systems. From the perspective of the lifted system, this article addresses the stable inversion problem in finite time for multivariate linear periodic time-varying systems leveraging the equivalence between the linear periodic time-varying system and its lifted system. Simulation is designed to validate the effectiveness of the results.