Solving Nonlinear Algebraic Loops Arising in Input-Saturated Feedbacks

• 成果类型: Article
• 署名作者: Blanchini, Franco; Giordano, Giulia; Riz, Francesco; Zaccarian, Luca
• 署名单位: University of Udine; University of Trento; University of Trento; University of Trento; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3170858
• 发表日期: 2023
• 页码: 2079-2093
• 关键词: Algebraic loop; anti-windup; Constrained control; deadzone loops; input saturation; nonlinear control systems

摘要

In this article, we propose a dynamic augmentation scheme for the asymptotic solution of the nonlinear algebraic loops arising in well-known input saturated feedbacks typically designed by solving linear matrix inequalities. We prove that the existing approach based on dynamic augmentation, which replaces the static loop by a dynamic one through the introduction of a sufficiently small time constant, works under some restrictive sufficient well-posedness conditions, requiring the existence of a diagonal Lyapunov matrix. However it can fail in general, even when the algebraic loop is well-posed. Then, we propose a novel approach whose effectiveness is guaranteed whenever well-posedness holds. We also show how this augmentation allows preserving the guaranteed region of attraction with Lyapunov-based designs, as long as a gain parameter is sufficiently large. We finally propose an adaptive version of the scheme where this parameter is adjusted online. Simulation results show the effectiveness of the proposed solutions.