Incremental Stabilization of Cascade Nonlinear Systems and Harmonic Regulation: A Forwarding-Based Design

• 成果类型: Article
• 署名作者: Giaccagli, Mattia; Astolfi, Daniele; Andrieu, Vincent; Marconi, Lorenzo
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Engineering & Systems Sciences (INSIS); Universite Claude Bernard Lyon 1; University of Bologna
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3358985
• 发表日期: 2024
• 页码: 4828-4835
• 关键词: Regulation; Harmonic analysis; trajectory; Feedforward systems; Closed loop systems; measurement; oscillators; Contraction theory; forwarding; harmonic regulation; incremental stability; minimum phase systems

摘要

In this work, we address the problem of designing a control law for a system in feedforward form to be globally incrementally exponentially stable. To do that, we develop an incremental version of the so-called forwarding mod {LgV} approach. Then, we apply such a control design to the problem of compensating matched disturbances assumed to be given by the superimposition of a finite number of harmonics with unknown amplitude. For this, we propose a dynamic controller made of L linear oscillators processing the regulation error and a stabilizer making the closed-loop system incrementally globally exponentially stable, uniformly with respect to the external signals. This guarantees that the closed-loop system asymptotically converges to a periodic trajectory having the first L-Fourier coefficients of the error to be zero. Then, we specialize our design for the class of linear systems with a scalar nonlinearity and of minimum-phase systems possessing contractive zero dynamics.