一种反馈镇定的新方法及其在多项式系统数据驱动控制中的应用
A New Approach for Feedback Stabilization and its Application for Data-Driven Control of Polynomial Systems
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中文总结 AI 辅助
该研究提出基于SOS优化的非线性系统状态反馈渐近镇定新条件，构建适用于含噪多项式系统数据驱动控制的迭代流程，克服传统SOS方法局限，经数值示例验证策略有效。
中文摘要 AI 辅助
受基于耗散性的控制最新进展启发，本研究提出了采用状态反馈实现非线性系统渐近镇定的新充分条件。我们证明该新框架适用于含噪声测量的多项式系统数据驱动控制，该主题近来已受到广泛关注。基于所提框架，提供了两种用于数据驱动状态反馈设计的迭代流程，采用和平方（SOS）优化。本文克服了传统基于交替（D-K）流程的SOS方法在控制器设计中的典型局限，例如需提供控制-李雅普诺夫函数（CLF）的初始化条件。数值示例验证了新策略的适用性与优势。
英文摘要
Inspired by recent developments in dissipativity-based control, this work proposes new sufficient conditions for asymptotic stabilization of nonlinear systems using state feedback. We prove that this new framework is well suited for data-driven control of polynomial systems using noisy measurements, a topic that has lately attracted considerable attention. Two iterative procedures for data-based state feedback design are provided using the proposed framework, that use sum-of-squares (SOS) optimization. Typical limitations of conventional SOS methods based on alternating (D-K) procedures for controller design, such as the need to provide an initialization for a control-Lyapunov function (CLF), are overcome in this paper. Numerical examples demonstrate the applicability and the advantages of the new strategies.
