Research Initiation Award: Robust Stabilization Using Phase Information

研究启动奖：使用相位信息的鲁棒稳定

• 批准号: 9109558
• 负责人: Wassim Haddad
• 金额: $ 3.29万
• 依托单位: Florida Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-15 至 1994-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9109558&HistoricalAwards=false
• 关键词: Research; Initiation; Award; Robust; Stabilization

Phase information has largely been neglected in robust control theory but is essential for maximizing achievable performance in controlling complex multivariable systems. Phase information, here, refers to the characterization of the phase of the modeling uncertainty in the frequency domain. Real parameter uncertainty modeling in the time domain provides phase information in the frequency domain. The objective is to develop effective methods for utilizing phase information in the analysis and design of robust controllers. A proposal is made to study numerous interrelated ideas that are relevant to phase properties of dynamical systems in general and feedback control systems in particular. Although quadratic Lyapunov functions provide the foundation for much robust control theory, connections with small-gain (H-infinity) theory illustrate limitations of this approach in the presence of phase information. Extensions of quadratic Lyapunov functions, such as parameter-dependent Lyapunov functions, and structured Lyapunov functions are some of the ideas being proposed to overcome these limitations. Also proposed, is to establish a theoretical foundation of robust stabilization with positive real uncertainty. Recent Riccati-based robustness results for positive real uncertainty obtained by the author form the starting point for these investigations. Finally, it is proposed to generalize classical frequency-domain stability criteria, such as the Popov and circle criteria, to state-space controller synthesis using a Riccati equation approach. This development will provide the necessary tools for controller synthesis for sector-bounded nonlinearities. This research will provide a new approach to robust stabilization--one that involves phase information that can be significantly less conservative than an H-infinity small-gain approach.

相位信息在鲁棒性分析中被很大程度上忽略了 控制理论，但对于最大化 在控制复杂的 多变量系统 相位信息在此指的是 到建模阶段的表征 频域的不确定性。 真实的参数 时域中的不确定性建模提供了 频域中的相位信息。 的 目的是开发有效的方法， 鲁棒分析与设计中的相位信息 控制器。 建议研究许多 与相位特性相关的概念 一般动力系统和反馈控制 特别是系统。 虽然二次李雅普诺夫 函数提供了强大的 控制理论，与小增益（H ∞）的联系 理论说明了这种方法的局限性 相位信息的存在。 二次扩张 李雅普诺夫函数，如参数依赖 李雅普诺夫函数和结构李雅普诺夫函数 有些想法是为了克服 这些限制。 还建议，建立一个 鲁棒镇定的理论基础 正的真实的不确定性。 最近基于Riccati的 获得了正真实的不确定度的稳健性结果 作者从这些出发点 调查事务所 最后，建议推广 经典的频域稳定性准则，如 Popov和圆准则，用于状态空间控制器 使用Riccati方程方法进行合成。 这 发展将提供必要的工具， 扇区有界非线性的控制器综合。 该研究将为鲁棒性 稳定化--涉及相位信息的稳定化， 比H无穷大的保守性要小得多 小增益方法。