Topics in Stabilization of Nonlinear Control Systems

非线性控制系统稳定性专题

• 批准号: 9411145
• 负责人: Carla Schwartz
• 金额: $ 14.73万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-09-01 至 1997-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9411145&HistoricalAwards=false
• 关键词: Topics; Stabilization; Nonlinear; Control; Systems

9411145 Schwartz The control of systems modeled by nonlinear differential equations is an important topic to study because of the prevalence of these models in manufacturing, chemical process, automotive, power, and aerospace industries. Normal form techniques have been successfully applied to simplify the state space expression of nonlinear ordinary differential equations. Here we propose to study the stabilization of nonlinear control systems using normal form techniques. Thus, we are interested in systems whose linearizations possess at least one uncontrollable critical mode. From some preliminary analysis, it can be inferred that there is a great advantage to using the normal form as a method to reduce the dimension of the system whose stability is to be analyzed. We propose to study this dimensional advantage in detail as it may be applied to various problems. One question of interest is to understand and characterize the decoupling of the critical and stable modes of a nonlinear control system in normal form. Another line of proposed study is to examine how the normal form characterizes the Lyapunov function associated with the nonlinear system. We would also estimate the region of attraction of stability for nonlinear systems using the normal form. We will study the relationship between the normal form and the center manifold techniques which have been previously used in stabilization analyses. Full and Partial feedback linearization, and approximate feedback linearization will also be studied, to see if these objectives can be achieved more simply using the normal form. Time scale techniques have been applied to control systems in order to simplify analysis and obtain stability results. A further direction of the research herein proposed will be to derive a deeper understanding of the relationship between stability and time scale, and the relevance of time scale techniques to existing center manifold and normal form techniques in stabilization of nonlinear control systems. ***

小行星9411145 由于非线性微分方程模型广泛应用于制造、化工、汽车、电力和航空航天等工业领域，因此非线性微分方程模型的控制是一个重要的研究课题。 规范形技术已成功地应用于简化非线性常微分方程的状态空间表达式。 在这里，我们建议研究非线性控制系统的稳定性使用规范形式技术。 因此，我们感兴趣的系统，其线性化具有至少一个不可控的临界模式。 初步分析表明，用规范形方法对稳定性分析对象进行降维具有很大的优越性。 我们建议详细研究这种尺寸优势，因为它可能适用于各种问题。 一个感兴趣的问题是理解和描述的非线性控制系统的临界模式和稳定模式的正常形式的解耦。 另一条建议的研究是检查规范形式如何表征与非线性系统相关的李雅普诺夫函数。 我们还将估计非线性系统的吸引区域的稳定性使用规范形式。 我们将研究规范形和中心流形技术之间的关系，这些技术以前曾用于稳定性分析。 还将研究完全和部分反馈线性化以及近似反馈线性化，以查看是否可以使用规范形式更简单地实现这些目标。 时标技术已被应用于控制系统，以简化分析，并获得稳定性的结果。 本文提出的进一步研究方向是更深入地了解稳定性与时间尺度之间的关系，以及时间尺度技术与非线性控制系统稳定性中现有中心流形和范式技术的相关性。 ***