Nonlinear System Design: Adaptive Feedback Linearization with Unmodeled Dynamics (Supplement: NSF-UC-NASA Workshop onNonlinear Control, Santa Barbara, CA., April 5-7, 1990)

非线性系统设计：具有未建模动力学的自适应反馈线性化（补充：NSF-UC-NASA 非线性控制研讨会，加利福尼亚州圣巴巴拉，1990 年 4 月 5-7 日）

• 批准号: 8818166
• 负责人: Petar Kokotovic
• 金额: $ 1.92万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-15 至 1991-04-01
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8818166&HistoricalAwards=false
• 关键词: Nonlinear; System; Design; Adaptive; Feedback

The proposed study of geometric-asymptotic properties of nonlinear dynamic systems with parametric and dynamic uncertainties is aimed at the development of a design methodology for robust adaptive feedback linearization. An analysis of the effects of uncertainties (Section 3) will reveal whether nonadaptive state-feedback (Section 4) or observer-based (Section 5) designs will guarantee robustness, and when an adaptive feedback linearization approach (Section 6) is more appropriate. New problem formulations in each of these areas motivate the development of a unified geometric-asymptotic-adaptive methodology. It is shown that the phenomenon of controller and/or observer peaking, which has been noticed but not thoroughly studied in the linear system theory, is of fundamental importance for robust nonlinear feedback design. Among the dangers of nonadaptive high-gain loops is a possible interference of peaking with uncertain nonlinearities that can result in a drastic decrease of the stability region. A fuller understanding of geometric-asymptotic properties will show when this type of interference can be avoided. Adaptive parameter updates reduce the effects of parametric uncertainties and avoid the need for high-gain loops. At present they are restricted to systems with known nonlinearities, when a "certainty-equivalence" form of feedback linearization is applicable. A crucial trade-off between adaptive and nonadaptive designs is to be made vis-a-vis unmodeled dynamics, which are known to cause instabilities in some linear adaptive systems. Robustness of nonlinear adaptive designs will be improved by algorithm modifications based on current research in linear adaptive control.

研究具有参数和动态不确定性的非线性动态系统的几何渐近性质，旨在发展一种鲁棒自适应反馈线性化设计方法。对不确定性的影响的分析(第3节)将揭示非自适应状态反馈设计(第4节)或基于观测器的设计(第5节)将确保稳健性，以及何时自适应反馈线性化方法(第6节)更合适。这些领域的新问题提法推动了几何-渐近-自适应统一方法论的发展。结果表明，控制器和/或观测器的尖峰现象在线性系统理论中已经被注意到，但没有得到深入的研究，这对鲁棒非线性反馈设计具有重要的意义。在非自适应高增益环路的危险中，可能存在峰值与不确定非线性的干扰，这可能导致稳定区域的急剧下降。对几何渐近性质的更全面的理解将表明，何时可以避免这种类型的干扰。自适应参数更新减少了参数不确定性的影响，并避免了高增益环路的需要。目前，当反馈线性化的“确定性等价”形式适用时，它们仅限于具有已知非线性的系统。自适应和非自适应设计之间的一个关键权衡是相对于未建模的动态，众所周知，未建模的动态在一些线性自适应系统中会导致不稳定。在现有线性自适应控制研究的基础上，对算法进行改进，可以提高非线性自适应设计的鲁棒性。