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

本文提出的非线性系统的几何渐近性质的研究， 针对具有参数和动态不确定性的动态系统， 鲁棒自适应反馈设计方法的发展 线性化 对不确定性影响的分析（第二节） 3)将揭示是否非自适应状态反馈（第4节）或 基于缓冲器（第5节）的设计将保证鲁棒性， 自适应反馈线性化方法（第6节）更多 适当 这些领域中的新问题公式激发了 统一的几何渐近自适应 方法论 它表明，控制器和/或 观察者峰化，已经注意到，但没有彻底研究， 线性系统理论，对于鲁棒性 非线性反馈设计 在非自适应高增益的危险中， 环路是一个可能的干扰峰与不确定的 非线性会导致稳定性急剧下降 地区 对几何渐近性质的全面理解 将显示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，并避免需要高增益环路。 目前他们 仅限于具有已知非线性的系统，当 反馈线性化的“确定性-等价”形式是适用的。 自适应和非自适应设计之间的一个关键权衡是 与未建模的动力学相比， 一些线性自适应系统的不稳定性。 鲁棒性 非线性自适应设计将通过算法修改得到改进 基于线性自适应控制的研究现状。

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.