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

研究具有参数不确定性和动态不确定性的非线性动态系统的几何渐近特性，旨在开发一种鲁棒自适应反馈线性化的设计方法。对不确定性影响的分析（第3节）将揭示非自适应状态反馈（第4节）或基于观测器（第5节）的设计是否能保证鲁棒性，以及自适应反馈线性化方法（第6节）何时更合适。这些领域的新问题公式激发了统一的几何渐近自适应方法的发展。研究表明，控制器和观测器的峰值现象是鲁棒非线性反馈设计的重要基础，这一现象在线性系统理论中已经被注意到，但尚未得到深入的研究。在非自适应高增益环路的危险中，不确定非线性的峰值干扰可能导致稳定区域的急剧减小。当这种干涉可以避免时，对几何渐近性质的更充分理解将显示出来。自适应参数更新减少了参数不确定性的影响，避免了对高增益环路的需要。目前，它们仅限于具有已知非线性的系统，当“确定性-等价”形式的反馈线性化是适用的。在自适应和非自适应设计之间的一个关键权衡是要与未建模的动力学进行比较，已知未建模的动力学会导致一些线性自适应系统的不稳定。在现有线性自适应控制研究的基础上，通过对算法的改进，可以提高非线性自适应设计的鲁棒性。

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.