Design of Robust Adaptive Control

鲁棒自适应控制是系统与控制理论中最有前途和最活跃的研究领域之一。在过去的两年中，已经发现了非鲁棒性行为的主要原因，并推荐了对抗不稳定机制的方法。现在可以使用信号相关判据确定尖锐的稳定-不稳定边界。为了推广这一线性化结果的有效性，提出了慢积分流形的概念。这个概念将被用作研究中的非线性几何渐近工具。本研究的目的是利用植物和信号的先验信息来降低自适应控制器的复杂性，从而提高其鲁棒性。这可以通过去除匹配性和正真实性假设并允许特定于问题的简化参数化来实现。本文将提出一种伪梯度方法来保证局部收敛。然后用非线性几何渐近方法使实际保证的收敛区域最大化，包括流形内和流形外边界的分析。初步的伪梯度方案被描述为更一般设计的可能起点。

Robust adaptive control is one of the most promising and most active research areas in systems and control theory. During the last two years major causes of nonrobust behavior have been discovered and means to counteract instability mechanisms have been recommended. A sharp stability-instability boundary can now be determined using a signal dependent criterion. To extend the validity of this linearized result, the concept of a slow integral manifold is proposed. This concept will be used as a nonlinear geometric-asymptotic tool in the research. The goal of this research is to employ a priori information about the plant and signals in order to reduce the complexity of the adaptive controller and thus improve its robustness. This is to be achieved by removing matchability and positive realness assumptions and allowing problem specific reduced parameterizations. A pseudo- gradient approach will be developed to guarantee local convergence. The practically guaranteed region of convergence will then be maximized by nonlinear geometric -asymptotic methods, including an analysis of in-manifold and off-manifold bounds. A preliminary pseudo-gradient scheme is described as a possible starting point for more general designs.