Qualitative Classification of the Behavior of Poorly ExcitedAdaptive Feedback Systems

在实际工程中有很多应用，可以描述为自适应反馈系统。自适应反馈系统的显著特征是反馈回路中的一个组件的参数根据规定的算法进行调整。制造系统中的自适应控制和电话线中的自适应回声消除器就是两个这样的例子。自适应反馈系统是非线性的，因为递归参数自适应律是由作为过去自适应参数的函数的信号驱动的。由于这种非线性性质，不同的设计参数选择以及不同的自适应算法选择会导致不同类型的行为。我们建议从系统动力学的角度着手对行为类型进行识别和分类。要使用的工具主要是标准的动力学分析技术，我们和其他人以前曾利用这些技术进行自适应系统分析。精心编排的分类的预期意义在于，它为制定所需的定性设计指南提供了基本知识，例如，为避免爆裂等有界不稳定而选择的泄漏系数。好的设计总是伴随着对问题及其“解决方案”候选者的充分理解。一个结构良好的分类法对于明智的设计选择至关重要。这样一个面向行为/设计的知识库将对新兴智能控制器的未来成功至关重要。为了促进自适应反馈系统理论的这种扩展，我们建议澄清和提出我们对低激励自适应反馈系统行为的定性分类的概念，并为这一新生分类的元素开发一些原型。

There are many practical engineering applications which can be described as an adaptive feedback system. The distinguishing feature of an adaptive feedback system is that one component in the feedback loop has its parameters adapted according to a prescribed algorithm. Adaptive control in manufacturing systems and adaptive echo cancellers in telephone lines are two such examples. Adaptive feedback systems are nonlinear because the recursive parameter adaption laws are driven by signals that are functions of the past adapted parameters. Due to this nonlinear nature, different selections of design parameters, as well as different selections of adaptive algorithms, bring about qualitatively different types of behavior. We propose to initiate an effort to discern and classify the types of behavior from a system dynamic point of view. The tools to be employed are primarily standard dynamics analysis techniques that we, and others, have utilized before for adaptive systems analysis. The expected significance of a carefully composed classification is in its provision of the fundamental knowledge for the development of needed qualitative design guidelines, e.g. leakage factor selection for avoidance of bounded instabilities such as bursting. Good design is always preceded by good understanding of the problem and its "solution" candidates. A well-structured taxonomy is critical to well-informed design choices. Such a behavior/design-oriented knowledge base will be vital for the future success of emerging intelligent controllers. To contribute to such an expansion of adaptive feedback systems theory, we propose to clarify and propound our notion of a qualitative classification of the behavior of poorly excited adaptive feedback systems, and to develop some prototypes for elements of this nascent taxonomy.