Adaptive Stabilization Theory

自适应控制理论缺乏一个足够简单的概念框架来帮助合格的非专业人员理解当前的理论，而不需要投入过多的时间，这也可能成为进一步发展的基础。我们建议继续我们最近发起的旨在构建这样一个框架的研究计划。现有的自适应算法可以在不需要足够激励的情况下证明全局稳定性，这些算法要么适用于满足假设的过程模型，而最近的结果表明这些假设是不必要的限制，要么执行效率低下，因此实用价值有限。其根本原因是，为了适用于过程模型的“大”类，即确定性等价控制所基于的参数设计模型，几乎总是在其参数空间中存在设计模型不可稳定的点--并且在这些点上，确定性等价控制是不可能的。我们建议以两种根本不同的方式来处理这个问题。首先，我们建议开发和利用新的参数化设计模型，这些模型在其参数化空间上是可稳定的，此外，还适用于“大”类过程模型。第二，作为另一种方法，我们建议利用“隐式调谐”的概念，它不要求设计模型在其参数空间中的每一点都是可稳定的。在这两种情况下，我们都将在很大程度上依赖计算机模拟来排除不可接受的算法，并指导我们开发可接受的算法。

Adaptive control theory lacks a conceptual framework which is sufficiently simple to help qualified nonspecialists to understand the current theory without making an inordinately large time investment and which might also serve as the basis for further development. We propose to continue our recently initiated research program aimed at constructing such a framework. Existing adaptive algorithms for which 'global' stability can be proved without requiring sufficient excitation are either applicable to process models satisfying assumptions which recent results show are unnecessary restrictive or perform inefficiently and consequently are of limited practical value. The underlying reason for this is that to be applicable to "large" classes of process models, the parameter design models upon which certainty equivalence control is based, almost always have points in their parameter spaces at which the design model is not stabilizable--and at such points, certainty equivalence control is impossible. We propose to deal with this problem in two fundamentally different ways. First, we propose to develop and utilize new parameterized design models which are stabilizable on their parameterized spaces and, in addition, are applicable to "large" classes of process models. Second, as an alternative approach we propose to exploit the concept of "implicit tuning" which does not require a design model to be stabilizable at every point in its parameter space. In both cases we shall rely heavily on computer simulation to rule out unacceptable algorithms and to guide us in the development of acceptable ones.