Adaptive Stabilization Theory

自适应控制理论缺乏概念框架 它足够简单， 非专业人士理解当前的理论， 投入了大量的时间， 也可以作为进一步发展的基础。 我们建议继续我们最近开始的研究 计划旨在构建这样一个框架。 现有的自适应算法， 不需要足够的激励就可以证明， 或者适用于满足假设的过程模型 最近的研究结果表明，这些限制是不必要的， 效率低下，因此， 实用价值 其根本原因是， 适用于“大”类流程模型， 参数设计模型， 等价控制是基于，几乎总是有点， 它们的参数空间，在这些参数空间中，设计模型不 稳定的，在这种情况下，确定性等价 控制是不可能的 我们建议处理这个问题 两个根本不同的问题。 一是 建议开发和利用新的参数化设计 可稳定的参数化模型 空间，此外，适用于“大”类 过程模型。 第二，作为一种替代方法， 我们建议利用“隐式调优”的概念 其不要求设计模型是可稳定的 在其参数空间中的每一点上。 在这两种情况下，我们 将严重依赖计算机模拟来排除 不可接受的算法，并指导我们在 发展可接受的。

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.