Adaptive Stabilization Theory

现有自适应控制 算法可以被证明是 能够“全球稳定” 无持久系统 激励适用于 过程模型满足 假设最近的结果 演出是不必要限制， 或者效率很低， 因此， 实用价值 底层 原因是， 适用于“大”类 过程模型，“参数化 设计模型”， “确定性等效控制”是 基于，几乎总是有点， 它们的参数空间 设计模型是不稳定的- 在这种情况下， 等效控制器设计 “设计模型稳定化”是 不可能的我们建议处理 解决这个问题， 特殊能力，如果标识符- 自适应控制器 采用开关。 我们建议 研究两种切换算法 不同的类型。 第一个，叫 “滞后切换”已经 成功解决了 一些长期存在的问题， 经典模型参考自适应 控制 第二个，叫 “循环切换”是在一个 早期发展阶段，但 有可能产生 自适应控制器 能力远远超过那些 现有算法。 自从 调谐误差的引入 Edgart在1978年进行了规范化， 这一概念一直在大力推广， 被剥削 的一个主要 正常化的好处是， 它能让人获得 稳定自适应控制器 这是非常简单的， 结构化算法， 不要使用标准化。 是 主要由于这个原因， 一种形式的误差标准化， 另一种被广泛使用 在参数自适应控制中。 对 另一方面，它最近 据观察，尽管 它们的相对复杂性， 算法不使用错误 规范化提供了几个明确的 与算法相比， 做 我们建议进一步发展 正常化原则- 自由自适应控制，研究 无归一化能力 算法，并比较他们的 性能与性能 标准化的算法- 依赖类型。

Existing adaptive control algorithms which can be shown to be capable of "globally stabilizing" a system without persistent excitation are either applicable to process models satisfying assumptions which recent results show are unnecessarily restrictive, or perform very inefficiently and consequently are of little practical value. The underlying reason for this is that to be applicable to "large" classes of process models, the "parameterized design models" upon which "certainty equivalence control" is based, almost always have points in their parameter spaces at which the design model is unstabilizable - and at such points certainty equivalence controller design via "design model stabilization" is impossible. We propose to deal with this problem by exploiting the special capabilities if identifier- based adaptive controllers employing switching. We propose to study switching algorithms of two different types. The first, called "hysteresis switching" has already been used to successfully resolve several long standing problems from classical model reference adaptive control. The second, called "cyclic switching," is in an earlier stage of development, but has the potential of yielding adaptive controllers with capabilities well beyond those existing algorithms. Ever since the introduction of tuning error normalization by Edgart in 1978, the concept has been vigorously exploited. One of the main benefits of normalization is that it enables one to obtain stabilizing adaptive controllers which are very much simpler in structure than are algorithms which do not use normalization. It is largely for this reason that tuning error normalization in one form or another has been so widely utilized in parameter adaptive control. On the other hand, it has recently been observed that, in spite of their relative complexity, algorithms not using error normalization offer several clear advantages over algorithms which do. We propose to further develop the principles of normalization- free adaptive control, to study the capabilities of normalization-free algorithms, and to compare their performance with the performance of algorithms of the normalization- dependent type.