Adaptive Stabilization Theory

现有的自适应控制算法能够在没有持续激励的情况下使系统“全局稳定”，它们适用于满足以下假设的过程模型最近的研究结果表明，它们的限制是不必要的，或者执行效率很低，因此没有什么实用价值。这样做的根本原因是，为了适用于“大”类过程模型，即“确定性等效控制”所基于的“参数化设计模型”，在其参数空间中，几乎总是存在设计模型不稳定的点，在这些点上，通过“设计模型稳定”进行确定性等效控制器设计是不可能的。我们建议利用基于标识符的自适应控制器的特殊功能来解决这个问题。我们提出研究两种不同类型的切换算法。第一种被称为“迟滞开关”的方法已经成功地解决了经典模型参考自适应控制中几个长期存在的问题。第二种被称为“循环切换”（cyclic switching），目前还处于早期开发阶段，但有可能产生自适应控制器，其功能远远超过现有的算法。自1978年Edgart引入调优误差归一化以来，这一概念得到了大力开发。归一化的主要好处之一是，它使人们能够获得稳定的自适应控制器，它在结构上比不使用归一化的算法简单得多。正是由于这个原因，各种形式的调谐误差归一化在参数自适应控制中得到了广泛的应用。另一方面，最近人们观察到，尽管它们相对复杂，与使用错误归一化的算法相比，不使用错误归一化的算法有几个明显的优势。我们建议进一步发展无归一化自适应控制的原理，研究无归一化算法的能力。并将其性能与归一化相关算法的性能进行比较。

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.