Stochastic Adaptive Control: Design and Analysis

控制工程师经常面临的任务是为参数变化非常严重的噪声系统设计控制器，以至于经典的或基于状态空间的控制器无法处理它。该问题为自适应控制理论的研究提供了素材。自适应控制理论有几个方面。设计上的问题是设计出能够实时调整控制设置的算法，以响应工厂的变化。分析问题是研究这类算法的行为和性能。分析可能(并且已经)导致(引导)设计变更。分析涉及全局稳定性问题，特别是在存在未建模的动态和性能(例如，获得的跟踪误差功率和所需的控制功率或努力)的情况下。这里提出的工作的目的是在随机环境中查看这些问题。为了设计新的算法，考虑对参数变化进行建模似乎是有用的，但这立即引发了维度问题；基于因子分析的思想提出了解决该问题的方法。接下来是自适应控制最基本的问题，即稳定性。回顾了三种可用于处理这一问题的随机工具，并探索了可能成功的途径。还对未建模动力学问题的影响方式进行了评估。最后，性能问题可以用自适应信号处理中发展的方式通过失调和额外滞后的想法来解决。由于良好的技术原因，到目前为止，确定性和随机自适应控制的发展在某种程度上是分开的，现在可能开始将它们结合在一起。

The control engineer is often confronted with the task of designing controllers for noisy systems whose parameter variation is so severe that classical or state space based controllers cannot handle it. This problem provides the material of Adaptive Control Theory. There are several aspects to Adaptive Control Theory. The design problem is to produce algorithms that will adjust control settings in real time in response to plant variations. The analysis problem is to study the behavior and performance of such algorithms. Analysis may (and has) lead(led) to design changes. Analysis involves questions of global stability particularly in the presence of unmodeled dynamics and performance (e.g. attained tracking error power and required control power or effort). The aim of the work proposed here is to look at these issues in a stochastic setting. To design new algorithms it seems useful to consider modelling the parameter variation, but this immediately raises a dimensionality problem; a resolution of this based on Factor Analysis ideas is suggested. Next is the issue most basic to Adaptive Control, namely stability. Three stochastic tools available to deal with this are reviewed and likely successful avenues explored. The way in which the unmodeled dynamics problem impinges is also assessed. Finally the performance issues can be tackled in a manner developed in Adaptive Signal Processing through the idea of misadjustment and excess lag. For good technical reasons, the deterministic and Stochastic Adaptive Control developments have hitherto been somewhat split, it may now be possible to begin to bring them together.