Stochastic Adaptive Control: Design and Analysis

控制工程师经常面临设计 控制器的噪声系统的参数变化是如此严重 经典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提供了素材。 自适应控制理论有几个方面。 设计 问题是产生算法，将调整控制设置， 真实的时间响应植物的变化。 分析问题是 来研究这些算法的行为和性能。 分析 可能（并且已经）导致（导致）设计变更。 分析涉及 全球稳定问题，特别是在存在 未建模动态和性能（例如，获得的跟踪误差 功率和所需的控制功率或努力）。 这里提出的工作的目的是从一个 随机设置 为了设计新的算法， 考虑对参数变化进行建模，但这立即 提出了一个维度问题;基于因子的解决方案 提出了分析思路。 接下来是最基本的问题， 自适应控制，即稳定性。 三种随机工具可用 处理这一问题的方法和可能成功的途径 探讨了 未建模的动力学问题 也被评估。 最后，性能问题可以通过 在自适应信号处理中通过以下思想开发的方式： 失调和过度滞后。 出于良好的技术原因，确定性和随机自适应 迄今为止，控制的发展有些分裂，现在可能是这样。 可能开始把他们聚在一起。

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.