Synthesis of Robust Controllers Under Perturbations of MixedType

自1985年以来，人们已经发展了非常有效的非保守方法来分析参数变化的控制系统的鲁棒稳定性分析。然而，目前还没有可用的合成程序。另一方面，H_无穷控制理论具有成熟的综合过程。然而，当应用于参数稳定性问题时，该理论是高度保守的。在这项提案中，我们打算为包含参数不确定性的控制问题开发综合程序。最近的结果(由PI得到)证明了在由Kharitonov定理导出的某些流形上存在极值稳定裕度(包括H-无穷裕度)，从而给出了一个很有希望的结果。这一联系表明，H-无穷大(和其他经典综合方法)可能被智能地定制，以给出参数变化问题的非保守综合程序。这将构成我们研究的主要领域。我们希望这一研究项目的结果将对许多应用中出现的控制系统的分析和设计产生影响。

Since about 1985, extremely efficient and nonconservative methods have been developed for the analysis of robust stability of control systems subject to parameter variations. However, there are no synthesis procedures available at all. On the other hand, H-infinity control theory has a well-developed synthesis procedure. This theory, however, is highly conservative when applied to the parametric stability problem. In this proposal we intend to develop synthesis procedures for control problems containing parameter uncertainty. A promising opening is given by recent results (obtained by the PI's) proving that the extremal stability margins (including H-infinity margins) occur on certain manifolds derived from Kharitonov's theorem. This link suggests that H-infinity (and other classical synthesis methods) might be intelligently tailored to give nonconservative synthesis procedures for parameter variation problems. This will form the main area of our research. We expect the results of this research project to have an impact on the analysis and design of control systems arising in many applications.