Synthesis of Robust Controllers Under Perturbations of MixedType

自1985年以来，人们发展出了非常有效的非保守方法来分析受参数变化影响的控制系统的鲁棒稳定性。然而，根本没有合成程序可用。另一方面，h∞控制理论有完善的综合程序。然而，当应用于参数稳定性问题时，该理论是高度保守的。在这个建议中，我们打算开发包含参数不确定性的控制问题的综合程序。最近的结果（由PI获得）证明了在由Kharitonov定理导出的某些流形上存在极端稳定边（包括h -∞边），给出了一个有希望的开端。这一联系表明，h -∞（以及其他经典合成方法）可能会被智能地调整，以给出参数变化问题的非保守合成过程。这将是我们研究的主要领域。我们期望这项研究项目的结果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.