EIA: Robust Control of Systems with Parameter Uncertainty: An Operator Theoretic Approach

鲁棒系统控制的一般问题包括为具有参数或建模不确定性的可能不稳定的系统族构造固定反馈控制器，以稳定给定族并满足一定的性能要求。本文提出了一种算子理论和泛函分析方法来解决多变量、分布甚至可能是非线性的问题。具体而言，将提出解决多元分布式系统的h -∞最优加权灵敏度问题的技术，并将开发用于获得非常一般的多变量增益裕度问题的新的定性和定量结果的方法。此外，将考虑经典插值理论的非线性版本，它将在自适应和鲁棒非线性控制中产生重要影响。期望所提出的算子理论方法有助于解决鲁棒设计中的一些基本问题，并阐明该领域的一些核心理论问题。此外，还将开发具体的算法，以便在计算机上实现这些方法。鲁棒系统控制的一般问题包括为具有参数或建模不确定性的可能不稳定的系统族构造固定反馈控制器，以稳定给定族并满足一定的性能要求。本文提出了一种算子理论和泛函分析方法来解决多变量、分布甚至可能是非线性的问题。

The general problem of robust system control consists of constructing fixed feedback controllers for possibly unstable families of systems with parameter or modelling uncertainty in order to stabilize the given family and in order to meet certain performance specifications. This proposal is concerned with an operator theoretic and functional analytic approach to this problem for multivariable, distributed, and even possibly nonlinear plants. Specifically, techniques will be proposed to solve the H-Infinity-optimal weighted sensitivity problem for multivariate distributed systems, and methods will be developed for obtaining new qualitative and quantitive results for very general multivariable gain margin problems. Moreover, a nonlinear version of classical interpolation theory will be considered and it should have important consequences in adaptive and robust nonlinear control. It is expected that the proposed operator theoretic approach should help resolve some fundamental problems in robust design and illuminate a number of central theoretical issues in this area. In addition, specific algorithms will be developed to implement the methods on the computer. The general problem of robust system control consists of constructing fixed feedback controllers for possibly unstable families of systems with parameter or modelling uncertainty in order to stabilize the given family and in order to meet certain performance specifications. This proposal is concerned with an operator theoretic and functional analytic approach to this problem for multivariable, distributed, and even possibly nonlinear plants.