Presidential Young Investigator Award: Optimization-Based Computer-Aided Design of Engineering Systems

结构奇异值的概念最近被引入作为分析和综合具有结构不确定性的反馈系统的一种工具。后来发现，它是在联合稳健性和性能规范下设计控制系统的关键，并且非常好地补充了控制系统设计的H；IO；IO方法。目前提出的计算结构奇异值的算法在计算上要求很高。因此，需要进行大量此类评估的相应设计程序目前是不切实际的。需要有效的方法来评估结构化奇异值，以及需要能够处理相应设计规范的优化算法。这项研究的目的就是朝着这个方向迈出第一步。更具体地说，研究了结构奇异值的代数性质和几何性质，并基于这些性质设计了计算结构奇异值的有效算法。

The concept of structured singular value was recently introduced as a tool for the analysis and synthesis of feedback systems with structured uncertainties. It was found later to be a key to the design of control systems under joint robustness and performance specifications and to very nicely complement the H;io;io approach to control system design. The algorithms proposed so far for the computation of the structured singular value are computationally very demanding. Thus, corresponding design procedures, requiring a large number of such evaluations, are currently impractical. There is a need for efficient methods for the evaluation of the structured singular value as well as for optimization algorithms capable of handling corresponding design specifications. The purpose of this research is to take a first step in that direction. More particularly, the algebraic and geometric properties of the structured singular value are studied and, based on these properties, efficient algorithms for its computation are devised.