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

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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.