Research Initiation Award: Synthesis of Robust Controllers for Systems with Structured Uncertainty

这个项目涉及到在存在不确定性的情况下处理控制系统的分析和综合的新理论和技术的发展。这个项目的主要成果是提供了一种系统的方法来设计控制器，使系统在存在对象和信号不确定性的情况下具有最优的稳定性和性能特性。这一理论是以结构化不确定性模型为基础的，该模型允许包括关于建模不确定性来源的信息，从而最大限度地减少分析和设计程序中的保守性。此外，通过采用L无穷大信号范数，可以自然地将时域目标包含在设计中。这一准则的使用使该方法有别于其他方法，并为解决控制不确定系统所涉及的问题提供了一种新的方法。该项目所采用的方法将利用最近发展起来的理论，这使得系统稳定性和性能鲁棒性的分析成为可能。还将开发实现所开发的控制器综合技术的数值算法，并将其应用于实际例子。此外，稳健性分析的理论将扩展到包括更大类别的系统，并允许更好地表示干扰和不确定性。

This project concerns the development of new theory and techniques dealing with the analysis and synthesis of control systems in the presence of uncertainty. The main outcome of this project is a theory that provides a systematic means for designing controllers which lead to systems possessing optimal stability and performance properties despite the presence of plant and signal uncertainty. This theory is based on the structured uncertainty model which allows the inclusion of information about the sources of modelling uncertainty thus minimizing conservatism in the analysis and design procedures. In addition, by adopting the l-infinity signal norm, time domain objectives can be included in the design in a natural way. The use of this norm distinguishes this approach from other approaches and provides a novel way for addressing the issues involved in controlling uncertain systems. The methods employed in the project will take advantage of recently developed theory which makes possible the analysis of system stability and performance robustness. Numerical algorithms implementing the developed controller synthesis techniques will also be developed and applied to practical examples. In addition, the theory for robustness analysis will be extended to incorporate a larger class of systems and to allow a better representation of disturbances and uncertainty.