Research Initiation: Controller Complexity in Linear Systems

线性系统框架下的反馈控制问题近年来得到了广泛的研究。尽管这些理论解决了许多重要问题，但它们通常未能解决由此产生的控制器的复杂性问题（即麦克米伦度）。本研究的目的是利用部分实现的方法来研究低复杂度控制器的相关问题。特别是，这项工作将包括部分实现问题的各个方面，如应用于h∞优化问题和动态输出反馈的极点放置问题。工作的动机是在第一个问题中，目前的理论中没有对控制器复杂性的规定，而在第二个问题中，现有的结果只是部分的。本文研究的意义在于，在反馈控制中，控制器的复杂度是一个重要的设计参数。因此，设计方法应给予工程师选择的自由，以满足设计规范。

The problem of feedback control in the framework of linear systems has been extensively investigated over the years. Although the theories developed settled a number of important issues, they generally failed to address the problem of the complexity (i.e., MacMillan degree) of the resulting controllers. The aim of this research is to investigate problems related to low complexity controllers, using the partial realization approach. In particular, the work will encompass aspects of the partial realization problem as applied to the H-infinity optimization problem and the problem of pole placement by dynamic output feedback. The motivation for the work is that in the first problem, no provision for controller complexity exists in the current theories and in the second problem, the existing results are only partial. The significance of the proposed research lies in the fact that the complexity of the controller is an important design parameter in feedback control. Consequently, the design methods should give the engineer the freedom of choosing it so as to meet design specifications.