System Theory and Control of Model Sets

系统理论与模型集控制

基本信息

批准号：
07455172
负责人：
KIMURA Hidenori
金额：
$ 0.51万
依托单位：
University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

项目摘要

Through this research, methodology for a systematic controller design based on an uncertain plant model has been sought. As a starting point of our research, we recognized that controlled plant should be modeled not using only one model but using a set of models because it is unavoidable that a plant model has some uncertainty. From this viewpoint, we considered several problems concerned with quantification of uncertainty as a size of a model set and control of uncertain system as control of a model set.In 1995, we obtained a procedure to quantify uncertainty and a mathematical formulation of a model set. Specifically, provided an upper bound of a plant gain and finite-length input-output data, a model set is defined as the set of all transfer functions consistent to these a priori data. Moreover, we developed an algorithm to calculate this set using a complex function theory. As for control, on the other hand, we extend a technique of quadratic stabilization so that it can be applied for a class of model sets of time-varying systems.In 1996, we achieved deeper understanding of model set identification and seeked to combine it with robust control techniques. namely, a model set identification based on Euclid norms is proposed and properties of structured singular values are investigated regarding systems whose transfer functions are reciprocal. Furthermore, we showed that we can make an uncertain control system estimate a value of an associated Lyapunov function by extending a quadratic stabilization method obtained in the previous year.

通过这项研究，寻求基于不确定植物模型的系统控制器设计的方法。作为我们研究的起点，我们认识到应将受控的植物不仅使用一个模型建模，而应使用一组模型，因为不可避免地要植物模型具有一定的不确定性。从这个角度来看，我们认为与量化不确定性有关的几个问题是模型集的大小和对模型集的控制。。具体而言，提供了植物增益和有限长度输入数据的上限，模型集被定义为与这些先验数据一致的所有传输函数的集合。此外，我们开发了一种使用复杂函数理论来计算该集合的算法。至于控制，另一方面，我们扩展了一种二次稳定技术，以便将其应用于一类时变系统的模型集。在1996年，我们对模型设置的识别进行了更深入的了解，并寻求将其结合起来使用强大的控制技术。也就是说，提出了基于欧几里得规范的模型集识别，并研究了结构化奇异值的特性，其传递函数是相互的系统。此外，我们表明我们可以通过扩展上一年获得的二次稳定方法来使不确定的控制系统估计相关的Lyapunov函数的值。