System Theory and Control of Model Sets

通过这项研究，系统的控制器设计方法的基础上不确定的植物模型已被寻求。作为我们研究的出发点，我们认识到，受控对象不应该只使用一个模型，而是使用一组模型建模，因为它是不可避免的对象模型具有一定的不确定性。从这个观点出发，我们考虑了几个与将不确定性量化为模型集的大小和将不确定系统的控制作为模型集的控制有关的问题，在1995年，我们得到了一个量化不确定性的过程和模型集的数学公式。具体地说，提供了一个上限的植物增益和有限长度的输入输出数据，一个模型集被定义为一组所有的传递函数一致，这些先验数据。此外，我们开发了一个算法来计算这个集合使用复变函数理论。在控制方面，我们将二次镇定技术推广到一类时变系统的模型集上，1996年，我们对模型集辨识有了更深的理解，并寻求将其与鲁棒控制技术联合收割机结合起来。即提出了一种基于欧几里得范数的模型集辨识方法，并研究了传递函数为倒数的系统的结构奇异值的性质。此外，我们表明，我们可以使一个不确定的控制系统估计的值相关联的李雅普诺夫函数的二次稳定化方法在前一年得到的扩展。

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.