System Theory and Control of Model Sets

通过本研究，探索了一种基于不确定对象模型的系统控制器设计方法。作为我们研究的起点，我们认识到受控植物不应该只使用一个模型，而应该使用一组模型，因为植物模型不可避免地具有一些不确定性。从这个观点出发，我们考虑了不确定性作为模型集大小的量化和不确定系统的控制作为模型集的控制的几个问题。1995年，我们获得了一个量化不确定性的程序和一个模型集的数学公式。具体地说，提供了植物增益和有限长度输入输出数据的上界，模型集被定义为与这些先验数据一致的所有传递函数的集合。此外，我们开发了一种算法来计算这个集合使用复变函数理论。另一方面，在控制方面，我们扩展了二次镇定技术，使其可以应用于一类时变系统的模型集。1996年，我们对模型集识别有了更深入的了解，并试图将其与鲁棒控制技术相结合。提出了一种基于欧几里德范数的模型集辨识方法，研究了传递函数互反的系统的结构奇异值的性质。此外，我们证明了我们可以使不确定控制系统估计一个相关的Lyapunov函数的值，通过推广前一年得到的二次镇定方法。

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.