System Theory and Control of Model Sets

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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.