The problem of adaptively controlling the power level changes of a nuclear reactor, by the use of a digital computer, is considered. It is established, that for the application of modern control theory a low-order linear model of the reactor is needed, but that the existing models are not sufficiently accurate-for the desired purpose. A new technique is therefore developed for finding low-order linear models of a given high-order system. Such models are shown to be suitable for the suboptimal control of the original system, subject to cost functions normally encountered in practice. The proposed methods of modelling and suboptimal control are applied to the adaptive control of a nuclear reactor. In order to emphasize practical realization, a model of an operating nuclear power plant is considered,with emphasis on the physical limitations imposed by the controller mechanism. It is shown, that despite wide variations in the model parameters as a function of the operating power level and of the temperature coefficient, the model can be updated on-line to a sufficient accuracy to produce negligible deviations between optimal model and suboptimal system performance. Apart from the realization of the adaptive controller, it is indicated that the proposed technique is also suitable for the fully computerized design of optimal and suboptimal feedback controllers for a wide variety of cost functions. / Thesis / Doctor of Philosophy (PhD)