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An adaptive system for the control of the power level of a nuclear reactor is described. The controller has a square-law element of variable gain, optimum values for which have been obtained from off-line computations for certain power levels and parameter values. When conditions in the reactor deviate from those assumed for the off-line optimization, the gain factor is adapted on-line, such that the difference between actual and demanded power levels is minimized. An existing power reactor and associated control system have been simulated, as well as the proposed adaptive scheme. The results show that the adaptive controller gives improvements by at least an order of magnitude in the accuracy of following power demand changes, and at the same time reduces the necessary control effort. Since the scheme entails only a small number of arithmetic and logical operations and has limited memory requirements, it may be implemented on a conventional process computer, or built as a special purpose digital control system.