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A new method is presented on constrained power synthesis for reconfigurable arrays of arbitrary geometry. Given a number of suitable masks, the algorithm yields excitation vectors whose array patterns belong to such masks, and for each array element the excitation amplitude holds constant during the pattern reconfiguration, so as to ensure phase-only control. Each excitation amplitude is optimized, and the method allows to control the dynamic range ratio (DRR) of the excitations. The solution to the synthesis problem is found as a point of the intersection between two suitable sets, by using the method of successive projections. The proposed method can also be used to solve problems of constrained beam scanning. To this aim it is sufficient to select a high number of masks, close to each other in the angular sector of interest and shaped in such a way as to reproduce the desired scanning beam. The algorithm yields array patterns belonging to these masks, thus performing a discrete scanning by phase-only control, and allows to control the DRR. Several numerical examples show the effectiveness and the capabilities of the method.