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The problem of designing a single-axis rigid-body flight vehicle attitude controller to minimize control fuel consumption is formulated in the framework of system optimization theory. A performance measure which consists of the integral-square position and rate errors plus control fuel expended, with arbitrary relative weighting factors, is employed. The Pontryagin Maximum Principle is invoked to show that the controller which minimizes this measure is of the bang-off-bang type. The calculations are carried through and an explicit design solution given for the problem of a minimum-fuel space-vehicle attitude control.