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A solution of the minimum time and minimum fuel problems for pulse frequency modulated systems is presented. The derivation of the optimal control is done by a heuristic argument. The optimal controller is found to be bang-bang with a dead zone in both cases. Then the optimal policies are derived by considering the dynamic properties of such systems. A specific second-order example is presented to show the application of the method.
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T. Pavlidis (1966) studied this question.
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