Abstract
ABSTRACT The nature of the optimum controller is investigated for control systems which are subject to saturation. It is shown that for a wide class of performance criteria the optimum controller simply generates an instantaneous non-linear function of the input phase coordinates and of the output phase coordinates. For relay control systems, the optimum controller is characterized by a switching surface in the phase space. For special cases, the dimensions of the phase space can be reduced in number by using error coordinates. These results systematize and generalize several known results, and explain the starting points of some recent abstract papers.
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