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Feedback synthesis of optimal saturating controls for linear systems is considered. An integral cost is introduced, with integrand comprised of quadratic and certain non-quadratic functions of the state. The latter (non-quadratic) functions are chosen so as to regularize the problem in the sense that an explicit feedback solution, of particularly simple form, is obtained. Finite and semi-infinite time horizon formulations are treated and several examples are presented.
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E.P. Ryan (1982) studied this question.
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