Abstract
This paper discusses the singular linear-quadratic (LQ) optimal control for the single-input linear digital system. Since the performance index does not contain the input explicitly, the optimal control becomes singular. First, by using the property of the linear digital system, the singular performance index is transformed into a nonsingular (normal) one. Then, singular LQ optimal controls for the free-end-point problem, for the fixed-end-point problem, and for the infinite control time problem are obtained. They are expressed by the state feedback with the bounded gains. Furthermore, the sufficiency of the singular LQ optimal control is shown. Finally, the relationship between the singular LQ optimal control and the nonsingular one is described.
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