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The problem of reaching a fixed, closed convex body, W, of a locally convex topological vector space X in minimum time, by a control system steered by a sequence of independently operating controls of the bounded amplitude type, is considered. Conditions are derived for the optimal control to exist, be unique and bang-bang, and in the case W is a ball in a Banach space, a necessary and sufficient condition for controllability is obtained. By means of examples, the application of these results to the control of distributed systems is shown, and extensions of results of Ergov [4] and Friedman [5] obtained.
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Greg Knowles (1976) studied this question.
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