Abstract
THE time-optimal problem is considered for linear controlled systems with elements from a Banach space and controls from a given set of a linear topological space, i.e., the problem of moving the system in minimal time from one set to another while satisfying phase constraints of a very general type. An iterative method for solving the problem approximately is described and proved, together with a modification of the method. The method is shown to be usable for the approximate solution of many time-optimal problems of practical importance, involving equations of mathematical physics. A regularizing algorithm, closely linked with the iterative method, is shown to exist.
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