Abstract
Bellman's functional equation is defined and derived for a class of optimal control problems. The derivation does not employ the Taylor series expansion or the mean value theorem of differential calculus, thus it avoids the differentiability requirements previously imposed on Bellman's equation. As a result, Bellman's functional equation can be used to solve a class of time-optimal control problems. A necessary condition theorem and a sufficient condition theorem are given. One example illustrates the use of Bellman's functional equation in the time-optimal control case.
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