Abstract
IN optimal control theory, the solutions of numerous problems are discontinuous functions. For certain topics, smoothed solutions are of interest [1, 2]. Various smoothing methods may be used; the one described here is similar to that given in [2]. Our aim will be to show, by taking the example of the linear problem of optimal control, that smoothed solutions may be obtained by the methods of classical variational calculus. We shall state the variational problem, the stability condition for which is equivalent in the limit to the maximum principle [3]. Existence and limit theorems will be proved for the smoothed solutions.
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