Abstract
Necessary conditions in an optimization problem for differential inclusions with convex right-hand side are given. The initial state of the inclusion being a random vector is unknown, or, in the more general case, is contained in some random closed set. We seek a trajectory of the inclusion which minimizes the expectation of a function of the inclusion’s final state, or, in the more general case, the similar trajectory which is a minimizer of an max-(or Choquet) integral. The theorem is proved that formulates necessary conditions of optimality for the mentioned problem, conditions which in certain cases are also sufficient.
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