On the one discrete control problem described by Volterra type difference equation and non-smooth quality criterion

The work devoted to study of one optimal control problem described by a system of nonlinear Volterra type difference equations, with a non-smooth quality functional assuming that the quality functional satisfies the Lipschis condition and has directional derivatives. Using method based on linearization of equation of process under several of assumptions necessary conditions of optimality in terms of derivatives in direction are established. The minimax control problems has been separately considered. That is that problem of finding the minimum value of the functional of the type maximum (problem by minimax). Using the derivative formula in a direction of the function of maximum type under the assumption of the convexity of the analogue of the set of permissible velocities, the necessary condition of optimality of the type of the maximum principle is proved. In the case of the convexity of the control domain, an analogue of the linearized principle of maximum is proved. The author declares no conflicts of interests.

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