## №2, 2011

# APPLICATION OF ARTIFICIAL NEURAL NETWORK IN OPTIMAL PURSUIT PROBLEM WITH RESPECT TO DOMAIN

In the present paper, the convex domain’s space is constructed and a scalar product is introduced. The derivative of a domain function in this space is defined. Using this approach, a method is proposed to investigate an optimal control pursuit problem with respect to domain. Unlike the traditional problem, here the controller and trajectory are a domain at each moment of time. In other words, controller and trajectory are a domain function. At first we show the existence of the solution of Cauchy problem where the process is described, and then prove the maximum principle for the considered optimal control problem. Using the obtained results, we offer an algorithm for its numerical solution and train it to neural network. (p. 38-48)

**Keywords:**

*support function, optimal pursuit, artificial neural network, network training.*

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