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This article presents the possibility of helping navigators direct the movement of an object, while safely passing through other objects, using an artificial neural network and optimization methods. It has been shown that the best trajectory of an object in terms of optimality and security, from among many possible options, can be determined by the method of dynamic programming with the simultaneous use of an artificial neural network, by depicting the encountered objects as moving in forbidden domains. Analytical considerations are illustrated with examples of simulation studies of the developed calculation program on real navigational situations at sea. This research took into account both the number of objects encountered and the different shapes of domains assigned to the objects encountered. Finally, the optimal value of the safe object trajectory time was compared on the setpoint value of the safe passing distance of objects in given visibility conditions at sea, and the degree of discretization of calculations was determined by the density of the location of nodes along the route of objects.

Multistage Dynamic Optimization with Different Forms of Neural-State Constraints to Avoid Many Object Collisions Based on Radar Remote Sensing