Investigation of differential pursuit games under perturbation of the motion equation
DOI:
https://doi.org/10.31471/2304-7399-2025-20(76)-65-81Keywords:
differential pursuit game, multi-frequency perturbation, disturbance, averaging method, oscillatory integral, resonance, control, small parameter, Wronskian determinantAbstract
The article investigates differential pursuit games in conditions where the movement of the pursuer and the escaper is affected by external small disturbances. Similar problems but without taking into account perturbations were considered in the works of A.O. Chikrii. In this article the problem is considered in the case where the control matrix changes slowly over time and is affected by multi-frequency disturbances.
The averaging method is justified in the case of slowly changing frequencies. Estimates of the deviation were constructed between the solutions of the exact and averaged systems under the same initial conditions on a finite time interval.
An example of a modified differential game "Crocodile and Boy" with imposed disturbances is given. The pursuit completion time for the averaged model is found. The influence of disturbances with different strength on the game completion time is analyzed. The obtained results can be applied in various control problems, where it is important to take into account the influence of external factors on the behavior of participants in dynamic processes.
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