Algorithm for Solving a Two-Level Game Problem of Dynamic System Trajectory Transfer
DOI:
https://doi.org/10.71310/pcam.5_69.2025.05Keywords:
dynamic system, game problem, support, algorithmAbstract
The game problem of transferring the trajectory of a dynamic system controlled by two players whose goals are opposite, from any point of a given set to a terminal set is considered. The given set is described by the control parameter of the first player. The first player chooses his control first, then, knowing the first player’s control, the second player chooses his control. The goal of the first player is to choose a control to prevent the trajectory of the dynamic system from entering the terminal set under any control of the second player, and the goal of the second player is to choose a control to transfer the trajectory of the dynamic system to the terminal set under any control of the first player. If the second player manages to transfer the system trajectory to the terminal set, then the additional goal of the first player is to maximize the minimum functional for the second player’s control, and the additional goal of the second player is to minimize the linear functional. An algorithm for solving the problem under consideration has been developed and substantiated. An illustrative example is given.
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