Modified Resolving-Functions Method for Game Problems of Approach of Controlled Objects with Different Inertia - Chikrii, A. A.; Rappoport, I. S. (Cybernetics and systems analysis, 2023)
The problem of the approach of controlled objects with different inertia in dynamic game problems is considered. Modified sufficient conditions for ending the game in a finite guaranteed time when Pontryagin’s condition is not satisfied are formulated. Some shift functions are considered instead of the Pontryagin selector, and special multi-valued mappings are introduced with their help. They generate the upper and lower resolving functions of a special type, and based on them, two types of modified schemes are proposed: the scheme of Pontryagin’s first method and the method of resolving functions. This ensures the completion of the conflict-controlled process for objects with different inertia in the class of quasi-strategies and counter-controls. New theoretical results are illustrated by a model example.