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September 10, 2025International Scientific Technical Journal Problems of Control and Informatics0 citationsOpen Access

Stages and main tasks of the century-long control theory and system identification development. Part IX. Countercontrol in game problems of dynamics

ACA. A. ChikriĭV.M. Glushkov Institute of Cybernetics VGVyacheslav F. GubarevState Space Agency of Ukraine VRViktor RomanenkoNational Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”

Key Points

The study introduces upper and lower resolving functions, allowing trajectories to meet a terminal set in finite time.
Sufficient conditions are established when Pontryagin’s condition is not satisfied, demonstrating alternate methodologies.
Various method schemes compare the proposed approach with Pontryagin’s first direct method for better insights.
By separating data and control blocks, the research opens avenues for a broader exploration of functional-differential systems.

Abstract

This paper considers the problem of bringing the trajectory of quasilinear conflict-controlled process to a given cylindrical set. We proceed with representation of a trajectory of dynamic system in the form, in which the block of initial data is separated from the control block. This makes it feasible to consider a wide spectrum of functional-differential systems. The method of resolving functions, based on use of the inverse Minkovski functionals, serves as ideological tool for study. Attention is focused on the case when Pontryagin’s condition does not hold. In this case the upper and lower resolving functions of two types are introduced. With their help sufficient conditions of approach a terminal set in a finite time are deduced. Various method schemes are provided and comparison with Pontryagin’s first direct method is given.

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