Root / CYBERNETICS AND PHYSICS / Volume 15, 2026, Number 1 / Control problem of a linear non-stationary system subject to an integral constraint

Control problem of a linear non-stationary system subject to an integral constraint

Vanya Barseghyan, Emil Barseghyan

This paper investigates a nonlocal control problem of a linear non-stationary dynamic system described by an ordinary differential equation subject to an integral constraint imposed on the components of the state vector over a certain subinterval of the system’s operating time. Conditions for complete controllability of the dynamic system under the imposed integral constraints are formulated. Conditions ensuring the existence of a solution to the control problem with such a nonlocal constraint are obtained. A constructive approach to solving the control problem is proposed, and the corresponding solution is constructed. The continuity and non-uniqueness of the control function are demonstrated. As an illustration, a control problem for the oscillatory motion of a material point with classical boundary conditions and an integral condition is solved.
CYBERNETICS AND PHYSICS, VOL. 15, NO. 1, 2026, 10–17
https://doi.org/10.35470/2226-4116-2026-15-1-10-17

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