On the Correctness of Some Problems of Control of a Mass Point

摘要

The mass point control problem, complicated by the boundary condition, is considered. The "usual" and asymptotic versions of the problem, which are connected with the question of process finishing at a fixed time moment, are considered. We found that for one of problem formulations, while changing the parameter which determined the boundary condition, the stability while weakening boundary condition (the case of nonnegative controls) took place for all but two values of the parameter. We also showed that one of the nonregular values of the parameter, while changing the class of admissible controls (passage to the class of alternating controls), ensured the stability property while weakening the boundary condition.