Abstract In this work, we mainly study the exact controllability of stochastic differential equations with memory. For time invariant systems, by applying forward backward stochastic differential equations, some rank criteria ensuring systems’ exact controllability are provided. For time variant systems, equivalent conditions guaranteeing systems’ exact controllability are given. For deterministic systems, as a special case of stochastic ones, more easily checkable rank criteria (for time invariant systems) and alternative conditions (for time variant systems) are proposed.

中文翻译：

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具有记忆的随机微分方程的精确可控性

摘要 本文主要研究具有记忆性的随机微分方程的精确可控性。对于时不变系统，通过应用前向后向随机微分方程，提供了一些保证系统精确可控性的秩准则。对于时变系统，给出了保证系统精确可控性的等效条件。对于确定性系统，作为随机系统的一个特例，提出了更容易检查的等级标准（对于时不变系统）和替代条件（对于时变系统）。