In this paper we perform a complete probabilistic study of a finite dimensional linear control system with uncertainty. The controllability condition with random initial data and final target is analysed. To conduct this investigation we determine the first probability density function of the control and the solution of the random control problem under different scenarios. To achieve this objective, Random Variable Transformation technique is extensively applied. Several examples illustrate the theoretical results.

中文翻译：

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具有初始和最终条件随机的有限维线性控制系统的全概率解

在本文中，我们对具有不确定性的有限维线性控制系统进行了完整的概率研究。分析了随机初始数据和最终目标的可控性条件。为了进行这项研究，我们确定了在不同情况下控制的第一概率密度函数和随机控制问题的解。为了实现该目标，广泛应用了随机变量变换技术。几个例子说明了理论结果。