控制参数带有乘性噪声的线性系的最优控制
Optimal control of a linear system with multiplicative noise at control parameter
摘要：
研究了一类由常微分方程组成的线性系所描述的控制过程，该系统中的控制参数具有一种特殊类型的噪声。作为代价泛函，考虑了最终状态向量进入相空间中给定集合的概率。最优性的必要条件（庞特里亚金最大值原理的形式）和存在定理。将初始控制问题转化为辅助确定性问题，讨论了辅助泛函的可微性。
英文摘要：
We investigate a control process described by a linear system of ordinary differential equations with a noise of special type acting to the control parameter. As the cost functional the probability of the final state vector to enter to a given set in the phase space is considered. Necessary conditions of optimality (of the Pontryagin maximum principle form) and existence theorems are developed. The initial control problem was trasformed to an auxiliary deterministic problem, the differentiability of the auxiliary functional was discussed.
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