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摘要: 本文研究线性终端状态约束下不定随机线性二次最优控制问题.首先利用Lagrange Multiplier 定理得到了存在最优线性状态反馈解的必要条件, 而在加强的条件下也得到了最优控制存在的充分条件. 从某种意义上讲, 以往关于无约束随机线性二次最优控制的一些结果可以看成本文主要定理的推论.
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关键词:
- 随机LQ最优控制 /
- 线性约束 /
- Lagrange Multiplier 定理 /
- 广义微分Riccati方程
Abstract: This paper studies indefinite stochastic linear quadratic optimal control problem with linear terminal state constraint. At first, we present a necessary condition for the existence of optimal linear state feedback control by means of Lagrange multiplier theorem. Then, a sufficient condition is also given under the strengthened conditions. To some extent, the previous results on stochastic linear quadratic optimal control without constraint can be viewed as corollaries of the main theorems of this paper. -
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