Optimal Stationary Control with State Control Dependent Noise
Optimal Stationary Control with State Control Dependent Noise
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DOI：
10.1137/0309016
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发表时间：
1971-05
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影响因子：
--
通讯作者：
U. Haussmann
中科院分区：
文献类型：
--
作者：
U. Haussmann
本文用类似于Wonham [1]的方法分析了具有状态和控制相关噪声的稳态最优线性调节器。对于状态相关噪声，我们指的是在状态变量中具有线性系数的高斯白色噪声，并且对于控制相关噪声也是类似的。由于Zakai的稳定概率分布的存在性使用李雅普诺夫准则，它是可能的处理方程导致扩散过程与退化的微分发生器。研究发现，如果噪声足够小，则存在最优控制。进一步的分析，再次使用李雅普诺夫方法，产生的条件下，存在一个最优控制，无论多大的噪音。
The steady state optimal linear regulator with state and control dependent noise is analyzed in a manner similar to that developed by Wonham [1]. By state dependent noise we mean Gaussian white noise with coefficient linear in the state variable, and similarly for control dependent noise. Using a Lyapunov criterion for the existence of stationary probability distributions due to Zakai, it is possible to treat equations leading to diffusion processes with degenerate differential generators. It is found that if the noise is sufficiently small, then an optimal control exists. Further analysis, again using Lyapunov methods, yields conditions under which an optimal control exists no matter how large the noise is.