On Optimal Control of a Non-Terminating Diffusion Process with Reflection
On Optimal Control of a Non-Terminating Diffusion Process with Reflection
复制标题
带反射的非终止扩散过程的最优控制
DOI：
10.1137/1114063
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发表时间：
1969
期刊：
影响因子：
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通讯作者：
Yakov A. Kogan
中科院分区：
文献类型：
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作者：
Yakov A. Kogan
非终止扩散过程的最优控制497段内由漂移和扩散系数定义，段末端由Feller-Ventzel边界条件定义的一维扩散过程的最优控制。控制量为漂移系数和扩散系数。注意[1]中基本定理的证明本质上是一维的。[2]讨论了区域内部和边界上多维非终止扩散过程的最优控制问题的表述。但是这个问题的解只在一维情况下给出。本文致力于将[1]的结果推广到当边界条件简化为与边界非切向的方向上的反射时的多维情况。这里，与[4]-[6]一样，只有漂移系数被认为是可控的。这种推广在应用中特别有意义，因为在控制通道中存在干扰（“白噪声”类型）的情况下，合成具有梯度自动优化的最优系统的问题简化为在边界上有反射的有界区域中非终止扩散过程的最优控制问题。
Optimal control ofa non-terminating diffusionprocess 497 of optimal control of one-dimensional diffusion processes defined withina segment by drift and diffusion coefficients and at the ends of the segment by the Feller-Ventzel’boundary conditions. The controlled quantities were the drift and diffusion coefficients. Note that proofs of the basic theorems in [1] were essentially one-dimensional.[2] deals with the formulation of the problem of optimal control of a multidimensional non-terminating diffusion process in the interioras well as on theboundary ofthe region. But the solution of the problemwas given for the one-dimensional case only.The present work is devoted to generalizing the results of [1] to the multidimensional case when the boundary conditions are reduced to reflection in the direction), which is non-tangential to the boundary. Here, as in [4]-[6], only the drift coefficients will be considered controlled. Such a generalizationis, in particular, of interest in applications, since the problem of synthesizing an optimal system with a gradient automatic optimization in the presence of interference (of" white noise" type) in the control channel reduces to theproblem of optimal control of non-terminating diffusion processes in a bounded region with reflection on its boundary.