Delay optimal control and viscosity solutions to associated Hamilton-Jacobi-Bellman equations
Delay optimal control and viscosity solutions to associated Hamilton-Jacobi-Bellman equations
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相关 Hamilton-Jacobi-Bellman 方程的延迟最优控制和粘度解
DOI：
10.1080/00207179.2018.1436769
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发表时间：
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影响因子：
2.1
通讯作者：
Jianjun Zhou
中科院分区：
文献类型：
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作者：
Jianjun Zhou
本文研究了一类时滞微分方程的最优控制问题，其中相应的Hamilton-Jacobi-Bellman（HJB）方程为非线性时滞偏微分方程.这类HJB方程以前没有被研究过，并且由于状态方程不具有光滑性质而难以求解。我们引入了一个新的概念的粘性解决方案，并确定值泛函的最优控制问题的唯一解决方案相关联的HJB方程。作为应用，给出了一个分析实例。
In this article, optimal control problems of differential equations with delays are investigated for which the associated Hamilton–Jacobi–Bellman (HJB) equations are nonlinear partial differential equations with delays. This type of HJB equation has not been previously studied and is difficult to solve because the state equations do not possess smoothing properties. We introduce a new notion of viscosity solutions and identify the value functional of the optimal control problems as the unique solution to the associated HJB equations. An analytical example is given as application.