A CLASS OF INFINITE-HORIZON STOCHASTIC DELAY OPTIMAL CONTROL PROBLEMS AND A VISCOSITY SOLUTION TO THE ASSOCIATED HJB EQUATION

Zhou Jianjun

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A CLASS OF INFINITE-HORIZON STOCHASTIC DELAY OPTIMAL CONTROL PROBLEMS AND A VISCOSITY SOLUTION TO THE ASSOCIATED HJB EQUATION

机译：一类无限时滞随机最优控制问题和HJB方程的粘性解

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In this paper, we investigate a class of infinite-horizon optimal control problems for stochastic differential equations with delays for which the associated second order Hamilton-Jacobi-Bellman (HJB) equation is a nonlinear partial differential equation with delays. We propose a new concept for the viscosity solution including time t and identify the value function of the optimal control problems as a unique viscosity solution to the associated second order HJB equation.

机译：在本文中，我们研究了一类带时滞的随机微分方程的无限水平最优控制问题，其中相关的二阶Hamilton-Jacobi-Bellman（HJB）方程是一个带时滞的非线性偏微分方程。我们为粘度解决方案提出了一个新的概念，包括时间t，并将最佳控制问题的值函数确定为相关二阶HJB方程的唯一粘度解决方案。

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《ESAIM》 |2018年第2期|639-676|共38页
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Zhou Jianjun;
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1. HJB EQUATIONS FOR THE OPTIMAL CONTROL OF DIFFERENTIAL EQUATIONS WITH DELAYS AND STATE CONSTRAINTS, I: REGULARITY OF VISCOSITY SOLUTIONS [J] . Federico S, Goldys B, Gozzi F SIAM Journal on Control and Optimization . 2010,第7a8期

机译：具有时滞和状态约束的微分方程的最优控制的HJB方程，I：粘度解的规律性
2. ON THE VISCOSITY SOLUTIONS OP HYBRID HJB EQUATIONS ARISING IN OPTIMAL CONTROL OF LOSS NETWORKS [J] . ZHONGJING MA, PETER E. CAINES, ROLAND P. MALHAME Communications in Information and Systems . 2008,第1期

机译：损失网络最优控制中的混合HJB方程粘性解的研究
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机译：具有时滞和状态约束的微分方程的最优控制的HJB方程，II：验证和最优反馈
4. Stochastic Control of Network Systems II: NETCAD Optimal Control the HJB Equation [C] . Zhongjing Ma, Caines, P.E., . 2006

机译：网络系统的随机控制II：NETCAD最优控制和HJB方程
5. Viscosity solutions of second order equations in a separable Hilbert space and applications to stochastic optimal control [D] . Kelome, Djivede Armel 2002

机译：可分离希尔伯特空间中二阶方程的粘滞解及其在随机最优控制中的应用
6. Existence and Uniqueness of Solution for a Class of Stochastic Differential Equations [O] . Junfei Cao, Zaitang Huang, Caibin Zeng 2013

机译：一类随机微分方程解的存在唯一性
7. HJB equations in Hilbert spaces related to optimal control of stochastic Navier-Stokes equations(Viscosity Solution Theory of Differential Equations and its Developments) [O] . Swiech Andrzej 2006

机译：希尔伯特空间中的HJB方程与随机Navier-Stokes方程的最优控制有关（微分方程的粘滞解理论及其发展）
8. Nearly Optimal Solution of HJB Equation Using Neural Networks: Applications to Control of DoD Systems and MEMS Assembly [R] . Lewis, F. L. 2005

机译：基于神经网络的HJB方程近似最优解：在DoD系统和mEms组件控制中的应用

A CLASS OF INFINITE-HORIZON STOCHASTIC DELAY OPTIMAL CONTROL PROBLEMS AND A VISCOSITY SOLUTION TO THE ASSOCIATED HJB EQUATION

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