具有随机脉冲的随机微分方程的最优控制和汉密尔顿-雅各比-贝尔曼方程

Qian‐Bao Yin, Xiao‐Bao Shu, Yu Guo, Zi‐Yu Wang
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摘要

本文研究了具有随机脉冲的随机微分方程的最优控制。我们优化了性能指标,并用随机补偿函数将随机脉冲的影响加入到性能指标中。利用随机分析思想和动态编程原理,得到了一个新的汉密尔顿-雅各比-贝尔曼(HJB)方程,并证明了其粘性解的存在性和唯一性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Optimal control of stochastic differential equations with random impulses and the Hamilton–Jacobi–Bellman equation
In this article, we study the optimal control of stochastic differential equations with random impulses. We optimize the performance index and add the influence of random impulses to the performance index with a random compensation function. Using the idea of stochastic analysis and dynamic programming principle, a new Hamilton–Jacobi–Bellman (HJB) equation is obtained, and the existence and uniqueness of its viscosity solution are proved.
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