Dynamic Programming of the Stochastic Burgers Equation Driven by Lévy Noise

被引：0

作者：

Mohan, Manil T. ^{[1
]}

Sakthivel, Kumarasamy ^{[2
]}

Sritharan, Sivaguru S. ^{[3
]}

机构：

[1] Indian Inst Technol Roorkee IIT Roorkee, Dept Math, Haridwar Highway, Roorkee 247667, Uttaranchal, India

[2] Indian Inst Space Sci & Technol IIST, Dept Math, Trivandrum 695547, India

[3] AFRL, Natl Acad, Dayton, OH 45431 USA

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2024年 / 201卷 / 02期

关键词：

Stochastic Burgers equation; Levy noise; Dynamic programming; Hamilton-Jacobi-Bellman equation; NAVIER-STOKES EQUATION; LARGE DEVIATIONS; INEQUALITIES; ERGODICITY;

D O I：

10.1007/s10957-024-02387-5

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this work, we study the optimal control of stochastic Burgers equation perturbed by Gaussian and Levy-type noises with distributed control process acting on the state equation. We use dynamic programming approach for the feedback synthesis to obtain an infinite-dimensional second-order Hamilton-Jacobi-Bellman (HJB) equation consisting of an integro-differential operator with Levy measure associated with the stochastic control problem. Using the regularizing properties of the transition semigroup corresponding to the stochastic Burgers equation and compactness arguments, we solve the HJB equation and the resultant feedback control problem.

引用

页码：490 / 538

页数：49

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