Journal of the Franklin Institute ( IF 4.1 ) Pub Date : 2021-02-12 , DOI: 10.1016/j.jfranklin.2021.02.005 Mengmeng Gao , Junsheng Zhao , Wei Sun
In this paper we consider the problem of stochastic control for Poisson jump-diffusion system driven by Brownian motion and Poisson process. Firstly, a mean-field stochastic bounded real lemma(SBRL) is derived in this paper. Secondly, a sufficient condition for the solvability of Poisson jump-diffusion linear quadratic (LQ) optimal control of discrete-time mean-field type is presented. Thirdly, based on the results of SBRL and LQ control, the sufficient conditions for the existence of mean-field stochastic control of Poisson jump-diffusion system are established by the solvability of the coupled matrix value equation. Finally, an example of recursive algorithm is presented to demonstrate the effectiveness of the proposed theory.
中文翻译:
随机 泊松跳跃的离散时间均场系统控制
在本文中,我们考虑了随机问题 布朗运动和泊松过程驱动的泊松跳跃扩散系统的控制 首先,推导了均值场有界实数引理(SBRL)。其次,给出了离散时间均场型泊松跳跃-扩散线性二次(LQ)最优控制的可解性的充分条件。第三,基于SBRL和LQ控制的结果,均值场随机存在的充分条件泊松跳跃-扩散系统的控制是通过耦合矩阵值方程的可解性建立的。最后,给出了一个递归算法的例子来证明所提理论的有效性。