%0 Journal Article
%T (x,u,v)-依赖噪声的离散时间平均场随机H<sub>2</sub>/H<sub>∞</sub>控制<br>Discrete-Time Mean-Field Stochastic H<sub>2</sub>/H<sub>∞</sub> Control with (x,u,v)-Dependent Noise
%A 贾亚琪
%A 张春梅
%A 杨路
%A 陈柏江
%J Advances in Applied Mathematics
%P 3860-3871
%@ 2324-8009
%D 2023
%I Hans Publishing
%R 10.12677/AAM.2023.129380
%X 本文研究了一类(x,u,v)(状态，输入，扰动)-依赖噪声的离散时间平均场随机系统的有限时域混合H<sub>2</sub>/H<sub>∞</sub>控制问题。首先，给出了已有的平均场随机有界实引理(SBRL)；其次，呈现了离散时间平均场随机线性二次(LQ)最优控制问题可解的充分条件。最后，基于SBRL和LQ最优控制的结果，通过耦合矩阵差分方程的可解性得到了离散时间平均场随机<span>H</span><sub>2</sub><span>/H</span><sub>∞</sub>控制存在的充分必要条件，延伸了之前的结果。<br />
This paper is concerned with the finite horizon mixed <span>H</span><sub>2</sub><span>/H</span><sub>∞</sub> control problem for a class of dis-crete-time mean-field stochastic systems with (x,u,v) -dependent noise. Firstly, the existing mean-field stochastic bounded real lemma (SBRL) is given. Then, we presented a sufficient condi-tion for the solvability of discrete-time mean-field stochastic linear quadratic (LQ) optimal control problem for the considered system. Finally, based on the results of SBRL and LQ optimal control, a necessary and sufficient condition is obtained for the existence of discrete-time mean-field stochas-tic <span>H</span><sub>2</sub><span>/H</span><sub>∞</sub> control via the coupled matrix difference equations, which extends the previous results.
%K 离散时间系统，H<sub>2</sub>/H<sub>∞</sub>控制，平均场<br>Discrete-Time Systems
%K H<sub>2</sub>/H<sub>∞</sub> Control
%K Mean-Field
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=72030