(x,u,v)-依赖噪声的离散时间平均场随机H₂/H_∞控制  

Discrete-Time Mean-Field Stochastic H2/H∞ Control with (x,u,v)-Dependent Noise

作　　者：贾亚琪 张春梅 杨路 陈柏江 

机构地区：[1]重庆理工大学理学院,重庆

出　　处：《应用数学进展》2023年第9期3860-3871,共12页Advances in Applied Mathematics

摘　　要：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H2/H∞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H2/H∞控制存在的充分必要条件,延伸了之前的结果。This paper is concerned with the finite horizon mixed H2/H∞ 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 H2/H∞ control via the coupled matrix difference equations, which extends the previous results.

关 键 词：离散时间系统 H₂/H_∞控制 平均场 

分 类 号：O17[理学—数学]