(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
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。
Abstract: 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.
文章引用：贾亚琪, 张春梅, 杨路, 陈柏江. (x,u,v)-依赖噪声的离散时间平均场随机H2/H∞控制[J]. 应用数学进展, 2023, 12(9): 3860-3871. https://doi.org/10.12677/AAM.2023.129380

参考文献

[1] Limebeer, D.J.N., Anderson, B.D.O. and Hendel, B. (1994) A Nash Game Approach to Mixed H2/H∞ Control. Auto-matic Control. IEEE Transactions on Automatic Control, 39, 69-82. [Google Scholar] [CrossRef] 
[2] Khargonekar, P.P. and Rotea, M.A. (1991) Mixed H2/H∞ Control: A Con-vex Optimization Approach. IEEE Transactions on Automatic Control, 36, 824-837. [Google Scholar] [CrossRef] 
[3] Chen, B.-S., Tseng, C.-S. and Uang, H.-J. (2000) Mixed H2/H∞ Fuzzy Out-put Feedback Control Design for Nonlinear Dynamic Systems: An LMI Approach. IEEE Transactions on Fuzzy Sys-tems, 8, 249-265. [Google Scholar] [CrossRef] 
[4] Zhang, W.H., Huang, Y.L. and Zhang, H.S. (2007) Stochastic H2/H∞ Con-trol for Discrete-Time Systems with State and Disturbance Dependent Noise. Automatica, 43, 513-521. [Google Scholar] [CrossRef] 
[5] Chen, B.-S. and Zhang, W.H. (2004) Stochastic H2/H∞ Con-trol with State-Dependent Noise. IEEE Transactions on Automatic Control, 49, 45-57. [Google Scholar] [CrossRef] 
[6] Huang, Y., Zhang, W. and Feng, G. (2008) Infinite Horizon H2/H∞ Control for Stochastic Systems with Markovian Jumps. Automatica, 44, 857-863. [Google Scholar] [CrossRef] 
[7] Zhang, W. and Feng, G. (2008) Nonlinear Stochastic H2/H∞ Control with -Dependent Noise: Infinite Horizon Case. IEEE Transactions on Automatic Control, 53, 1323-1328. [Google Scholar] [CrossRef] 
[8] Hou, T., Zhang, W. and Ma, H. (2008) Robust H2/H∞ Control for Discrete-Time Stochastic Systems with Markovian Jumps and Multiplicative Noise: Finite Horizon Case. 2008 27th Chinese Control Conference, Kunming, 16-18 July 2008, 754-758. [Google Scholar] [CrossRef] 
[9] Li, X., Wang, W., Xu, J. and Zhang, H. (2018) Solution to Mixed H2/H∞ Control for Discrete-Time Systems with -Dependent Noise. International Journal of Control Au-tomation & Systems, 17, 273-285. [Google Scholar] [CrossRef] 
[10] Ma, L., Zhang, T., Zhang, W. and Chen, B.-S. (2015) Finite Horizon Mean-Field Stochastic H2/H∞ Control for Continuous-Time Systems with -Dependent Noise. Journal of the Franklin Institute, 352, 5393-5414. [Google Scholar] [CrossRef] 
[11] Zhang, W., Ma, L. and Zhang, T. (2017) Discrete-Time Mean-Field Stochastic H2/H∞ Control. Journal of Systems Science & Complexity, 30, 765-781. [Google Scholar] [CrossRef] 
[12] Yong, J. (2013) Linear-Quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equations. SIAM Journal on Control and Optimization, 51, 2809-2838. [Google Scholar] [CrossRef] 
[13] Huang, J., Li, X. and Yong, J. (2015) A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations in Infinite Horizon. Mathematical Control & Related Fields, 5, 97-139. [Google Scholar] [CrossRef] 
[14] Elliott, R., Li, X. and Ni, Y.-H. (2013) Discrete Time Mean-Field Stochastic Linear-Quadratic Optimal Control Problems. Automatica, 49, 3222-3233. [Google Scholar] [CrossRef] 
[15] Ni, Y.-H., Elliott, R. and Li, X. (2015) Discrete-Time Mean-Field Stochastic Linear-Quadratic Optimal Control Problems, II: Infinite Horizon Case. Automatica, 57, 65-77. [Google Scholar] [CrossRef] 
[16] Ni, Y.-H., Li, X. and Zhang, J.-F. (2016) Mean-Field Sto-chastic Linear-Quadratic Optimal Control with Markov Jump Parameters. Systems and Control Letters, 93, 69-76. [Google Scholar] [CrossRef] 
[17] Ma, L., Zhang, T., and Zhang, W. (2016) H∞ Control for Con-tinuous-Time Mean-Field Stochastic Systems. Asian Journal of Control, 18, 1630-1640. [Google Scholar] [CrossRef] 
[18] Ma, L. and Zhang, W. (2015) Output Feedback H∞ Control for Dis-crete-Time Mean-field Stochastic Systems. Asian Journal of Control, 17, 2241-2251. [Google Scholar] [CrossRef] 
[19] Ma, H. (2022) A Bounded Real Lemma for Discrete-Time Linear Mean-Field Stochastic Systems. In: Jia, Y., Zhang, W., Fu, Y. and Zhao, S., Eds., Proceedings of 2022 Chinese Intelli-gent Systems Conference. CISC 2022. Lecture Notes in Electrical Engineering, Vol. 950, Springer, Singapore, 881-890. [Google Scholar] [CrossRef] 
[20] Song, T. and Liu, B. (2021) Discrete-Time Mean-Field Sto-chastic Linear-Quadratic Optimal Control Problem with Finite Horizon. Asian Journal of Control, 23, 979-989. [Google Scholar] [CrossRef] 

为你推荐