时滞非线性随机系统的无限时间H2/H∞控制  

Infinite Time Horizon H2/H∞ Control for Delayed Nonlinear Stochastic Systems

作　　者：朱怀念[1] 李方超 张成科[1] ZHU Huai-nian;LI Fang-chao;ZHANG Cheng-ke(School of Economics&Commence,Guangdong University of Technology,Guangzhou 510520,China;School of Management,Guangdong University of Technology,Guangzhou 510520,China)

机构地区：[1]广东工业大学经济与贸易学院,广东广州510520 [2]广东工业大学管理学院,广东广州510520

出　　处：《控制工程》2020年第2期278-287,共10页Control Engineering of China

基　　金：国家自然科学基金资助项目(71571053);广东省自然科学基金资助项目(2015A030310218,2016A030313701)。

摘　　要：研究了一类噪声依赖于状态、控制和干扰的时滞非线性随机系统的H2/H∞控制问题。首先,借助于4个耦合的Hamilton–Jacobi方程组(HJEs)得到了带时滞的非线性随机H2/H∞控制存在的充分性条件。然后,基于T–S模糊模型给出了噪声依赖状态和控制的时滞非线性随机系统的H2/H∞控制器的设计方案。控制器的设计可通过求解一组线性矩阵不等式(LMIs)获得,从而避开了求解耦合HJEs的困难。最后,数值仿真算例验证了文中所得结论的有效性。This paper investigates the problem of H2/H∞ control for nonlinear time-delay stochastic systems with state, control, and disturbance–dependent noise. Firstly, a sufficient condition for the existence of the nonlinear stochastic H2/H∞ control with time-delay is presented in terms of coupled Hamilton–Jacobi equations(HJEs). Secondly, by using the T-S fuzzy model, the stochastic H2/H∞ controller can be designed via solving a set of linear matrix inequalities(LMIs) instead of coupled HJEs. Finally, a numerical example is employed to show the effectiveness of the results obtained.

关 键 词：非线性随机系统 时滞 H2/H∞控制 T–S模糊模型 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]