Control Engineering of China ›› 2020, Vol. 27 ›› Issue (02): 278-287.
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Abstract: 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.
Key words: Nonlinear stochastic systems, time-delay, H2/H∞ control, T-S fuzzy model
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。
关键词: 非线性随机系统, 时滞, H2/H∞控制, T–S模糊模型
ZHU Huai-nian, LI Fang-chao, ZHANG Cheng-ke. Infinite Time Horizon H2/H∞ Control for Delayed Nonlinear Stochastic Systems[J]. Control Engineering of China, 2020, 27(02): 278-287.
朱怀念, 李方超, 张成科. 时滞非线性随机系统的无限时间H2/H∞控制[J]. 控制工程, 2020, 27(02): 278-287.
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