Reliable Robust H∞ Fuzzy Control for Uncertain Nonlinear Systems With Markovian Jumping Actuator Faults
Reliable Robust H∞ Fuzzy Control for Uncertain Nonlinear Systems With Markovian Jumping Actuator Faults
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DOI：
10.1115/1.2718236
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发表时间：
2007-05
影响因子：
1.7
通讯作者：
Huai‐Ning Wu
中科院分区：
文献类型：
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作者：
Huai‐Ning Wu
本文主要研究具有马尔可夫跳跃执行器故障的不确定非线性连续时间系统的可靠鲁棒H ∞ 模糊控制的设计。采用Takagi和Sugeno模糊模型来表示具有马尔可夫跳跃执行器故障的不确定非线性系统。首先，基于并行分布式补偿(PDC)方案，推导了闭环模糊系统鲁棒随机稳定且满足规定的H ∞ 扰动衰减水平的充分条件。在推导过程中，使用随机Lyapunov函数来测试系统的稳定性和H ∞ 性能。然后，将一种新的改进的线性矩阵不等式（LMI）公式应用于该条件，以减轻随机 Lyapunov 矩阵与包含控制器变量的系统矩阵之间的相互关系，从而产生可靠且鲁棒的 H ∞ 模糊控制器存在的基于 LMI 的易于处理的条件。提出了次优模糊控制器来最小化受 LMI 约束的干扰衰减水平。最后给出一个仿真例子来说明该方法的有效性。
This paper is concerned with the design of reliable robust H ∞ fuzzy control for uncertain nonlinear continuous-time systems with Markovian jumping actuator faults. The Takagi and Sugeno fuzzy model is employed to represent an uncertain nonlinear system with Markovian jumping actuator faults. First, based on the parallel distributed compensation (PDC) scheme, a sufficient condition such that the closed-loop fuzzy system is robustly stochastically stable and satisfies a prescribed level of H ∞ -disturbance attenuation is derived. In the derivation process, a stochastic Lyapunov function is used to test the stability and H ∞ performance of the system. Then, a new improved linear matrix inequality (LMI) formulation is applied to this condition to alleviate the interrelation between the stochastic Lyapunov matrix and system matrices containing controller variables, which results in a tractable LMI-based condition for the existence of reliable and robust H ∞ fuzzy controllers. A suboptimal fuzzy controller is proposed to minimize the level of disturbance attenuation subject to the LMI constraints. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.