A Novel Finite-Frequency Optimization Fault Detection for Fuzzy Systems by Membership Functions Iterative Learning
针对T-S模糊系统，提出一种有限频率优化故障检测策略，通过加权模糊故障检测观测器和在线隶属函数迭代学习算法，使残差信号对外部干扰鲁棒、对故障敏感，并用仿真验证了方法的可行性。
This article presents the finite-frequency optimization fault detection (FD) strategy for Takagi-Sugeno (T-S) fuzzy systems. Under the imperfect premise matching (IPM) policy, a weighted fuzzy FD observer (WFFDO) with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{\infty }/L_{2}$ </tex-math></inline-formula> robustness performance and the finite-frequency <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ H_{-}$ </tex-math></inline-formula> fault sensitivity performance is first proposed, which signifies the residual signal is robust to the external interference and sensitive to potential faults. Some parameters and slack matrices are introduced to obtain more relaxed conditions of designing the WFFDO with mixed performance. Afterward, a new online membership functions (MFs) iterative learning algorithm with the exponential decay learning rate is proposed for the sake of updating the observer MFs in real-time such that optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{\infty }/L_{2}$ </tex-math></inline-formula> performance can be achieved in this article. In addition, sufficient criterion is established so as to ensure the convergence of the structured mean squared error cost function by means of Lyapunov stability theory. Eventually, two simulation examples are given for illustrating the feasibility and superiority of the developed optimization FD technique.