This paper addresses the problem of robust actuator fault reconstruction for Takagi-Sugeno (T-S) fuzzy systems subjects to actuator faults, unknown inputs and time-varying delays via a Fuzzy Synthesized Learning and Luenberger Observer (FSL2O). Through a coordinate transformation, the original T-S fuzzy system is decomposed into two subsystems: subsystem-1 effected by actuator faults and subsystem-2 effected by unknown inputs. In the presented FSL2O methodology, a Reduced-Order Fuzzy Learning Observer (ROFLO) is explored for the subsystem-1 to reconstruct actuator faults accurately while a Reduced-Order Fuzzy State (Luenberger) Observer (ROFSO) is designed for the subsystem-2 based on the H∞ control technique such that it has strong robustness against the unknown inputs. The synthesized design of the ROFLO and the ROFSO is formulated in a unified manner in terms of Linear Matrix Inequalities (LMIs) that can be conveniently solved using LMI optimization technique. In addition, as a comparison, a full-order FLO is suggested for robust actuator fault reconstruction. Finally, a numerical example and simulation are provided to demonstrate the effectiveness of the proposed approaches.

中文翻译：

---

通过综合学习和 Luenberger 观测器对时变延迟的 Takagi-Sugeno 模糊系统进行鲁棒的执行器故障重建

本文通过模糊综合学习和 Luenberger Observer (FSL2O) 解决了受执行器故障、未知输入和时变延迟影响的 Takagi-Sugeno (TS) 模糊系统的鲁棒执行器故障重建问题。通过坐标变换，原始的 TS 模糊系统被分解为两个子系统：受执行器故障影响的子系统 1 和受未知输入影响的子系统 2。在提出的 FSL2O 方法中，为子系统 1 探索了降阶模糊学习观察器 (ROFLO) 以准确重建执行器故障，而降阶模糊状态 (Luenberger) 观察器 (ROFSO) 则为基于子系统 2 设计H∞ 控制技术，使其对未知输入具有很强的鲁棒性。ROFLO 和 ROFSO 的综合设计是根据线性矩阵不等式 (LMI) 以统一方式制定的，可以使用 LMI 优化技术方便地求解。此外，作为比较，建议使用全阶 FLO 进行稳健的执行器故障重建。最后，提供了一个数值例子和仿真来证明所提出方法的有效性。