IEEE Trans Cybern. 2017 Jul;47(7):1630-1640. doi: 10.1109/TCYB.2016.2554141. Epub 2016 May 2.
In this paper, we investigate the stability of Takagi-Sugeno fuzzy-model-based (FMB) functional observer-control system. When system states are not measurable for state-feedback control, a fuzzy functional observer is designed to directly estimate the control input instead of the system states. Although the fuzzy functional observer can reduce the order of the observer, it leads to a number of observer gains to be determined. Therefore, a new form of fuzzy functional observer is proposed to facilitate the stability analysis such that the observer gains can be numerically obtained and the stability can be guaranteed simultaneously. The proposed form is also in favor of applying separation principle to separately design the fuzzy controller and the fuzzy functional observer. To design the fuzzy controller with the consideration of system stability, higher order derivatives of Lyapunov function (HODLF) are employed to reduce the conservativeness of stability conditions. The HODLF generalizes the commonly used first-order derivative. By exploiting the properties of membership functions and the dynamics of the FMB control system, convex and relaxed stability conditions can be derived. Simulation examples are provided to show the relaxation of the proposed stability conditions and the feasibility of designed fuzzy functional observer-controller.
本文研究了 Takagi-Sugeno 模糊模型的基于观测器的控制稳定性。当系统状态不可测时，设计了模糊观测器来直接估计控制输入，而不是系统状态。虽然模糊观测器可以降低观测器的阶数，但会导致许多观测器增益需要确定。因此，提出了一种新的模糊观测器形式，以方便稳定性分析，使得可以数值地获得观测器增益，并同时保证稳定性。所提出的形式也有利于应用分离原理来分别设计模糊控制器和模糊观测器。为了在考虑系统稳定性的情况下设计模糊控制器，使用了李雅普诺夫函数的更高阶导数（HODLF）来减少稳定性条件的保守性。HODLF 推广了常用的一阶导数。通过利用隶属函数的性质和 FMB 控制系统的动力学，可以推导出凸和宽松的稳定性条件。提供了仿真示例以显示所提出的稳定性条件的放宽程度和设计的模糊观测器-控制器的可行性。
