Tseng Chung-Shi
IEEE Trans Syst Man Cybern B Cybern. 2006 Aug;36(4):940-5. doi: 10.1109/tsmcb.2005.860131.
To date, nonlinear Linfinity-gain filtering problems have not been solved by conventional methods for nonlinear dynamic systems with persistent bounded disturbances. This study introduces a fuzzy filtering design to deal with the nonlinear Linfinity-gain filtering problem. First, the Takagi and Sugeno fuzzy model is employed to approximate the nonlinear dynamic system. Next, based on the fuzzy model, a fuzzy filter is developed to minimize the upper bound of Linfinity-gain of the estimation error under some linear matrix inequality (LMI) constraints. Therefore, the nonlinear Linfinity-gain filtering problem is transformed into a suboptimal filtering problem, i.e., to minimize the upper bound of the Linfinity-gain of the estimation error subject to some LMI constraints. In this situation, the nonlinear Linfinity-gain filtering problem can be easily solved by an LMI-based optimization method. The proposed methods, which efficiently attenuate the peak of estimation error due to persistent bounded disturbances, extend the Linfinity-gain filtering problems from linear dynamic systems to nonlinear dynamic systems.
迄今为止，对于具有持续有界干扰的非线性动态系统，传统方法尚未解决非线性无穷增益滤波问题。本研究引入一种模糊滤波设计来处理非线性无穷增益滤波问题。首先，采用高木-菅野模糊模型对非线性动态系统进行逼近。其次，基于该模糊模型，开发一种模糊滤波器，以在一些线性矩阵不等式（LMI）约束下最小化估计误差的无穷增益上界。因此，非线性无穷增益滤波问题被转化为一个次优滤波问题，即在一些LMI约束下最小化估计误差的无穷增益上界。在这种情况下，非线性无穷增益滤波问题可以通过基于LMI的优化方法轻松解决。所提出的方法能够有效衰减由于持续有界干扰导致的估计误差峰值，将无穷增益滤波问题从线性动态系统扩展到非线性动态系统。
