State and Fault Estimation for T-S Fuzzy Nonlinear Systems Using an Ensemble UKF

This paper introduces a new filter based on a Takagi-Sugeno (T-S) fuzzy augmented ensemble unscented Kalman filter (FAEnUKF) for a class of nonlinear stochastic systems with multiplicative fault and noise. Multiplying a nonlinear term on the fault signal generates a non-Gaussian noise which cannot be optimally estimated by the Kalman filter. One way to resolve this problem is to transform the nonlinear system to several T-S fuzzy systems with Gaussian noise. Using the sector nonlinearity model, the nonlinear term can be derived as constant matrices for each fuzzy rule. Thus, fuzzy augmented UKFs (AUKFs) are designed for state and fault estimation. Using Lyapunov's stability theory, the convergence conditions of the developed filter algorithm are presented as a theorem. In addition, the boundedness of the error covariance matrix of the proposed algorithm is discussed theoretically. Finally, selected illustrative examples to evaluate the effectiveness of the FAEnUKF are presented. Comparisons between the FAEnUKF and the augmented extended Kalman filter (AEKF) and the AUKF are made in a numerical example. The simulation results showed the robustness of the fuzzy ensemble UKF for modeling the non-Gaussian noise. Despite the increase in the number of calculations in this method, the root-mean-square error (RMSE) is less than other filters.