Distributed recursive filtering for discrete time-delayed stochastic nonlinear systems based on fuzzy rules

Abstract

The distributed recursive filtering problem is investigated in this paper for discrete time-delayed nonlinear stochastic systems, where the well-known Takagi–Sugeno (T-S) fuzzy model is used to approximate the nonlinearities. According to obtain the system dynamics, a novel structure of distributed filters is developed, where the difference of estimated states from neighboring sensors is exploited to improve the one-step prediction, and the desired estimation is obtained by fusing the estimation under different rules. Attention is focused on the design of a distributed recursive filter such that, in the presence of time-delays and defuzzifying operations, an upper bound of the filtering error covariance is obtained and then minimized by properly designing filter parameters via elaborate mathematical analysis. With the exception of the desired gains with the online recursive form are dependent on the solutions of two Riccati-type difference equations, and the upper bound is further optimized via the introduced parameters. As a final point, a simulation examples is exploited to show the applicability of the developed filtering scheme.