Fuzzy Filtering Problem Research Articles

Event-Triggered Fault Detection Filtering of Fuzzy-Model-Based Systems With Prescribed Performance

This article deals with the fault detection filtering problem for a nonlinear dynamic system in the Takagi–Sugeno fuzzy framework. An event-triggered scheme considering network bandwidth utilization rate and fault occurrence probability is utilized, which can conserve communication resources and reduce computational burden. The fault detection fuzzy filter is used as a residual generator, and the proposed event-based fault detection scheme is formulated as a fuzzy filtering problem. Moreover, the generated residual is robust against exogenous disturbances while being sensitive to system faults, and the resulting fault detection system has asymptotic stability with a specified <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> error property. The corresponding solvability conditions of the fault detection filter are constructed by converting the nonconvex feasibility problem into a series of optimization problems. Finally, a numerical simulation is conducted to demonstrate the feasibility and validity of the proposed scheme.

Sampled-data H∞ fuzzy filtering for nonlinear systems with missing measurements

In this paper, a sampled-data H∞ fuzzy filtering problem is considered for nonlinear systems with missing measurements. The nonlinear sampled-data system and missing measurements are assumed to be represented by a Takagi–Sugeno (T–S) fuzzy system and an independent, identically distributed Bernoulli random process, respectively. Based on the fuzzy system, the H∞ fuzzy filtering problem is formulated to design the sampled-data fuzzy filter. By using the exponential mean-square stability definition, the stability condition with an H∞ performance is guaranteed for the fuzzy system with the sampled-data fuzzy filter, and its sufficient condition is converted into the linear matrix inequality (LMI) format. Finally, an example is provided to verify the effectiveness of the proposed fuzzy filtering technique.

Fault Detection Filtering for Nonlinear Switched Stochastic Systems

In this note, the fault detection filtering problem is solved for nonlinear switched stochastic system in the T-S fuzzy framework. Our attention is concentrated on the construction of a robust fault detection technique to the nonlinear switched system with Brownian motion. Based on observer-based fault detection fuzzy filter as a residual generator, the proposed fault detection is formulated as a fuzzy filtering problem. By the utilization of the average dwell time technique and the piecewise Lyapunov function technique, the fuzzy-parameter-dependent fault detection filters are designed that guarantee the resulted error system to be mean-square exponential stable with a weighted ${\mathcal H}_{\infty}$ error performance. Then, the corresponding solvability condition for the fault detection fuzzy filter is also established by the linearization procedure technique. Finally, simulation has been presented to show the effectiveness of the proposed fault detection technique.

L ∞ Fuzzy filter design for nonlinear systems with missing measurements: Fuzzy basis-dependent Lyapunov function approach

In this paper, l∞ fuzzy filtering problem is dealt for nonlinear systems with both persistent bounded disturbances and missing probabilistic sensor information. The Takagi–Sugeno (T–S) fuzzy model is adopted to represent a nonlinear dynamic system. The measurement output is assumed to contain randomly missing data, which is modeled by a Bernoulli distributed with a known conditional probability. To design the l∞ fuzzy filter and guarantee tracking performance, the effect of the perturbation against persistent bounded disturbances is reduced by using the minimum l∞ performance. By using the fuzzy basis-dependent Lyapunov function approach, a sufficient condition is established that ensure the mean square exponential stability of the filtering error. The proposed sufficient condition is represented as some linear matrix inequalities (LMIs), and the filter gain is obtained by the solution to a set of LMIs. Finally, the effectiveness of the proposed design method is shown via an example.

Fuzzy Filtering With Randomly Occurring Parameter Uncertainties, Interval Delays, and Channel Fadings

In this paper, the H∞ fuzzy filtering problem is investigated for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with randomly occurring uncertainties and randomly occurring interval time-varying delays, as well as channel fadings. A sequence of random variables obeying the Bernoulli distribution is utilized to govern the randomly occurring uncertainties and probabilistic interval time-varying delays. Simultaneously, the Rice fading model is employed to describe the phenomena of channel fadings by setting different values of the channel coefficients. Our attention is focused on the design of an H∞ fuzzy filter such that the filtering error dynamics is exponentially mean-square stable and the disturbance rejection attenuation is constrained to a given level by means of the H∞-performance index. In the presence of the randomly occurring phenomena, sufficient conditions are derived, via stochastic analysis and Lyapunov functional approach, for the existence of desired filter ensuring both the exponential mean-square stability and the prescribed H∞ performance. The filter parameters can be obtained by solving a convex optimization problem via the semidefinite program method. Finally, a numerical example is utilized to illustrate the usefulness and effectiveness of the proposed design technique.

Stationary Fuzzy Fokker–Planck Learning and Stochastic Fuzzy Filtering

The application of nonlinear optimization to the estimation of fuzzy model parameters is well known. To do the reverse of this, the concept of stationary fuzzy Fokker-Planck learning (SFFPL) is introduced, i.e., SFFPL applies the fuzzy modeling technique in nonlinear optimization problems. SFFPL is based on the fuzzy approximation of the stationary cumulative distribution function of a stochastic search process associated with the nonlinear optimization problem. A carefully designed algorithm is suggested for SFFPL to locate the optimum point. This paper also considers the variational Bayes (VB)-based inference of a stochastic fuzzy filter whose consequents, as well as antecedents, are random variables. The problem of VB inference of stochastic antecedents, because of the nonlinearity of the likelihood function, is analytically intractable. The SFFPL algorithm for high-dimensional nonlinear optimization that does not require the derivative of the objective function can be used to numerically solve the stochastic fuzzy filtering problem.

H ∞ Fuzzy Filtering for Discrete-Time Nonlinear Systems via Fuzzy Lyapunov Function Approach

This paper is concerned with the H ? fuzzy filtering problem for a class of discrete-time fuzzy systems. The objective is to design a stable filter guaranteeing the asymptotic stability and a prescribed H ? performance of the filtering error system. Motivated by the parallel distributed compensation (PDC) technique, a new filter model is proposed in this paper. Both full-order and reduced-order filters are established, and they can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired H ? fuzzy filter is given. A numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach.