Reliable H ∞ filter design for T–S fuzzy model‐based networked control systems with random sensor failure

This paper investigates robust and reliable H _∞ filter design for a class of nonlinear networked control systems: (i) a T‐S fuzzy model with its own uncertainties is used to approximate the nonlinear dynamics of the plant, (ii) a new sensor failure model with uncertainties is proposed, and (iii) the signal transfer of the closed‐loop system is under a networked communication scheme and therefore is subject to time delay, packet loss, and/or packet out of order. Four new theorems are proved to cover the conditions for the robust mean square stability of the systems under study in terms of LMIs, and a decoupling method for the filter design is developed. Two examples, one of them is based on a model of an inverted pendulum, are provided to demonstrate the design method. Copyright © 2011 John Wiley & Sons, Ltd.     

Event-triggered fuzzy filtering in networked control system for a class of non-linear system with time delays

This paper focuses on the design of H _∞ filter and event-triggered scheme for a class of continuous non-linear networked control systems (NCSs) based on fuzzy system appeared with time delays. First, we consider the discrete event-triggered (ET) scheme to make efficient utilisation of bandwidth. Under this ET-scheme, sensor releases the data only when our sampled-data plant violates the specific event-triggered condition. Second, the T-S fuzzy system is used to model the non-linear NCSs. Another purpose of this paper is to design filters involving delays. Such filters have a more general form than the delay-free filters that have been mostly considered in the traditional studies. By using the time-delay system, co-design of event-triggered scheme and H _∞ filter for the delayed NCSs is presented in a unified frame work. To choose the latest data packet and discard the dis-ordered packet logic, zero-order hold is inserted between the fuzzy filter and event generator. Then, by using the novel fuzzy Lyapunov–Krasovskii function approach with free-weighting matrix technique, H _∞ filter design of event-triggered delay NCSs is proposed. Finally, to show the effective result of our co-design method, a tunnel-diode example is given.     

Input–output method to fault detection for discrete-time fuzzy networked systems with time-varying delay and multiple packet losses

The fault detection (FD) problem for discrete-time fuzzy networked systems with time-varying delay and multiple packet losses is investigated in this paper. The communication links between the plant and the FD filter (FDF) are assumed to be imperfect, and the missing probability is governed by an individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete-time delayed fuzzy networked system is first transformed into the form of interconnect ion of two subsystems by applying an input–output method and a two-term approximation approach, which are employed to approximate the time-varying delay. Our attention is focused on the design of fuzzy FDF (FFDF) such that, for all data missing conditions, the overall FD dynamics are input–output stable in mean square and preserves a guaranteed performance. Sufficient conditions are first established via H_∞ performance analysis for the existence of the desired FFDF; meanwhile, the corresponding solvability conditions for the desired FFDF gains are characterised in terms of the feasibility of a convex optimisation problem. Moreover, we show that the obtained criteria based on the input–output approach can also be established by applying the direct Lyapunov method to the original time-delay systems. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed approaches.     

Robust fault detection filter design for networked control systems with delay distribution characterisation

In this article, robust fault detection (RFD) is investigated for networked control systems with delay distribution characterisation. By utilising an observer-based fault detection filter as a residual generator, the RFD of networked control systems with non-uniformly distributed network‐induced time-varying delay is formulated as an H _∞ model-matching problem. Delay-interval-dependent and delay-interval-occurrence-rate-dependent sufficient conditions are obtained by employing the Lyapunov–Krasovskii functional approach. Especially, the robust fault detection filters guarantee strong robustness from residual signal to disturbance as well as high sensitivity to faults. A numerical example is given to illustrate the effectiveness of the proposed design techniques.     

Finite-time non-fragile filtering for nonlinear networked control systems via a mixed time/event-triggered transmission mechanism

This paper is aimed at investigating the problem of mixed time/event-triggered finite-time non-fragile filtering for nonlinear networked control systems with delay. First, a fuzzy nonlinear networked control system model is established by interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy model, the designed non-fragile filter resolves the filter parameter uncertainties and uses different membership functions from the IT2 T-S fuzzy model. Second, a novel mixed time/event-triggered transmission mechanism is proposed, which decreases the waste of network resources. Next, Bernoulli random variables are used to describe the cases of random switching mixed time/event-triggered transmission mechanism. Then, the error filtering system is designed by considering a Lyapunov function and a sufficient condition of finite-time boundedness. In addition, the existence conditions for the finite-time non-fragile filter are given by the linear matrix inequalities (LMIs). Finally, two simulation results are presented to prove the effectiveness of the obtained method.     

Adaptive fuzzy output-feedback fault-tolerant tracking control of a class of uncertain nonlinear switched systems

ABSTRACT

This paper considers the output-feedback fault-tolerant tracking control problem for a class of uncertain nonlinear switched systems with nonlinear faults and strict-feedback form, where the faults which are nonaffine occur on the actuator. As a kind of specialised function approximating tool, fuzzy logic systems (FLSs), are employed to approximate the unknown smooth nonlinear functions. A switched fuzzy observer is designed to address the problem of unmeasurable states, filtered signals are used to address algebraic loop problem and the average dwell time (ADT) method is further utilised to prove the stability of the resulting closed-loop systems under a type of slowly switching signals. Based on the backstepping recursive design technique and Lyapunov function method, an adaptive fuzzy output-feedback control scheme is developed. The developed control method can ensure all the signals are semi-globally uniformly ultimately bounded (SGUUB) and the system output tracks the reference signal tightly even if unknown fault occurs. A simulation carried on an example demonstrates the validity of the obtained control scheme.     

<Emphasis Type="Italic">l</Emphasis><Subscript>∞</Subscript> 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.     

Fault detection for nonlinear networked control systems with stochastic interval delay characterisation

In this article, we are concerned with the fault detection (FD) problem for nonlinear networked control systems (NCSs) with network-induced stochastic interval delay. By employing the information of probabilistic distribution of networked-induced time-varying delay, nonlinear constraint and the FD filter, nonlinear stochastic delay system model is established. Based on the obtained nonlinear model, utilising FD filter as residual generator, FD of nonlinear NCSs is formulated as nonlinear H _∞-filtering problem. Especially, the stochastic stability and prescribed H _∞ attenuation level are achieved using the Lyapunov functional approach, the desired FD filter is constructed in terms of certain linear matrix inequalities, which depends on not only nonlinear level but also on delay-interval and delay-interval-occurrence-rate. Numerical examples are provided to illustrate the effectiveness and applicability of proposed technique.     

Fuzzy model‐based fault detection for Markov jump systems

The robust fault detection filter (RFDF) design problems are studied for nonlinear stochastic time‐delay Markov jump systems. By means of the Takagi–Sugeno fuzzy models, the fuzzy RFDF system and the dynamics of filtering error generator are constructed. Moreover, taking into account the sensitivity to faults while guaranteeing robustness against unknown inputs, the H_∞ filtering scheme is proposed to minimize the influences of the unknown inputs and another new performance index is introduced to enhance the sensitivity to faults. A sufficient condition is first established on the stochastic stability using stochastic Lyapunov–Krasovskii function. Then in terms of linear matrix inequalities techniques, the sufficient conditions on the existence of fuzzy RFDF are presented and proved. Finally, the design problem is formulated as a two‐objective optimization algorithm. Simulation results illustrate that the proposed RFDF can detect the faults shortly after the occurrences. Copyright © 2008 John Wiley & Sons, Ltd.     

Simultaneous fault estimation and fault-tolerant tracking control for uncertain nonlinear discrete-time systems

This paper deals with simultaneous fault estimation and control for a class of nonlinear systems with parameter uncertainty, which is described by Takagi–Sugeno (T–S) fuzzy model with parameter uncertainties and unknown disturbance. In this paper, a fuzzy reference model is used to generate error dynamic for tracking control. By considering actuator fault as an auxiliary state vector, we construct an augmented error system and propose a fault estimator/controller to achieve simultaneous fault estimation and fault-tolerant tracking control. H_∞ approach is used in the design of estimator/controller to attenuate the effect of the unknown disturbance and parameter uncertainties. The design conditions are formulated into a set of linear matrix inequalities (LMIs), which can be efficiently solved. Finally, a pitch-axis nonlinear missile model is used to illustrate the effectiveness of the proposed method.     

H∞ fuzzy control design of discrete‐time nonlinear active fault‐tolerant control systems

This paper is concerned with the problem of H_∞ fuzzy controller synthesis for a class of discrete‐time nonlinear active fault‐tolerant control systems (AFTCSs) in a stochastic setting. The Takagi and Sugeno (T–S) fuzzy model is employed to exactly represent a nonlinear AFTCS. For this AFTCS, two random processes with Markovian transition characteristics are introduced to model the failure process of system components and the fault detection and isolation (FDI) decision process used to reconfigure the control law, respectively. The random behavior of the FDI process is conditioned on the state of the failure process. A non‐parallel distributed compensation (non‐PDC) scheme is adopted for the design of the fault‐tolerant control laws. The resulting closed‐loop fuzzy system is the one with two Markovian jump parameters. Based on a stochastic fuzzy Lyapunov function (FLF), sufficient conditions for the stochastic stability and H_∞ disturbance attenuation of the closed‐loop fuzzy system are first derived. A linear matrix inequality (LMI) approach to the fuzzy control design is then developed. Moreover, a suboptimal fault‐tolerant H_∞ fuzzy controller is given in the sense of minimizing the level of disturbance attenuation. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method. Copyright © 2008 John Wiley & Sons, Ltd.     

具有多通道数据传输的飞行器网络控制系统故障检测

研究具有多通道数据传输的飞行器网络控制系统故障检测滤波器(FDF)设计问题.考虑每个通道存在各自的网络时延,且丢包符合Markov随机过程.首先,将系统建模为转移概率部分已知的离散Markov跳变线性系统,并设计了基于观测器的故障检测滤波器,将故障检测问题转化为H∞滤波问题;然后,利用LMI工具给出了FDF的可解条件和求解方法;最后,通过某飞行器网络控制系统的数值仿真实验验证了所提出方法的有效性.     

Exponential sampled-data control for T–S fuzzy systems: application to Chua's circuit

ABSTRACT

This study deals with the chaotic phenomenon of nonlinear Chua's circuit for power generator systems. Takagi–Sugeno (T–S) fuzzy model of a nonlinear system is established. By constructing a suitable Lyapunov functional, exponential stability conditions are obtained for fuzzy systems. Based on the sampled-data control theory, extreme sensitivity is visualised in the state trajectory depending on the initial conditions and sampled-data fuzzy controllers are designed in the form of linear matrix inequality (LMI). Finally, some numerical simulation results are shown that the sampled-data fuzzy control system adopts a well-designed methodology.     

Fault detection for a class of uncertain nonlinear Markovian jump stochastic systems with mode-dependent time delays and sensor saturation

This paper considers the problem of robust H_∞ fault detection for a class of uncertain nonlinear Markovian jump stochastic systems with mode-dependent time delays and sensor saturation. We aim to design a linear mode-dependent H_∞ fault detection filter that ensures, the fault detection system is not only stochastically asymptotically stable in the large, but also satisfies a prescribed H_∞-norm level for all admissible uncertainties. By using the Lyapunov stability theory and generalised Itô formula, some novel delay-dependent sufficient conditions in terms of linear matrix inequality are proposed to guarantee the existence of the desired fault detection filter. Explicit expression of the desired mode-dependent linear filter parameters is characterised by matrix decomposition, congruence transformation and convex optimisation technique. Sector condition method is utilised to deal with sensor saturation, a definite relation of sector condition parameters with fault detection system robustness against disturbances and sensitivity to faults is put forward, and weighting fault signal approach is employed to improve the performance of the fault detection system. A simulation example and an industrial nonisothermal continuous stirred tank reactor system are utilised to verify the effectiveness and usefulness of the proposed method.     

Fault Estimation for Nonlinear Networked Systems with Time‐Varying Delay and Random Packet Dropout

In this paper, the fault estimation problem is studied for a class of nonlinear networked control systems with imperfect measurements. A novel measurement model is proposed to take time‐varying delays, random packet dropouts, and the packet‐dropout compensation into consideration simultaneously. After properly augmenting the states of the original system and the fault estimation filter, the addressed fault estimation problem is converted into an auxiliary H_∞ filtering problem for a stochastic parameter system. In terms of matrix inequalities, a sufficient condition for the existence of the fault estimation filter is derived that depends on the packet dropout rate, the upper and lower bounds of time delays, and the size of the consecutive packet dropouts. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.     

具有随机丢包的一类网络控制系统的故障检测

针对存在随机数据包丢失的网络环境,研究了一类网络控制系统的故障检测问题.考虑随机丢包同时发生在传感器与控制器以及控制器与执行器之间,将网络控制系统建模为含有4个模态的马尔可夫跳变线性系统.基于此类模型,构造了系统的残差发生器,相应的故障检测问题转化为H∞滤波问题.利用马尔可夫跳变线性系统理论,设计了故障检测滤波器,使得...     

Adaptive event-triggered robust H∞ control for Takagi–Sugeno fuzzy networked Markov jump systems with time-varying delay

This paper considers an adaptive event-triggered robust H_∞ control for the Takagi–Sugeno (T-S) fuzzy under the networked Markov jump systems (NMJSs) with time-varying delay. First, a new adaptive event-triggered scheme is developed to guarantee the T-S fuzzy NMJSs, and as a result, communication energy consumption reduced while device efficiency is maintained. Besides, an asynchronous operation method is adopted to deal with the mismatched premise variables between the fuzzy system and the fuzzy controller. One of the main objectives of this article is to construct the fuzzy state-feedback controller (mode-dependent) in a closed-loop form for stochastic stability for all admissible parameter uncertainties with an H_∞ performance index. Different from the conventional triggering mechanism, in this paper, the parameters of the triggering function are based on a new adaptive law that is obtained online rather than a predefined constant. To achieve the less conservative control design, a new type of stochastic Lyapunov–Krasovskii functional is designed by decomposing method, in which the delay interval transforms into various equidistant subintervals in terms of linear matrix inequalities. An example of a truck-trailer application is used to demonstrate the effectively of the proposed algorithms.     

Finite-frequency fault detection for two-dimensional Fornasini–Marchesini dynamical systems

This paper is concerned with the fault detection problem for two-dimensional (2-D) discrete-time systems described by the Fornasini–Marchesini local state-space model. The goal of the paper is to design a fault detection filter to detect the occurrence of faults in finite-frequency domain. To this end, a finite-frequency H_? index is used to describe fault sensitivity performance, and a finite-frequency H_∞ index is used to describe disturbance attenuation performance. In light of the generalised Kalman–Yakubovich–Popov lemma for 2-D systems and matrix inequality techniques, convex conditions are derived for this fault detection problem. Based on these conditions, a numerical algorithm is put forward to construct a desired fault detection filter. Finally, a numerical example and an industrial example are given to illustrate the effectiveness of the proposed algorithm.