Fault Diagnosis and Sliding Mode Fault Tolerant Control for Non‐Gaussian Stochastic Distribution Control Systems Using T‐s Fuzzy Model

For the non‐Gaussian stochastic distribution control system using Takagi‐Sugeno fuzzy model, a new fault diagnosis and sliding mode fault tolerant control algorithm is presented. First, a new adaptive fault diagnosis algorithm is adopted to diagnose the fault that occurred in the system, and the observation error system is proven to be uniformly bounded. Second, the sliding mode control algorithm is used to reconfigure the controller, based on the fault estimation information. The post‐fault probability density function can still track the given distribution, leading to fault tolerant control of non‐Gaussian stochastic distribution control systems using Takagi‐Sugeno fuzzy model. Finally, simulation results show the effectiveness of the proposed method.     

Sensor cascading fault estimation and control for hypersonic flight vehicles based on a multidimensional generalized observer

This study presents a sensor cascading fault estimation and fault‐tolerant control (FTC) for a nonlinear Takagi‐Sugeno fuzzy model of hypersonic flight vehicles. Sensor cascading faults indicate the occurrence of source fault will cause another fault and the interval between them is really short, which makes it difficult to handle them in succession. A novel multidimensional generalized observer is used to estimate faults by integrating constant offset and time‐varying gain faults. Then, a fault‐tolerant controller is used to solve system nonlinearity and sensor fault problems. The observer and controller satisfy the performance index and are robust to external disturbances. A sufficient condition for the existence of observer and controller is derived on the basis of Lyapunov theory. Simulation results indicate the effectiveness of the proposed fault estimation and FTC scheme.     

Static Output Feedback Control for Interval Type‐2 T‐S Fuzzy Systems Based on Fuzzy Lyapunov Functions

This study aims to design an interval type‐2 (IT2) fuzzy static output feedback controller to stabilize the IT2 Takagi‐Sugeno (T‐S) fuzzy system. Conservative results may be obtained when a common quadratic Lyapunov function is utilized to investigate the stability of T‐S fuzzy systems. A fuzzy Lyapunov function is employed in this study to analyze the stability of the IT2 fuzzy closed‐loop system formed by the IT2 T‐S fuzzy model and the IT2 fuzzy static output feedback controller. Stability conditions in the form of linear matrix inequalities are derived. Several slack matrices are introduced to further reduce the conservativeness of stability analysis. The membership‐function shape‐dependent analysis approach is also employed to relax the stability results. The numerical examples illustrate the effectiveness of the proposed conditions.     

Stability Analysis and Controller Design of Discrete Interval Type‐2 Fuzzy Systems

This paper is concerned with trajectory stabilization of a computer simulated model car with uncertain velocity via type‐2 fuzzy control systems. First, stability conditions of discrete interval type‐2 fuzzy control systems are given in accordance with the definition of stability in the sense of Lyapunov. Then, we approximate a computer simulated model car, whose dynamics are nonlinear and velocity is uncertain. A type‐2 Takagi–Sugeno TS fuzzy controller is designed to handle system uncertainty. The control rules, which guarantee stability of the system, are derived from the approximated model. The simulation results show that the type‐2 fuzzy control rules can effectively stabilize the car model.     

A nonlinear state‐feedback state‐feedforward tracking control strategy for a boiler‐turbine unit

A boiler‐turbine unit is a primary module for coal‐fired power plants, and an effective automatic control system is needed for the boiler‐turbine unit to track the load changes with the drum water level kept within an acceptable range. The aim of this paper is to develop a nonlinear tracking controller for the Bell‐Åström boiler‐turbine unit. A Takagi‐Sugeno fuzzy control system is introduced for the nonlinear modeling of the Bell‐Åström boiler‐turbine unit. Based on the Takagi‐Sugeno fuzzy models, a nonlinear tracking controller is developed, and the proposed control law is comprised of a state‐feedforward term and a state‐feedback term. The stability of the closed‐loop control system is analyzed on the basis of Lyapunov stability theory via the linear matrix inequality approach and Schur complement. Moreover, model uncertainties are also considered, and it is proved that with the proposed control law the tracking error converges to zero. To assess the performance of the proposed nonlinear state‐feedback state‐feedforward control strategy, a nonlinear model predictive control strategy and a linear strategy are presented as comparisons. The effectiveness and the advantages of the proposed nonlinear state‐feedback state‐feedforward control strategy are demonstrated by simulations.     

Fast adaptive fault estimation and accommodation for nonlinear time‐varying delay systems

This paper studies the problem of fault estimation and accommodation for a class of nonlinear time‐varying delay systems using adaptive fault diagnosis observer (AFDO). A novel fast adaptive fault estimation algorithm that does not need the derivative of the output vector is proposed to enhance the performance of fault estimation. Meanwhile, a delay‐dependent criteria is obtained based on free weighting matrix method with the purpose of reducing the conservatism of the AFDO design. On the basis of fault estimation, an observer‐based fault‐tolerant controller is designed to guarantee the stability of the closed‐loop system. In terms of matrix inequality, we derive sufficient conditions for the existence of the adaptive observer and fault‐tolerant controller. Simulation results are presented to illustrate the efficiency of the proposed method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust fast adaptive fault estimation and tolerant control for T-S fuzzy systems with interval time-varying delay

This paper studies the problem of fault estimation (FE) and the active fault tolerant control (FTC) for Takagi–Sugeno (T-S) fuzzy systems with interval time-varying delay and norm-bounded external disturbance. Based on the fast adaptive fault estimation (FAFE) algorithm, our attention focuses on designing an adaptive observer-based controller to guarantee the filtering error system to be asymptotically stable and satisfy theH_∞ performance index. By constructing a new Lyapunov–Krasovskii functional including the information of the lower and upper delay bounds, the sufficient delay-dependent conditions have been established to guarantee the existence of adaptive observer-based controller in terms of linear matrix inequalities (LMIs). Compared with the constant delay and time-varying delay, the interval time-varying delay is the less conservative form. Furthermore, we make full use of the information of the delay and no terms are ignored when the stability of the system is analysed. In addition, the results for the systems with time-varying structured uncertainties are established. The results of the active FTC are showed in terms of LMIs. Finally, two examples are given to verify the effectiveness of the proposed method.     

Delay‐dependent fault estimation for uncertain time‐delay nonlinear systems: an LMI approach

This paper deals with the problem of robust fault estimation for uncertain time‐delay Takagi–Sugeno (TS) fuzzy models. The aim of this study is to design a delay‐dependent fault estimator ensuring a prescribed ??_∞ performance level for the fault estimation error, irrespective of the uncertainties and the time delays. Sufficient conditions for the existence of a robust fault estimator are given in terms of linear matrix inequalities (LMIs). Membership functions' (MFs) characteristics are incorporated into the fault estimator design to reduce the conservativeness of neglecting these characteristics. Finally, a numerical example is given to illustrate the effectiveness of the proposed design techniques. Copyright © 2006 John Wiley & Sons, Ltd.     

Simultaneous Actuator and Sensor Faults Reconstruction Based on Robust Sliding Mode Observer for a Class of Nonlinear Systems

This paper proposes a new robust fault reconstruction and estimation design for a class of nonlinear system described by the Takagi‐Sugeno model with unmeasurable premise variables subject to faults affecting actuators, sensor faults, and unknown disturbances. The augmented Takagi‐Sugeno system is introduced with a new fault vector which has two origins: the first one represents actuator faults, the second one denotes faults affecting sensors. The main contribution is focused primarily to conceive a sliding mode observer with two discontinuous terms designed to compensate for fault behavior and disturbance variation from the system states estimation. In the formalism of linear matrix inequalities, we derive sufficient conditions to guarantee the state estimation error stability and to obtain the observer gains. Meanwhile, additional effort is made to achieve simultaneous faults and disturbance reconstruction. Simulation results are given to illustrate the proposed approach performances.     

Distributed adaptive fault‐tolerant leader‐following formation control of nonlinear uncertain second‐order multi‐agent systems

This paper presents a distributed integrated fault diagnosis and accommodation scheme for leader‐following formation control of a class of nonlinear uncertain second‐order multi‐agent systems. The fault model under consideration includes both process and actuator faults, which may evolve abruptly or incipiently. The time‐varying leader communicates with a small subset of follower agents, and each follower agent communicates to its directly connected neighbors through a bidirectional network with possibly asymmetric weights. A local fault diagnosis and accommodation component are designed for each agent in the distributed system, which consists of a fault detection and isolation module and a reconfigurable controller module comprised of a baseline controller and two adaptive fault‐tolerant controllers, activated after fault detection and after fault isolation, respectively. By using appropriately the designed Lyapunov functions, the closed‐loop stability and asymptotic convergence properties of the leader‐follower formation are rigorously established under different modes of the fault‐tolerant control system.     

Reliable control design for composite‐driven scheme based on delay networked T‐S fuzzy system

This paper is focused on reliable controller design for a composite‐driven scheme of networked control systems via Takagi‐Sugeno fuzzy model with probabilistic actuator fault under time‐varying delay. The proposed scheme is distinguished from the other schemes as mentioned in this paper. Aims of this article are to solve the control problem by considering the H_∞, dissipative, and L₂?L_∞ constraints in a unified way. Firstly, to improve the efficient utilization of bandwidth, the adaptive composite‐driven scheme is introduced. In such a scenario, the channel transmission mechanism can be adjusted between adaptive event‐triggered generator scheme and time‐driven scheme. In this study, the threshold is dependent on a new adaptive law, which can be obtained online rather than a predefined constant. With a constant threshold, it is difficult to get the variation of the system. Secondly, a novel fuzzy Lyapunov‐Krasovskii functional is constructed to design the fuzzy controller, and delay‐dependent conditions for stability and performance analysis of the control system are obtained. Then, LMI‐based conditions for the existence of the desired fuzzy controller are presented. Finally, an inverted pendulum that is controlled through the channel is provided to illustrate the effectiveness of the proposed method.     

Adaptive diagnosis and compensation for hypersonic flight vehicle with multisensor faults

This study proposes an improved adaptive fault diagnosis and compensation scheme for multisensor faults of hypersonic flight vehicles (HFVs). The faults are detected and isolated through a series of sensor output residuals and thresholds that consider observation error and disturbances. Via an adaptive augmented observer, the faults are estimated accurately and a time‐varying disturbance is handled by an additional differential part. Sensor faults are compensated on the basis of estimation results, and disturbances are considered in the fault‐tolerant control (FTC) design, thereby improving the tracking accuracy of the altitude and velocity and robustness with respect to external disturbances for HFVs. The stability of diagnosis and FTC is analyzed by Lyapunov theory. Numerical simulation results explain the validity of the proposed diagnosis and compensation methods.     

Robust H2 guaranteed cost fuzzy control for uncertain discrete‐time fuzzy systems via poly‐quadratic Lyapunov functions

In this paper, new approaches regarding H₂ guaranteed cost stability analysis and controller synthesis problems for a class of discrete‐time fuzzy systems with uncertainties are investigated. The state‐space Takagi‐Sugeno fuzzy model with norm‐bounded parameter uncertainties is adopted. Based on poly‐quadratic Lyapunov functions, sufficient conditions for the existence of the robust H₂ fuzzy controller can be obtained in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design a suboptimal fuzzy controller which minimizes the upper bound on the quadratic cost function. The effectiveness of the proposed design approach is illustrated by two examples. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Poly‐quadratic stability of discrete‐time nonlinear systems in Takagi‐Sugeno's form

This paper studies poly‐quadratic stability of nonlinear systems represented by a Takagi‐Sugeno (T‐S) discrete fuzzy model. A system is poly‐quadratically stable when its stability can be verified by a parameter dependent Lyapunov function. There are already some results in this area. This paper, however, presents less conservative results by adopting more slack‐matrix‐variables in the linear matrix inequalities (LMIs). The parallel distributed compensation (PDC) law is utilized in both the analysis and the synthesis problems. The effectiveness of the new results in this paper is validated by a simulation example. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.     

Robust fuzzy control for continuous perturbed time‐delay affine takagi–sugeno fuzzy models

The stability analysis and controller synthesis methodology for a continuous perturbed time‐delay affine (CPTDA) Takagi–Sugeno (T‐S) fuzzy model is proposed in this paper. The CPTDA T‐S fuzzy models include both linear nominal parts and uncertain parameters in each fuzzy rule. The proposed fuzzy control approach is developed based on an iterative linear matrix inequality (ILMI) algorithm to cope with the stability criteria and H_∞ performance constraints for the CPTDA T‐S fuzzy models. Finally, a numerical simulation for the nonlinear inverted pendulum system is given to show the application and availability of the present design approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust fuzzy stabilisation of interval plants

The paper deals with the problem of stabilisation of interval systems. To this end, by using Takagi–Sugeno fuzzy mechanism, a Mamdani-type PID-like fuzzy controller is modified and extended to develop a new PID-like Takagi–Sugeno fuzzy stabilising controller for the plant described by an interval system. Indeed, a PID-like Takagi–Sugeno fuzzy controller and an interval plant are considered in the forward path of a unity feedback system, and parameters in Takagi–Sugeno fuzzy controller are determined so that the stability of the closed-loop system is assured. The closed-loop system has a multilinear uncertainty structure. Therefore, based on the Zero Exclusion Condition for multilinear uncertain systems, a new theorem presenting sufficient conditions for the Takagi–Sugeno fuzzy controller to be robust stability guaranteed is also derived. An example is given to illustrate the application and the effectiveness of the proposed controller.     

Variable Structure Control with Chattering Reduction of a Generalized T‐S Model

In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) is presented. The main objective is to obtain an improved performance of highly non‐linear unstable systems. New functions for chattering reduction and error convergence without sacrificing invariant properties are proposed. The main feature of the proposed method is that the switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules; together with the state variables. In this work, a tuning of the well known weighting parameters approach is proposed to optimize local and global approximation and modelling capability of the Takagi‐Sugeno (T‐S) fuzzy model to improve the choice of the performance index and minimize it. The main problem encountered is that the T‐S identification method can not be applied when the membership functions are overlapped by pairs. This in turn restricts the application of the T‐S method because this type of membership function has been widely used in control applications. The approach developed here can be considered as a generalized version of the T‐S method. An inverted pendulum mounted on a cart is chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of the proposed estimation approach in comparison with the original T‐S model. Simulation results indicate the potential, simplicity and generality of the estimation method and the robustness of the chattering reduction algorithm. In this paper, we prove that the proposed estimation algorithm converge the very fast, thereby making it very practical to use. The application of the proposed FLC‐VSC shows that both alleviation of chattering and robust performance are achieved.     

Observer‐based fault‐tolerant control of hypersonic scramjet vehicles in the presence of actuator faults and saturation

An adaptive sliding mode observer (SMO)–based fault‐tolerant control method taking into consideration of actuator saturation is proposed for a hypersonic scramjet vehicle (HSV) under a class of time‐varying actuator faults. The SMO is designed to robustly estimate the HSV states and reconstruct the fault signals. The adaptive technique is integrated into the SMO to approximate the unknown bounds of system uncertainties, actuator faults, and estimation errors. The robust SMO synthesis condition, which can be formulated as a set of linear matrix inequalities, is improved by relaxing structure constraints to the Lyapunov matrix. An anti‐windup feedback control law, which utilizes the estimated HSV states and the fault signals, is designed to counteract the negative effects of actuator saturation induced by actuator faults. Simulation results demonstrate that the proposed approach can guarantee stability and maintain performance of the closed‐loop system in the presence of HSV actuator faults and saturation.