Fuzzy Fault-tolerant Control Research Articles

Adaptive fault-tolerant control with prescribed performance for switched nonlinear pure-feedback systems

In this paper, the problem of adaptive fuzzy fault-tolerant control is investigated for a class of switched uncertain pure-feedback nonlinear systems under arbitrary switching. The considered actuator failures are modeled as both lock-in-place and loss of effectiveness. By utilizing mean value theorem, the considered pure-feedback systems are transformed into a class of switched nonlinear strict-feedback systems. Under the framework of backstepping design technique and common Lyapunov function (CLF), an adaptive fuzzy fault-tolerant control (FTC) method with predefined performance bounds is developed. It is proved that under the proposed controller, all the signals of the close-loop systems are bounded and the state tracking error for each step remains within the prescribed performance bound (PPB) regardless of actuator faults and the system switchings. In addition, the tracking errors and magnitudes of control inputs can be reduced by adjusting the PPB parameters of errors in the first and last steps. The simulation results are provided to show the effectiveness of the proposed control scheme.

Fuzzy Adaptive Fault-Tolerant Output Feedback Attitude-Tracking Control of Rigid Spacecraft

This paper proposes a stable adaptive fuzzy fault-tolerant attitude-tracking controller for a rigid spacecraft in the presence of unavailable velocities, external disturbance, actuator faults, and actuator saturation. Fuzzy logic systems are applied to approximate the unknown nonlinear function vector, and a fuzzy adaptive observer is designed to estimate the unmeasured velocity of the rigid body. By using the backstepping technique, a novel adaptive fuzzy attitude-tracking fault-tolerant control scheme is developed. It has been testified that this control approach guarantees that all signals of the rigid spacecraft are bounded and the tracking error between the system output and the reference signal converges to a small neighborhood of zero. Simulation examples with constant faults and time-variant faults are provided to show the fault-tolerant effectiveness of the control method.

Adaptive fuzzy fault‐tolerant control for multiple high‐speed trains with proportional and integral‐based sliding mode

In this study, novel adaptive fuzzy fault-tolerant control method is proposed for multiple high-speed trains (HSTs) in the presence of actuator faults, unknown non-linear dynamics and external disturbances. The fuzzy logic system is used to approximate the unknown functions. Based on proportional and integral-based sliding mode technique, two adaptive fuzzy control schemes are then proposed to achieve string stability. In the first scheme, the actuator faults are not considered. In the second scheme, a novel fuzzy fault-tolerant control with fewer adjustable parameters is constructed to further reduce the online computational load. By using Lyapunov analysis, the individual stability and string stability of whole multiple HSTs are proven. In addition, all signals of the closed-loop system are uniformly ultimately bounded and all HSTs track the reference trajectory to a small compact set around zero. Finally, comparative simulation is introduced to verify the reliability and effectiveness.

Single-parameter-learning-based fuzzy fault-tolerant output feedback dynamic surface control of constrained-input nonlinear systems

This paper addresses the problem of adaptive fuzzy fault-tolerant dynamic surface control for a class of constrained-input nonlinear systems. To resolve this problem, the design of an observer-based single-parameter-learning (SPL) control method using output feedback is proposed. The Takagi-Sugeno (T-S) fuzzy system is used to identify and approximate online the uncertain nonlinear dynamics, requiring no knowledge. The barriers that restrict the applications of the traditional backstepping and approximation-based approach, including the explosion of complexity and the dimension curse problems, are circumvented via dynamic surface control and SPL techniques. The merit of the proposed method lies in that only one parameter in the entire control scheme requires online adjustment, regardless of the number of parameters in the T-S fuzzy system that characterizes the fuzzy rules; the calculation burden, in this sense, is reduced to the extent of the minimum value. The truncated adaptation method is used to avoid the chattering and instability caused by constrained input. It is shown with rigorous proof using the Lyapunov and invariant set theorems that all the closed-loop signals are guaranteed semi-globally uniformly ultimately bounded. The output tracking error is adjustable by means of design parameters in an explicit form, and can be adjusted to an arbitrarily small value around zero by appropriately chosen control parameters, even under faulty and constrained actuators. Simulation and comparative results are provided to demonstrate the effectiveness of the proposed control approach.

Fault tolerant trajectory tracking control design for interval-type-2 Takagi-Sugeno fuzzy logic system

The interval type-2 Takagi-Sugeno fuzzy logic system (IT2 TS FLS) has been recently used in several control applications to handle nonlinear systems subjected to various uncertainties. This paper considers the problem of fault tolerant control (FTC) for discrete-time nonlinear system described by IT2 TS fuzzy model affected by actuator faults via state feedback control method. The IT2 fuzzy controller is designed to compensate the effect of the fault such that the stability of the closed loop system is ensured. Stability conditions for the IT2 faulty system are presented in terms of linear matrix inequalities (LMIs). Simulation results performed on the three tank system are presented to demonstrate the efficiency of the proposed controller over the traditional type-1 fuzzy fault tolerant controller.

Adaptive fuzzy fault‐tolerant control for a class of unknown non‐linear dynamical systems

This study investigates the adaptive fuzzy fault-tolerant control (FTC) problem for a class of non-linear multi-input multi-output systems with interconnections among subsystems and external unknown disturbance. The introduced multiple coupling terms have unknown non-linear forms relying on the system outputs and the corresponding subsystems, which cause that the system is no longer pure-feedback. Moreover, the considered actuator failures have a lock-in-place type and a type of loss of effectiveness. To solve the problem of actuator faults, compensative adaptive laws are constructed by taking advantages of the global fuzzy approximation property and a novel backstepping design procedure. According to the Lyapunov stability theorem, it is shown that all the signals in the closed-loop system are bounded and the outputs can converge to a giving compact set. In addition, simulation examples are presented to validate the effectiveness of the proposed adaptive fuzzy FTC protocol. Compared with previous researches on non-linear systems with unknown coupling terms, the proposed adaptive fuzzy FTC approach is more general, which may provide promising prospects of implementing in practical industrial systems.

Adaptive output feedback fault‐tolerant control for MIMO non‐affine non‐linear systems based on disturbance observer

In this study, the fault-tolerant control problem is investigated for a class of non-affine output-constrained multi-input multiple-output non-linear systems with actuator faults. The controlled systems contain unknown non-linear functions, unknown external disturbance and immeasurable states. The fuzzy logic systems and a robust compensation function are employed to deal with the unknown non-linear functions and non-affine non-linear actuator fault problems. Then, the state observer and the non-linear disturbance observer are developed for estimating the immeasurable states and unknown compounded disturbance, respectively. By using the barrier Lyapunov function method and in the unified framework of adaptive backstepping output feedback control design, a novel adaptive fuzzy fault-tolerant controller design scheme is developed. It is shown that all the variables of the closed-loop system are semi-globally uniformly bounded. Moreover, the system outputs cannot violate their predefined bounds in the presence of the non-affine non-linear faults. A simulation is given to validate the effectiveness of the proposed approach.

Reliable fuzzy H∞ control for active suspension of in-wheel motor driven electric vehicles with dynamic damping

A fault-tolerant fuzzy H∞ control design approach for active suspension of in-wheel motor driven electric vehicles in the presence of sprung mass variation, actuator faults and control input constraints is proposed. The controller is designed based on the quarter-car active suspension model with a dynamic-damping-in-wheel-motor-driven-system, in which the suspended motor is operated as a dynamic absorber. The Takagi-Sugeno (T-S) fuzzy model is used to model this suspension with possible sprung mass variation. The parallel-distributed compensation (PDC) scheme is deployed to derive a fault-tolerant fuzzy controller for the T-S fuzzy suspension model. In order to reduce the motor wear caused by the dynamic force transmitted to the in-wheel motor, the dynamic force is taken as an additional controlled output besides the traditional optimization objectives such as sprung mass acceleration, suspension deflection and actuator saturation. The H∞ performance of the proposed controller is derived as linear matrix inequalities (LMIs) comprising three equality constraints which are solved efficiently by means of MATLAB LMI Toolbox. The proposed controller is applied to an electric vehicle suspension and its effectiveness is demonstrated through computer simulation.

Optimal adaptive fuzzy FTC design for strict-feedback nonlinear uncertain systems with actuator faults

In this paper, the optimal fault-tolerant control (FTC) design problem is investigated for strict-feedback nonlinear systems. The considered nonlinear systems contain actuator faults, which are bias fault and gain fault. The problem of actuator faults is solved by utilizing the adaptive compensation technique. Applying the backstepping design technique, a main fault-tolerant controller is established. Via the designed main fault-tolerant control strategy, the controlled nonlinear system can be converted to an equivalent nonlinear system in affine form. Subsequently, a fuzzy logic system (FLS) is introduced to approximate the unknown cost function, and an adaptive fuzzy feedback optimal controller is developed. The whole adaptive fuzzy fault-tolerant optimal control scheme consists of a main controller and a feedback optimal controller. Based on the Lyapunov theory, it is proved that all the signals in the closed-loop system are bounded, the system output can track a bounded reference signal. In addition, the proposed control method can guarantee the cost function is the smallest. Simulation results are provided to illustrate the effectiveness of the proposed fault-tolerant optimal control scheme.

Reliable mixed [formula omitted]/passive control for T–S fuzzy delayed systems based on a semi-Markov jump model approach

This paper investigates the problem of the reliable mixed H∞/passive control for Takagi–Sugeno (T–S) fuzzy delayed systems based on a semi-Markov jump model (SMJM) approach. The focus is to design a fuzzy fault-tolerant controller such that the resulting closed-loop system is stochastically stable with a prescribed mixed H∞/passive performance level even if the actuator failures appear. A semi-Markov process is employed to describe the encountered failures of the actuator. By applying the Lyapunov–Krasovskii method, in combination with some novel inequalities, some conditions on the performance analysis are established, where some negative quadratic terms are fully considered to reduce the conservatism. Based on the conditions, an explicit expression for the desired controller is given. Three numerical examples are presented to show the effectiveness and reduced conservatism of the proposed method.

A new global fuzzy fault-tolerant control for a double inverted pendulum based on time-delay replacement

In this paper, a delay replacement-based adaptive fault-tolerant control method is proposed for a double inverted pendulum connected by an unknown device. By combining fuzzy approximation and integer backstepping, a new time-delay assumption-independent state feedback decentralized control scheme is developed based on directly replacing the unbounded time-delay argument of fuzzy approximators with the bounded reference signals. Furthermore, all of the two typical types of actuator faults can be compensated for on-line. Compared with the existing results, the time-delay assumptions that need to be test and verify in applications are eliminated, and global bounded stability of the closed-loop system is guaranteed. Simulation results are provided to show the effectiveness of the control approach.

Adaptive fuzzy fault tolerant tracking control for a class of uncertain switched nonlinear systems with output constraints

This paper studies the adaptive fuzzy fault tolerant tracking control problem for a class of switched multi-input multi-output (MIMO) nonlinear systems with output constraints under arbitrary switchings. The actuator faults under study consist of unknown stuck and loss of effectiveness. In the design procedure, the unknown control signals are approximated directly by fuzzy logic systems. To prevent constraints violation, a tan-type barrier Lyapunov function is incorporated into the Lyapunov function design. Based on the idea of estimating the bound on switching parameters, a novel adaptive fuzzy fault tolerant tracking control technique for the problem studied is set up by exploiting the common Lyapunov function method and backstepping. It is shown that under the proposed control law and adaption rules, all the signals remain bounded and the system output tracking error can be guaranteed to exponentially converge to a neighborhood of origin, while the constraints on the system output will not be violated during operation. Finally, simulation results are presented to show the effectiveness of the proposed approaches.

Fuzzy fault tolerant predictive control for a diesel engine air path

This paper proposes a Fuzzy Fault Tolerant Predictive Control (FFTPC) with integral action method for a class of nonlinear systems. The Takagi-Sugeno (T-S) fuzzy approach is introduced as a modelling technique in order to consider the active control methods adapted to linear models. The proposed control strategy is based on a combination between Parallel Distributed Compensation (PDC) control law and Model Predictive Control (MPC) where the T-S fuzzy aspect uses the Unmeasurable Premise Variables (UPV). A T-S fuzzy observer provides an L2 norm estimation of system state vector and faults. The controller and observer gains are obtained by solving Linear Matrix Inequalities (LMIs) derived from the Lyapunov theory. The validity of the proposed Fault Tolerant Control (FTC) strategy is illustrated through an application to a Diesel Engine Air Path (DEAP) system.

Output feedback fault-tolerant control for a class of discrete-time fuzzy bilinear systems

This paper studies the fault-tolerant control problem for a class of discrete-time fuzzy bilinear systems with unmeasurable states. A fuzzy detective observer is designed to detect the faults. Based on the fuzzy detective observer, a fuzzy controller is designed by solving a set of linear matrix inequalities (LMIs) to ensure that the closed-loop system without faults is asymptotically stable. For the discrete-time fuzzy bilinear system with faults, a fuzzy adaptive diagnostic observer is designed to estimate the faults by solving a set of LMIs. Then, a fuzzy faulttolerant controller is designed based on the fuzzy diagnostic observer to ensure that the closed-loop system with faults is asymptotically stable. At last, simulation results are presented to verify the effectiveness of the proposed output feedback fault-tolerant control method.

Robust Sensor Fault-Tolerant Control of Induction Motor Drive

This paper presents an active fuzzy fault-tolerant control (FTC) strategy for induction motor that ensures the performances of the field-oriented control (FOC). In the proposed approach, a robust controller is synthesized in order to compensate for both the resistance variation, the load torque disturbance, and the sensor fault. The physical model of induction motor is approximated by the Takagi–Sugeno (T–S) fuzzy technique in the synchronous d-q rotating frame. Fuzzy descriptor observer is introduced to estimate simultaneously the system state and the sensor faults. A robust feedback state tracking control is proposed to guarantee the control performances by minimizing the effect of the load torque and the uncertainties. The proposed controller is based on a T–S reference model in which a desired trajectory has been specified. The performances of the trajectory tracking are analyzed using the Lyapunov theory and the \(L_2\) optimization. Observer and controller gains are obtained by solving a set of LMIs constraint. To highlight the effectiveness of the proposed control simulation, results are introduced for a 1.5 KW induction motor.

Robust adaptive fault-tolerant control for a class of uncertain nonlinear systems with multiple time delays

This study is concerned with the problem of robust adaptive fuzzy fault-tolerant control for a class of uncertain nonlinear systems with mismatching parameter uncertainties, external disturbances, multiple state time delays perturbations and actuator failures, which include loss of effectiveness, outage and stuck modes. A novel direct adaptive fuzzy tracking control scheme is developed to achieve the fault-tolerant control objective. First, by introducing a positive nonlinear control gain function, the effects of state time delays and actuator failures are effectively compensated. Then, a suitable fuzzy logic system (FLS), which is used to approximate the corresponding nonlinear function, is constructed to eliminate the influences on mismatched parameter uncertainty and external disturbance. Moreover, it is shown that all the closed-loop system signals are uniformly bounded and that the tracking error converges to a small neighborhood of the origin via Lyapunov–Krasovskii stability analysis. Finally, the proposed adaptive fuzzy fault-tolerant tracking design approach is illustrated on a two stage chemical reactor system with delayed recycle streams.

Robust adaptive fuzzy fault-tolerant control for a class of non-lower-triangular nonlinear systems with actuator failures

In this paper, the problem of adaptive fuzzy fault-tolerant tracking control is studied for a class of non-lower-triangular nonlinear systems with actuator failures. According to the same structure of virtual control inputs and the monotonously increasing property of the bounding functions, a variable separation approach is proposed. By applying the backstepping technique, an adaptive fuzzy control approach is presented which can guarantee the semi-global boundedness of all signals within the closed-loop system. The tracking error using the proposed control scheme eventually converges to a small neighborhood of the origin.

Decentralized adaptive fuzzy fault-tolerant tracking control of large-scale nonlinear systems with actuator failures

This study is concerned with the problem of decentralized adaptive fault-tolerant control for a class of large-scale non-affine and nonlinear systems with external disturbances and actuator failures including loss of effectiveness and bias. Based on fuzzy logic systems (FLSs) to approximate the appropriate nonlinear functions, a novel decentralized adaptive fuzzy fault-tolerant control scheme is developed via direct adaptive control technique. To tackle the non-affine term with actuator failures, with the help of a non-affine compensation term, the corresponding adaptive mechanism that depends on the unknown upper bound of a defined compounded disturbance is introduced. Meanwhile, by utilizing the on-line estimating information of the unknown upper bound and the unknown parameters of necessary FLSs, a new adaptive fuzzy fault-tolerant controller with the adjustable parameter updated laws is designed to achieve robust tracking performance. Furthermore, it is shown that all the closed-loop signals of the interconnected subsystems are uniformly bounded and the tracking errors asymptotically converge to zero via Lyapunov stability analysis. Finally, numerical simulation results are provided to demonstrate the efficiency of the presented decentralized adaptive fuzzy fault-tolerant tracking design scheme.

Adaptive fuzzy fault-tolerant control with guaranteed tracking performance for nonlinear strict-feedback systems

In this study, we propose two backstepping-based adaptive fuzzy fault-tolerant control (FTC) methods for a class of nonlinear strict-feedback systems with actuator failures. First, a traditional FTC (TFTC) method is considered. Our analysis shows that TFTC has poor tracking performance due to the existence of approximation errors and external disturbances. Inspired by the idea that the magnitudes of control inputs decrease as the error of the last step decreases in the backstepping procedure, we propose a new prescribed performance FTC (NPP–FTC) method based on the improved error transformation technique. Compared with previous methods where only the output tracking error is guaranteed within the prescribed performance bound (PPB), we show that the state tracking error for each step between the intermediate control and virtual control remains within the PPB regardless of actuator faults. The main advantage of the NPP–FTC method is that the tracking errors and magnitudes of the control inputs can be reduced by adjusting the PPB parameters of the errors in the first and last steps. Our simulation results demonstrate the effectiveness of the proposed NPP–FTC method.

Adaptive output feedback fault-tolerant control of switched fuzzy systems

This paper investigated the adaptive fault-tolerant control problem for a class of switched Takagi–Sugeno fuzzy systems. The considered switched fuzzy systems contain unmeasured states and actuator failures. In the control design, a switched state observer is designed to estimate the unmeasured states. Under the parallel-distributed compensation (PDC) design scheme and using the online estimation of actuator faults, an adaptive fuzzy fault-tolerant control scheme is proposed, in which a compensation control term is introduced in order to reduce the effect of actuator faults. Utilizing the estimated states and a segmentation of state space, the switching law is constructed. The sufficient conditions for ensuring the asymptotic stability of the switched fuzzy systems are proposed and formulated in the form of linear matrix inequalities (LMIs). By using the single Lyapunov function method, it is proved that the proposed control approach can guarantee the asymptotic stability of the closed-loop system. One practical example and a numerical example are given to illustrate the effectiveness of the proposed control method.