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As for a class of strict‐feedback nonlinear systems with simultaneous sensor and actuator faults, the article focuses on the problem of fixed‐time fault‐tolerant control. Both fixed‐time command filters and a compensation mechanism are utilized to cope with these issues of differential explosion and filter errors. Meanwhile, through the fusion of fixed‐time control, fuzzy logic systems, adaptive control and the backstepping technology, a n$$ n $$‐step design scheme is presented. Our proposed controller ensures the fixed‐time convergence of all the signals in the system even with sensor/actuator faults, and allows the designers to acquire the upper limit value of the fixed convergence time only by tuning the design parameters. And this scheme takes into account rapidity, adaptability and fault tolerance of the system simultaneously. Based on the numerical simulation analysis, it is shown that the better tracking performance can be achieved. So it is concluded that our strategy is effective. [ABSTRACT FROM AUTHOR]

The study targets uncertain coupling faults in robotic arm actuators and proposes a new fault-tolerant visual servo control strategy. Specifically, it considers both multiplicative and additive actuator faults within the dynamic of the robotic arm, treating the coupling faults and time-varying disturbances as an aggregate of concentrated uncertainties. A radial basis function neural network-based state observer is introduced to online approximate these concentrated uncertainties, which include fault information, eliminating the need for prior knowledge of faults. Furthermore, a fault-tolerant controller based on a non-singular fast terminal sliding mode is proposed, which separately decouples the nominal quantities and concentrated uncertainties and develops individual adaptive control laws for each. This effectively reduces the detrimental impact of coupled faults and disturbances on the system's performance, facilitating image feature trajectory tracking control with minimal jitter, high precision, and strong transient response capabilities. The stability of the state observer and the fault-tolerant controller has been substantiated through Lyapunov's theory. Lastly, numerical simulations validate the efficacy and robustness of the proposed fault-tolerant visual servo control approach. [ABSTRACT FROM AUTHOR]

The problem of retargeting rigid body attitude with attitude constraints has been extensively investigated, whereas the challenge persists in maneuvering rigid-body attitude with multiple concurrent attitude constraints and finite sequential actuator faults. Finite sequential actuator faults, which can reduce controllability or destabilize the system, necessitate the implementation of fault-tolerant control strategies. Therefore, this paper aims to address the issue of redirecting spacecraft attitude subject to multiple attitude constraints and finite sequential actuator faults comprehensively. Firstly, we represent spacecraft attitude using unit quaternions and employ an artificial potential function to effectively handle multi-attitude constraints. The negative gradient direction guides the rigid-body spacecraft towards seamless convergence with the desired attitude. Our proposed unwinding strategy effectively avoids unwinding phenomena during large-angle spacecraft reorientation as well. Additionally, we design an adaptive compensation strategy for finite sequential actuator faults that enables real-time calculation of the fault compensation matrix under such actuator faults. Importantly, we propose an improved adaptive fault-tolerant back-stepping controller integrated with a potential function that effectively addresses both attitude constraints and finite sequential actuator faults simultaneously. Subsequently, stability analysis is conducted on the proposed controller to ensure its stability in practical applications rigorously. Finally, numerical simulations are performed meticulously to demonstrate the effectiveness and robustness of our proposed controller. [ABSTRACT FROM AUTHOR]

The L2$$ {L}_2 $$‐gain analysis and fault‐tolerant control of a class of uncertain nonlinear discrete‐time switched systems with time‐varying delay and actuator saturation are studied by using the multiple Lyapunov functions method. The fault‐tolerant state feedback controllers and the switching law are designed such that the closed‐loop system with actuator failures satisfies the disturbance attenuation performance indicator. The problem of estimating the capacity of admissible disturbance is transformed into a constrained optimization problem to ensure that the state trajectory of the closed‐loop system is bounded under the action of external disturbances. The upper bound of restricted L2$$ {L}_2 $$‐gain is estimated by solving constrained optimization problems. Then, when the fault‐tolerant controller can be regard as the design variable, the optimization problems above are adjusted for solving control synthesis problems. Finally, the numerical example is given to verify the effectiveness of the design method. [ABSTRACT FROM AUTHOR]

In this paper, a finite time fault estimation and fault‐tolerant control method is proposed for a class of uncertain nonlinear systems that have both actuator faults and sensor faults. First, the outputs of the original system pass through the low‐pass filters to obtain the augmented states, and then an augmented system is composed of the states of the low‐pass filters and the original system, so as to realize the conversion of the sensor faults of the original system into partial actuator faults of the augmented system. Next, design state observers to reconstruct the unknown states of the augmented system, and develop extended state observers to estimate the actuator faults and disturbance of the augmented system. Again, the fault‐tolerant controllers are completed based on the backstepping control and the finite time control, and the finite time convergences of the designed observers and controllers are proved by theoretical analyses. Finally, based on a permanent magnet synchronous motor (PMSM) speed system, the simulation research and dSPACE simulated experiment research are conducted to verify the effectiveness of the proposed control method and its feasibility in the actual application. [ABSTRACT FROM AUTHOR]

This paper proposes the finite-time state-constrained adaptive fault-tolerant control method for a class of heavy launch vehicles subject to quantized input signals and actuator faults. Firstly, the attitude dynamic model of the heavy launch vehicles suffering from the actuator faults and disturbances is formulated. Secondly, to deal with the completely unknown nonlinear functions, radial basis function neural networks (RBFNNs) are introduced for approximation and compensation. Meanwhile, the barrier Lyapunov function (BLF) is introduced to ensure that all the states in the closed-loop system are bounded and the constraints of the system states are satisfied. As a result, the finite-time state-constrained adaptive fault-tolerant control structure is constructed for the heavy launch vehicles and the semi-globally practical finite-time stability (SGPFS) of the closed-loop control system is proved. Finally, numerical simulation results show the effectiveness and the satisfactory performance of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

Submerged aquatic vegetation plays a fundamental role as a habitat for the biodiversity of marine species. To carry out the research and monitoring of submerged aquatic vegetation more efficiently and accurately, it is important to use advanced technologies such as underwater robots. However, when conducting underwater missions to capture photographs and videos near submerged aquatic vegetation meadows, algae can become entangled in the propellers and cause vehicle failure. In this context, a neurobiologically inspired control architecture is proposed for the control of unmanned underwater vehicles with redundant thrusters. The proposed control architecture learns to control the underwater robot in a non-stationary environment and combines the associative learning method and vector associative map learning to generate transformations between the spatial and velocity coordinates in the robot actuator. The experimental results obtained show that the proposed control architecture exhibits notable resilience capabilities while maintaining its operation in the face of thruster failures. In the discussion of the results obtained, the importance of the proposed control architecture is highlighted in the context of the monitoring and conservation of underwater vegetation meadows. Its resilience, robustness, and adaptability capabilities make it an effective tool to face challenges and meet mission objectives in such critical environments. [ABSTRACT FROM AUTHOR]

The paper introduces a robust adaptive fault-tolerant control system for the six-degree-of-freedom (six-DOF) dynamics of quadrotor unmanned aerial vehicles (UAVs), incorporating disturbances and abrupt actuator faults to represent real-world conditions. The proposed control scheme employs robust control terms to manage unknown disturbances. However, robust control performance may degrade due to sudden fault impacts. To handle this issue, we introduce adaptive laws to ensure continuous adaptation. The control architecture ensures the tracking system's stability by combining robust control using sliding-mode control (SMC) with adaptive control developed using the certainty equivalence principle. The sliding-surface error limits the adaptive laws, in which the convergence of estimated parameters to the actual unknown variables is not required as they fully rely on the convergence of the tracking error. We provide rigorous mathematics to validate the proposed control design. Furthermore, we conduct numerical simulations for a quadrotor UAV to showcase the effectiveness of the proposed scheme. The results demonstrate the efficacy of the proposed design in handling external disturbances and abrupt actuator faults. [ABSTRACT FROM AUTHOR]

This paper investigates the prescribed performance adaptive fault‐tolerant control problem for nonlinear systems with actuator faults and input dead‐zone (IDZ). The partial loss of effectiveness fault and bias fault are considered. First, the asymmetric nonlinear IDZ is transformed into an affine function in the backstepping process. Second, the radial basis function neural network technique is applied to deal with the unknown uncertainty of the studied system. The state observer is designed to estimate the unmeasurable states in the nonlinear systems. Third, a fault‐tolerant controller is developed such that all signals are semi‐globally uniformly ultimately bounded for the closed‐loop system, and the tracking error remains within the specified performance requirements even though the actuator faults and IDZ occur. Finally, an electromechanical system example is provided to exhibit the utilizability of the obtained control technique. [ABSTRACT FROM AUTHOR]

In this article, the issue of fixed‐time fault‐tolerant control is studied for a class of nonlinear systems with sensor/actuator faults. The tuning functions and command filters are used to solve the problem of over‐parameterization and differential explosion in traditional backstepping method. The above methods simplify the derivation and reduce the calculation burden of the system respectively. Moreover, the introduction of fixed‐time control further improves the rapidity of the system. Another feature of this design is that the fixed‐time stability is finally realized by introducing a special Lyapunov function, rather than the practical fixed‐time stability. The tracking error can be guaranteed to converge to the origin in a fixed time. Simulation results show that the proposed control strategy is effective even if there are actuator/actuator faults in the system. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fault‐tolerant fixed‐time control problem is considered via command‐filter technique for stochastic nonlinear systems with sensor fault and actuator hysteresis. With the application of command‐filtering technique, a novel command‐filter compensate mechanism is designed, which implies that the improved control scheme not only eliminates "the explosion of complexity" but also realizes the compensate signal is bounded within fixed‐time interval. The unavailability of state variables caused by sensor fault is solved by applying parameter separation and regrouping approach. Meanwhile, an adaptive auxiliary signal is designed to cope with the backlash‐like hysteresis phenomenon, which can avoid singularity, reduce chattering, and facilitate controller design. Combining backstepping technique and Lyapunov stability theorem, an adaptive fault‐tolerant control approach is developed, which can guarantee all closed‐loop signals remain semi‐globally practical fixed‐time stable (SGPFS) in probability. The validity of the proposed strategy is illustrated by simulation examples. [ABSTRACT FROM AUTHOR]

The unmanned surface vessel (USV) is an emerging marine tool with its advantages of automation and intelligence in recent years; the good trajectory tracking performance is an important capability. This paper proposes a novel prescribed performance fixed-time fault-tolerant control scheme for an USV with model parameter uncertainties, unknown external disturbances, and actuator faults, based on an improved fixed-time disturbances observer. Firstly, the proposed observer can not only accurately and quickly estimate and compensate the lumped nonlinearity, including actuator faults, but also reduce the chattering phenomenon by introducing the hyperbolic tangent function. Then, under the framework of prescribed performance control, a prescribed performance fault-tolerant controller is designed based on a nonsingular fixed-time sliding mode surface, which guarantees the transient and steady-state performance of an USV under actuator faults and meets the prescribed tracking performance requirements. In addition, it is proved that the closed-loop control system has fixed-time stability according to Lyapunov's theory. Finally, upon conducting numerical simulations and comparing the proposed control scheme with the SMC and the finite-time NFTSMC scheme, it is evident that the absolute error tracking performance index of the proposed control scheme is significantly lower, thus indicating its superior accuracy. [ABSTRACT FROM AUTHOR]

In this paper, the adaptive finite-time fault-tolerant control (FTC) problem is investigated for uncertain nonlinear strict-feedback systems. The strict-feedback nonlinear system considered in this paper contains unknown nonlinear dynamics and actuator faults (both lock-in-place and loss of effectiveness). In this control process, adaptive laws are used to approximate unknown nonlinear functions. By using the sliding mode control technique and combining it with the adaptive backstepping control design, an adaptive terminal sliding mode FTC scheme is proposed. It is proved that the closed-loop system is finite-time stable and that the system output can track a given reference signal. Simulation results further show the efficacy of the designed control approach. [ABSTRACT FROM AUTHOR]

This article focuses on the robust fault tolerant control (FTC) problem for a class of Lipschitz nonlinear multi‐agent systems(MASs) subject to sensor faults. Firstly, sensor faults are transformed into actuator faults via introducing a new intermediate auxiliary state variable, and a distributed adaptive fault estimation observer is designed to estimate the state information and the concerned faults by using the relative output estimation error. Then, the sufficient existence conditions for the observer to satisfy the robust performance index are given. Thirdly, based on the results of observer design, a new design method of dynamic output feedback controller is proposed to implement consensus of MASs and ensure the desired disturbance rejection performance. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article introduces a new fault-tolerant control method based on type-2 fuzzy systems with PID fast terminal sliding mode control. By integrating the advantages of proportional-integral-derivative (PID) control with fast terminal sliding mode (FTSM) control, a novel proportional-integral-derivative fast terminal sliding mode (PID-FTSM) is developed to accelerate convergence and decrease steady-state error. To provide outstanding fault tolerant control performance and approximation of system uncertainties, a type-2 fuzzy logical switching approach law eliminates the chattering phenomenon and reduce the need of prior knowledge without affecting the system's robustness. The overall stability of the system is verified using the Lyapunov function. Finally, several experiments demonstrate that the suggested technique outperforms alternatives. [ABSTRACT FROM AUTHOR]

This work mainly studies the issue of predefined time and accuracy adaptive fault-tolerant control for strict-feedback nonlinear systems with multiple faults. The faults in the controlled system include actuator faults and external system faults. The unknown functions for nonlinear systems are approximated by fuzzy logic systems (FLSs). And then, according to the backstepping technique and the predefined time stability theory, an adaptive fuzzy control algorithm is presented, which can make sure that all closed-loop system signals remain predefined time bound and the tracking error converges to a predefined accuracy within the predefined time. Ultimately, the effectiveness of the presented control algorithm is proved through two simulation examples. [ABSTRACT FROM AUTHOR]

Summary: Due to the long‐term operation of the tower crane, various faults will inevitably occur, such as actuator faults, which further increases the difficulty of controller design. In this paper, a fault‐tolerant control method with adaptive gain is proposed for the double‐pendulum tower crane with distributed payload beam (DTCDPB) system in the existence of external disturbances and actuator failures. First, a nonlinear fault‐tolerant observer is designed for fault diagnosis. Second, an S‐shaped trajectory functions are coupled online and embedded into the system target trajectories for payload swing suppression. Then, feedforward compensation is applied in the controller for the observed faults. Moreover, the adaptive suppression term to be activated is also designed in the controller taking into account the errors existing in the observation. Finally, the effectiveness of the proposed observer and controller is experimentally verified. [ABSTRACT FROM AUTHOR]

The practical preset time fault‐tolerant control (FTC) problem is explored in this article for uncertain Euler–Lagrange systems with input saturation and guaranteed performance. To cope with the uncertainty of the Euler–Lagrange systems, the adaptive neural network (NN) is exploited to approximate the unknown continuous function. Most existing results that consider input saturation and actuator faults simultaneously need to design compensation strategies separately, which increases the complexity of control algorithms. To overcome the above obstacle, the Nussbaum gain technique is used to deal with the effects of input saturation and actuator faults in this article. Besides, with the help of error transformation technology and speed function, the proposed control algorithm can ensure that the tracking error converges within the preset time and its overshoot is constrained within the prescribed performance boundaries. Furthermore, the boundedness of all closed‐loop system signals is confirmed. Finally, comparative simulation results are depicted to highlight the superiority of the designed control algorithm. [ABSTRACT FROM AUTHOR]

This article is concerned with the fixed‐time fault‐tolerant control problem of multiple Euler–Lagrange systems (MELSs) with intermittent communication, actuator faults and input disturbances. A nonsingular fixed‐time control framework with three parts is built for the above problem. In the first part, a novel adaptive controller is proposed for MELSs to ensure the fixed‐time stability of sliding modes while successfully solving the actuator faults, parameter uncertainties and unknown disturbances. In the second part, the fixed‐time estimators based on event‐triggered communication are designed by an error decomposition approach. In the third part, an auxiliary system is introduced for the singularity problem and sufficient condition for achieving the consensus is rigorously proved by synthesizing the results of the above two parts. The key feature of the proposed control framework is that the convergence time is constrained by a constant without involving initial states, and the singularity problems of fixed‐time control is avoided. Finally, simulation examples are provided to prove the efficacy of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to construct an event-triggered finite-time fault-tolerant formation tracking controller, which can achieve a time-varying formation control for multiple unmanned aerial vehicles (UAVs) during actuator failures and external perturbations. Design/methodology/approach: First, this study developed the formation tracking protocol for each follower using UAV formation members, defining the tracking inaccuracy of the UAV followers' location. Subsequently, this study designed the multilayer event-triggered controller based on the backstepping method framework within finite time. Then, considering the actuator failures, and added self-adaptive thought for fault-tolerant control within finite time, the event-triggered closed-loop system is subsequently shown to be a finite-time stable system. Furthermore, the Zeno behavior is analyzed to prevent infinite triggering instances within a finite time. Finally, simulations are conducted with external disturbances and actuator failure conditions to demonstrate formation tracking controller performance. Findings: It achieves improved performance in the presence of external disturbances and system failures. Combining limited-time adaptive control and event triggering improves system stability, increase robustness to disturbances and calculation efficiency. In addition, the designed formation tracking controller can effectively control the time-varying formation of the leader and followers to complete the task, and by adding a fixed-time observer, it can effectively compensate for external disturbances and improve formation control accuracy. Originality/value: A formation-following controller is designed, which can handle both external disturbances and internal actuator failures during formation flight, and the proposed method can be applied to a variety of formation control scenarios and does not rely on a specific type of UAV or communication network. [ABSTRACT FROM AUTHOR]

This paper focuses on the trajectory tracking problem of nth-order uncertain nonlinear systems with sensor faults. The proposed approach utilizes a fuzzy observer to estimate the unmeasurable states in the systems. Moreover, the finite-time control strategy and the command filtered technique are added in the controller design. The former aims to enhance the systems' response speed, and the latter is to mitigate the "differential explosion" problem. Meanwhile, the adaptive technique is incorporated to compensate for sensor faults. The boundedness of all the signals within the closed-loop systems is confirmed through stability analysis. Finally, the effectiveness of the proposed approach is verified through two simulation examples. [ABSTRACT FROM AUTHOR]

Due to the widespread application and significant investment required for a single crane, there is an increased emphasis on crane safety and service life. Fault-tolerant control as an effective solution to unexpected faults has been widely studied recently. However, most fault-tolerant control methods require redundant actuators or a complex design process, which is unsuitable for the tower crane. Following these problems, a fault-tolerant controller based on an adaptive backstepping technique is proposed. Firstly, the system states are reconstructed and written as a cascade system. Secondly, a fixed-time convergence optimized backstepping controller is proposed to achieve smooth control of the tower crane without generating sudden or abrupt values. Then, an adaptive approach has been proposed to update fault parameters for the crane system in case of a sudden fault occurrence. Finally, after conducting comparison tests, it has been determined that the proposed controller not only performs exceptionally well in terms of position accuracy and swing elimination, but also maintains a satisfactory control performance when faced with sudden faults. • The jib and trolley positioning and load swing suppression problems for tower cranes are investigated. • The adaptive backstepping fault-tolerant controller is designed. • The control performance is demonstrated by comparative experiments. [ABSTRACT FROM AUTHOR]

The problem of adaptive fault-tolerant fixed-time control is studied for a class of strict-feedback nonlinear systems with multiple faults and multiple disturbances. We incorporate the tuning functions and the command filter technique into the controller design. Note that the former reduces the order of the controller, and the latter simplifies the derivation and calculation process and avoids the high calculation cost and differential explosion. In addition, since our proposed strategy is based on fixed-time control, it can ensure that the closed-loop system keeps the practically fixed-time stable, and the tracking error converges to a small neighborhood near the origin within fixed-time. As for the unknown items in the systems, fuzzy logic systems are used to approximate them. The simulation results show that the proposed control strategy is effective even if there exist actuator faults and multiple disturbances. [ABSTRACT FROM AUTHOR]

It is the first report about fault-tolerant-based prescribed performance control of switched nonlinear systems under multiple faults. The concerned faults include not only external faults but also actuator faults. In the process of backstepping control design, prescribed performance control is fully considered, and the combination of unknown nonlinear functions is estimated by multi-dimensional Taylor network. Finally, the developed adaptive fault-tolerant control strategy guarantees the boundedness of all controlled signals while prescribed tracking performance is satisfied. In an effort to further manifest the validity of the fault-tolerant controller, a numerical simulation and a practical simulation are introduced. • This paper is dedicated to balancing prescribed tracking performance and multiple faults. • It is the first time that actuator fault, external fault are discussed in the complicated switching framework. • The adaptive fault-tolerant MTN-based controller is developed to cope with performance constraints. [ABSTRACT FROM AUTHOR]

The research investigates the fixed-time command-filtered composite adaptive neural fault-tolerant (FCCANF) control issue of strict-feedback nonlinear systems (SFNSs). There exist unknown functions and bounded disturbances in the considered systems. Radial basis function neural networks (RBFNNs) will be used in the estimate of the unknown functions. By the serial–parallel estimation models (SPEMs), the forecast biases and the track biases can change the weights of RBFNNs and the approximate characteristics of RBFNNs will be improved. Then, utilizing the novel fixed-time command filter and adaptive disturbance observers, the issue of complex explosion will be effectively solved and the external disturbance is effectively compensated. Subsequently, by utilizing the adaptive control technique, a novel FCCANF controller is developed. Additionally, we have that the system internal variables are bounded and the output variable inclines to a little interval around zero in fixed time which is not determined by the system initial variables. Eventually, numerical and practical examples are shown to prove the availability of the obtained control technique. • For the paper [23], a second-order fixed-time command filter with the symbolic function is introduced to estimate the derivatives of the virtual controllers. However, in this manuscript, a first-order fixed-time command filter with the smooth hyperbolic tangent function is designed to estimate the derivatives of the virtual controllers. Then, the compensation of filtering errors is not considered in the paper [23]. However, in this manuscript, the compensation of filtering errors is considered. • To improve the RBFNN approximation, the novel fixed-time convergence SPEMs are created and it is the first time to use the matrix element technique to solve the fixed-time patchwork problems for the adaptive laws. Then, to estimate the lumped disturbance, the fixed-time convergence adaptive neural disturbance observers are utilized firstly. • Compared with the papers [22] and [24], based on [25], the hyperbolic tangent functions are introduced to solve the singular problem. [ABSTRACT FROM AUTHOR]

This paper gives a fault-tolerant control scheme concerning with the optimal and near-optimal system performance for a class of nonlinear systems with time-varying actuator faults, time-varying disturbances, and identification errors of the neural network-based identifier. In this paper, the adaptive dynamic programming method is directly used to design the optimal sliding surface, so that the designer can design the target dynamics of the sliding mode in advance. In addition, the barrier function-based sliding-mode control is used to cope with the bounded but boundary-unknown estimation errors of the identifier, and the method ensures that the sliding-mode variable converges to the designer's predefined neighborhood of zero in finite time and the control gain is not overestimated. Specifically, first, by adaptive dynamic programming, near-optimal sliding surface is designed in the sense of the quadratic optimal criterion. Second, a neural network identifier is designed to model the lumped uncertainties including actuator faults and disturbances. Third, a barrier function-based adaptive sliding-mode control is used to cope with the identification errors of the neural network identifier and has no control gain overestimation, which can guarantee to confine the sliding variable to a predefined vicinity of the proposed sliding surface. For this system with faults and disturbances, it is shown that near-optimal property is achieved by this scheme, the chattering phenomenon is effectively suppressed, and the reconstruction error of the neural network identifier with unknown boundary is effectively handled by the adaptive sliding-mode control based on the barrier function. The proof of stability is given by Lyapunov's direct method and the effectiveness of this control scheme is verified by applying it to the spacecraft attitude system. [ABSTRACT FROM AUTHOR]

In this article, the attitude tracking problem for rigid spacecraft subject to external disturbance, inertia uncertainties, and actuator faults is investigated. A novel continuous control strategy is proposed to guarantee that the attitude tracking errors converge with desired performance before an appointed time. In addition, the proposed control law can enable the closed‐loop system to be unwinding‐free. For the purpose, a modified appointed‐time performance function (APF) is used to construct a disturbance observer‐based adaptive attitude control law based on the special orthogonal group (SO(3)). With the aid of the modified APFs, desired performance metrics, including transient and steady‐state performance, on the attitude tracking error can be specified in advance without the requirement for initial values of the tracking system to avoid singularity. By resorting to error transformation and backstepping technique, the control design process is simplified and a few control gains are involved in the proposed control law. Rigorous stability analysis based on the Lyapunov theory is provided to prove the appointed‐time stability of the attitude tracking error as well as the boundedness of all signals in the closed‐loop system despite external disturbance, inertia uncertainties, and actuator faults. Finally, numerical simulations are conducted to support the analysis. [ABSTRACT FROM AUTHOR]

This article investigates the adaptive fault‐tolerant tracking control problem for nonlinear systems with prescribed performance and input dead‐zone. First, a new composite variable is constructed by using the characteristics of actuator fault and input dead‐zone for the modeling purpose. Second, an adaptive neural network observer is designed to estimate the system states in the presence of inaccurate feedback information. Third, the proposed control strategy effectively counteracts the effects of sensor failure and unknown nonlinear functions, which makes the tracking error confined within the performance boundary and all the signals of the closed‐loop system semi‐globally uniformly ultimately bounded. Finally, an application oriented example is provided to demonstrate the effectiveness of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

A fixed‐time fault‐tolerant control scheme based on sliding mode observer is proposed, which makes the system more stable and stronger anti‐jamming ability. In our design, its distinct characteristic is to combine the passive fault‐tolerant control and non‐singular fast terminal sliding mode (NFTSM). And it ensures that the system states can converge to a very small neighborhood near the equilibrium point in a fixed time no matter in normal condition or fault condition. In addition, a novel sliding‐mode observer and a fast variable power reaching law are added to make the system converge faster and chattering smaller. Finally, the computer simulation results of a two‐joint manipulator demonstrate the feasibility of the proposed strategy. [ABSTRACT FROM AUTHOR]

This paper investigates the fault-tolerant prescribed performance control problem for a class of multiple-input single-output unknown nonlinear systems subject to process faults and actuator failures. In contrast to the related works, we consider a general class of nonlinear systems with both multiplicative nonlinearities and additive nonlinearities corrupted by the process faults; only the boundedness of the process faults and the continuity of the nonlinear functions are required, without the explicit or fixed structures of the fault functions. To conquer this problem, a less-demanding and low-complexity fault-tolerant prescribed performance control approach is proposed. The controller is independent of the specific information of faults or the system model and does not invoke fault diagnosis or neural/fuzzy approximation to acquire such knowledge. It achieves the reference tracking with the predefined rate and accuracy. A comparative simulation on a single-link robot is conducted to illustrate the effectiveness and superiority of the proposed approach. • Both process faults and actuator failures are considered. • The virtual control coefficients are time-varying nonlinear functions. • We consider a general class of systems with multiplicative and additive nonlinearities. • Both multiplicative and additive nonlinearities are impacted by process faults. • The reference tracking with predefined rate and accuracy is achieved. [ABSTRACT FROM AUTHOR]

In this paper, the adaptive robust H ∞ fault-tolerant control problem for a class of switched nonlinear systems with parameter uncertainty, disturbances and actuator failures is concerned based on event-triggered control strategy. The adaptive laws based on state-dependent switched strategy are designed to eliminate the effects of actuator faults and parameter uncertainties by using the estimations of the unknown upper bounds of uncertain parameters. Then, the robust H ∞ fault-tolerant technique and multiple Lyapunov functions method are used, the designed controller can guarantee that all signals of the switched closed-loop systems are uniformly bounded. Meanwhile, the desired H ∞ performance of the systems is promised. Finally, the simulation results are given to illustrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

An adaptive sliding mode fault‐tolerant control strategy is proposed for a quadrotor unmanned aerial vehicle in this article to accommodate actuator faults and model uncertainties. First, a new reaching law is proposed, with which a sliding mode control (SMC) law is constructed. The proposed reaching law is made up of a sliding variable and the distance between it and a designated boundary layer, and it can effectively suppress the unexpected control chattering while preserving the necessary system tracking performance. Then, an adaptive SMC scheme is proposed to further solve the fault and uncertainty compensation problem. The proposed adaptation law helps to prevent overestimation of the adaptive control parameters, as well as avoiding control chattering. Finally, a number of comparative simulation tests are carried out to validate the effectiveness and superiority of the proposed control strategy. The demonstrated quantitative comparison results confirm its advantages. [ABSTRACT FROM AUTHOR]

This paper describes a solution to the problem of fault-tolerant control (FTC) problem for leader-following heterogeneous linear multi-agent systems (MASs) subject to loss of effectiveness and time-varying additive actuator faults. The main goal of the proposed FTC approach is to maintain the behaviour of the heterogeneous MASs in spite of actuator faults and to save on bandwidth required for the MASs communication by using a dynamic event-triggered communication mechanism. Firstly, a fault estimation observer, which deals with linear systems with matched disturbances, is constructed to estimate simultaneously the actuator faults and the followers' states. Then, an FTC with dynamic event-triggered communication is proposed. The latter is based on a dynamic internal reference for each agent and exploits the estimated faults. Thus, it is at first shown that the FTC problem can be indirectly solved through the consensus tracking of the defined internal references. Then, a sufficient condition of consensus tracking for the internal references with a dynamic event-triggered communication is proposed. Finally, a sufficient and necessary condition is derived for the FTC of linear heterogeneous multi-agent systems. The effectiveness of the proposed approach is illustrated with a numerical simulation. [ABSTRACT FROM AUTHOR]

The combination of nonlinear indirect and direct adaptive control with an active fault-tolerant framework is proposed in this paper for quadrotor position tracking control under uncertain and fault conditions. An inner loop direct model reference adaptive controller generates the required force while moving along the reference trajectory, while nonlinear indirect adaptive controller maintains the required attitude angles. Furthermore, for uncertain conditions, our proposed framework provides significantly stable characteristics. Otherwise, when a fault occurs at actuators or sensors, the quadrotor vehicle cannot guarantee global asymptotic stability. This study contributes to an active fault-tolerant control strategy for solving the complex position tracking problem using the adaptive two-stage Kalman filter (ATSKF). Based on the fault information, a fault compensation term is added to the control law to improve convergence and system robustness in the presence of uncertain and fault conditions. Finally, simulation results show satisfactory performance for quadrotor vehicle position tracking, even with actuator faults and uncertainties. [ABSTRACT FROM AUTHOR]

This paper investigates the fault‐tolerant control problem for a dual‐redundant hydraulic actuation system on active/active (A/A) mode subject to servovalve leakage and disturbances. The change in system dynamics caused by servovalve leakage is modeled as an additive time‐varying fault. Then, an enhanced iterative learning observer with improved robustness against abrupt unknown input is designed for fault reconstruction. In view of the high relative degree of the plant, an auxiliary variable is adopted to facilitate the controller design. Combined with the fault reconstruction results, an adaptive continuous nonsingular fast terminal sliding mode (NFTSM) fault‐tolerant controller is developed, in which an NFTSM manifold is constructed based on the auxiliary variable to achieve fast convergence of trajectory tracking errors. An adaptive continuous reaching law with less chattering is designed to compensate for the influence of the lumped disturbance. Lyapunov stability analysis demonstrates that this method can ensure finite‐time convergence of sliding variable and can guarantee the trajectory tracking errors converge to the neighborhood of the origin exponentially. Finally, the effectiveness of the proposed method is verified through a comparative simulation study. [ABSTRACT FROM AUTHOR]

A class of fault-tolerant safety-critical controller design methods based on high-order control barrier function (HOCBF) is proposed to address the problem of safety and stability of system affected by actuator faults in safety-constrained nonlinear affine system. Firstly, the fault information is incorporated into the conventional HOCBF to obtain a new type of HOCBF with faults. Secondly, in the case of a strictly required range of control inputs, a sufficient condition is proposed to satisfy the existing constraints, where the control inputs are always within the restricted range and the sufficient condition is expressed as feasibility constraints. Next, based on the quadratic programming (QP) method, the control Lyapunov function, fault HOCBF, and feasibility constraints are incorporated together to ensure that the overall feasibility, stabilization, and safety are guaranteed of the considered closed-loop system. Finally, the adaptive cruise control system is taken as an example to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, for a class of stochastic pure-feedback nonlinear systems with simultaneous actuator and sensor faults, the problem of adaptive fault-tolerant control is examined. The stochastic pure-feedback nonlinear system is first converted into a strict-feedback by applying the mean value theorem and radial basis function neural networks are used to approximate the unknown functions. Only one adaptive parameter needs to be calculated online rather than the actual weight vector elements by determining the greatest value of the norm of the neural network weight vector. With the help of regrouping and parameter separation methods, the unavailability of state variables caused by sensor faults is addressed. The Lyapunov function methods and the backstepping recursive design technique are used to design an adaptive fault-tolerant controller. It is shown that by choosing proper the design parameters, the tracking errors converge to a small region of the origin, and all the signals in the closed-loop system are bounded in probability. The performance of the proposed controller is illustrated using a numerical example and a real-world example of a rigid robot manipulator system. [ABSTRACT FROM AUTHOR]

This paper mainly studies fault-tolerant control for a class of semi-linear fractional-order multi-agent systems with diffusion characteristics, where the actuator fault is considered. The adaptive fault-tolerant control protocol based on the adjacency relationship of agents is firstly designed, which can adjust the coupling gain online through the adaptive mechanism. Using the Lyapunov stability theory, the adaptive fault-tolerant control protocol can drive the agents to achieve consensus for leader-following and leaderless cases. Finally, the simulation experiment is carried out, showing the effectiveness of the proposed theory. [ABSTRACT FROM AUTHOR]

This article investigates the issue of adaptive neural optimal fault‐tolerant control for a class of nonlinear uncertain systems subject to dynamic state constraints and external disturbances. To handle more general dynamic constraints, a unified tangent‐type nonlinear mapping is first proposed to transform the state‐constrained system into one free of constraints. To solve the problem of actuator faults and external disturbances, a single network adaptive dynamic program method is designed, which consists of a feed‐forward fault‐tolerant control scheme and a feedback differential game control strategy. Neural networks are employed to approximate the uncertainties and cost function, respectively. To handle the issue of "explosion of complexity," a finite‐time convergent differentiator is established to estimate the derivative of virtual control signals in the backstepping design. Via Lyapunov stability analysis, asymptotic stability of the original and transformed nonlinear system is theoretically guaranteed. Two comparative simulation examples are provided to evaluate the efficacy of the proposed control approach. [ABSTRACT FROM AUTHOR]

This paper proposes an output‐feedback fault‐tolerant tracking control scheme for coupled 2×2$$ 2\times 2 $$ hyperbolic PDE systems with multiplicative sensor faults. In order to estimate the system states, an observer is designed by constructing four filters, which impose time delays to their input signals. For sensor fault identification problem, the gradient descent method is utilized based on a parametric model to estimate the fault parameter. With the filter‐based observer and the estimated fault parameters, a novel control strategy is proposed via backstepping design technique to achieve the tracking objective. Finally, the simulation studies are given to verify the tracking performance of the proposed fault‐tolerant tracking control scheme. [ABSTRACT FROM AUTHOR]

A deflating subspace approach is applied to the unknown input observer (UIO) design. The associated matrix pencil (MP) to the transfer matrix from the unknown input to the measured output is arbitrary. A unique necessary and sufficient condition is given, in terms of a proper stable left-deflating subspace (PSL-DS) of the MP. For the class of plants such that UIO exists, a UIO-based controller design is presented, based on obtaining a constant coefficient matrix that is a part of the controller, instead of a rational controller matrix. Then the design is applied to a fault-tolerant control (FTC). Illustrative examples are presented. [ABSTRACT FROM AUTHOR]

Summary: This article contributes with a fault‐tolerant control (FTC) for uncertain systems under the effect of some possible time‐ and state‐dependent actuator faults and/or failures, and component faults, which are zero at the initial time. The proposed scheme is based on a continuous integral sliding‐mode control approach and a fixed control allocation technique. The integral sliding‐mode control strategy allows us to design a robust linear controller and a multivariable Super‐Twisting algorithm, which deals with the faults. The proposed scheme guarantees the fulfilment of an output regulation task, with an arbitrarily small regulation error, and does not require a fault diagnosis stage but full‐state availability. The performance of the proposed FTC is illustrated through some simulations on a benchmark B747 aircraft model. [ABSTRACT FROM AUTHOR]

• An adaptive fault-tolerant control framework for spacecraft formation flying is proposed. • A special function is introduced to guarantee the prescribed performance. • A nonsingular fast terminal sliding mode control scheme is adopted to account for external disturbances and uncertainties. This paper investigates an adaptive fault-tolerant control problem for spacecraft formation flying (SFF) with actuator faults, external disturbances, and unknown inertial uncertainties. First, fault factors are introduced to describe the SFF orbit model with consideration of actuator bias faults and loss of actuator effectiveness. Then, an adaptive fault-tolerant controller is proposed by incorporating prescribed performance function, improved terminal sliding mode control and the proposed adaptive law. Finally, rigorous theoretical analysis ensures the uniformly ultimately bounded stability of the system through Lyapunov theory and simulation verifies the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive fault‐tolerant control (FTC) scheme is proposed for a class of flexible air‐breathing hypersonic vehicles with unknown inertial and aerodynamic parameters and even input constraints. The fault model under consideration covers the case that all actuators suffer from unknown time‐varying faults. In the controller design and stability analysis, we introduce new Lyapunov functions, some differentiable auxiliary functions, a bound estimation approach, and a Nussbaum function, which help us successfully circumvent the obstacle caused by the faults, input constraints, and flexible modes. In addition to higher reliability, the proposed scheme is able to ensure that all closed‐loop signals are globally uniformly bounded and to steer the tracking errors of altitude and velocity into predefined arbitrarily small residual sets. As a result, the tracking accuracy can be designated in advance. Simulation results illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper solves the problem of adaptive fault‐tolerant control of uncertain switched nonlinear systems with unknown parameters and actuator failures. Based on the multi‐Lyapunov function method, a novel adaptive switched controller with tuning function is designed using the backstepping procedure. Meanwhile, a switched fault‐tolerant adaptation mechanism is also given to compensate the fault efficiency. Furthermore, it is certificated that all the signals of the closed‐loop system are uniformly bounded and the tracking error restrain to a small neighbor. Finally, the simulation results verify the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

The issue of active attitude fault-tolerant stabilization control for spacecrafts subject to actuator faults, inertia uncertainty, and external disturbances is investigated in this paper. To robustly and accurately reconstruct actuator faults, a novel mixed learning observer (MLO) is explored by combining the iterative learning algorithm and the repetitive learning algorithm. Moreover, to guarantee robust spacecraft attitude fault-tolerant stabilization, by synthesizing the mixed learning algorithm with the sliding mode controller, a novel mixed learning sliding-mode controller (MLSMC) is designed based on the separation principle, in which the mixed learning algorithm is used to update composite disturbances online, including fault errors, inertia uncertainty, and external disturbances. Finally, a numerical example is provided to demonstrate the effectiveness and superiority of our proposed spacecraft attitude fault-tolerant stabilization control approach. [ABSTRACT FROM AUTHOR]

Summary: This paper focuses on the issue of the adaptive fuzzy fault‐tolerant control for a type of nonlinear system with input delay and disturbances. Fuzzy logic systems (FLSs) are used to estimate the unknown nonlinear quantities of the system. The Pade approximation is applied to counteract the negative effects of input delay on the system. The prescribed performance control based on error transformation helps to guarantee the transient performance of system errors. A fuzzy state observer is established to estimate the unmeasurable states of the system. Then, in presence of disturbances and actuator faults, a finite‐time control scheme is designed using the Lyapunov function and the backstepping technique. Based on Lyapunov stability, it is proved that the tracking error can converge to a specified range in a finite time, and all signals in the system are bounded in the controller design. In the end, the simulations of a second‐order system and a multi‐area interconnected power system certify the feasibility and effectiveness of the control strategy. [ABSTRACT FROM AUTHOR]

Summary: This paper solves the finite‐time fault estimation (FE) and fault‐tolerant control (FTC) problem for discrete‐time Markov jump systems with actuator and sensor faults. A new extended state system is constructed by taking the fault as a state. For this system, a novel observer is shown to estimate states, actuator and faults of considered systems, simultaneously. Based on the utilized estimation, a fault‐tolerant controller is proposed to ensure the finite‐time boundedness of closed‐loop ones with H∞$$ {H}_{\infty } $$ performance. The feasibility of the proposed finite‐time FE and FTC scheme is illustrated based on a simulation example. [ABSTRACT FROM AUTHOR]

This paper proposes a distributed fault‐tolerant control for over‐actuated multi‐agent systems with uncertain perturbations and faults including partial loss of effectiveness or even complete failures. The entire distributed control law is divided into two parts that are the distributed observer and the decentralised controller with a hierarchical structure. The adaptive distributed observer estimates not only the leader's state, but also the leader's system matrix, which makes the whole distributed design more rigorous. For each over‐actuated subsystem, the control allocation based hierarchical control structure is used. The virtual control is developed based on adaptive optimal control approaches to cope with uncertain perturbations robustly. The model reference adaptive control is used to design the control allocator without the need for the fault detection and diagnosis module. The stability and robustness of the systems are rigorously demonstrated, and the feasibility and effectiveness of the control law are verified in simulations on the attitude dynamics system of spacecraft. [ABSTRACT FROM AUTHOR]