This article studies the distributed predefined-time formation control problem for a specific heterogeneous multiagent system. This system includes completely different unmanned autonomous helicopters (UAHs), unmanned ground vehicles (UGVs), and autonomous underwater vehicles (AUVs) in the presence of actuator faults. First, a distributed prescribed-time observer is developed for followers to estimate the leader states, which can decrease the network flow. Then, an adaptive predefined-time fault-tolerant optimal formation controller is constructed to continuously optimize performance index and approach optimal formation tracking. Moreover, in the designed control framework, adaptive updating laws are constructed for the unknown parameters of actuator loss of efficiency and the lumped uncertainty, respectively. Compared with the relevant finite/fixed-time cooperative tracking works, here the settling time is independent of any existing control gains and the initial conditions of the studied heterogeneous multiagent systems (MASs), thus it can be uniformly prescribed. Finally, the control performance of the designed method is further illustrated by a simulation experiment.

In most of the existing fault-tolerant control (FTC) results, only a uniform ultimate bound on the tracking error can be guaranteed, while achieving zero tracking error is a more desirable control objective. This article addresses the zero-error formation control problem for cross-dimensional heterogeneous fully actuated MASs subject to hybrid faults consisting of intermittent actuator faults and communication link faults (CLFs). To accurately estimate the leader's state when CLFs are present, distributed observers are developed specifically in the shape of an upper triangular chain of first-order low-pass filters. Then, for the agents with intermittent actuator faults, adaptive fault-tolerant tracking controllers are developed utilizing the fully actuated system (FAS) approach. Based on the Lyapunov stability theory, rigorous theoretical analysis is provided to prove that all signals in the closed-loop system are bounded and the formation errors asymptotically converge to zero. Finally, a simulation example is presented to prove the suggested control strategy's effectiveness.

In the aerospace field, equipment failures can lead to substantial economic losses and pose significant safety risks, making effective fault diagnosis crucial. Traditional fault diagnosis methods typically require large, precisely labeled datasets, which are challenging to obtain in aerospace applications due to the rarity and unpredictability of faults. To overcome these limitations, this article proposes a novel conditioned multiscale generative adversarial networks (GANs) approach designed to enhance fault diagnosis performance under small-sample conditions. Initially, raw vibration signals undergo preprocessing using the short-time Fourier transform, which expands frequency-domain features while preserving essential time-frequency characteristics. Subsequently, conditioned multiscale GANs are trained on these limited datasets, employing multiscale convolutional kernels to extract and fuse rich features, thus generating high-quality synthetic samples. Finally, these synthetic samples are combined with the original dataset to train a convolutional neural network offline, which can subsequently perform real-time online fault diagnosis. Extensive validation on two aerospace-related datasets demonstrates that the proposed method significantly enhances fault diagnosis accuracy and efficiency, even when the available training data is severely limited.

To elevate the robustness and optimality of helicopter formation, this article proposes the incremental fully actuated system approach (FASA) integrated with reinforcement learning (RL) for the formation control of multiple helicopters with faulty swash plates. First, the helicopter model encompassing aerodynamics, flapping dynamics, and swash plate dynamics under actuator faults is established. Then, the entire helicopter formation is reinterpreted and stabilized by the incremental FASA that offers the replacement of model information, the suppression of lumped uncertainty, and the rearrangement of system dynamics, with mitigated reliance on model accuracy and computing resources. Next, considering the influence of the actuator faults of a single helicopter on the convergence of the entire formation, RL is applied to pursue the optimal control strategy against fault impact through the critic network, which updates along the dynamics revised by the incremental FASA, ensuring satisfactory formation performance throughout the flight, augmenting the cost efficiency of the control scheme, and relieving any means of identification or approximation on helicopter dynamics. Finally, the stability of the control scheme is proved, and numerical simulations are conducted to illustrate it is efficiency.

This paper studies practical prescribed-time control of fully actuated heterogeneous multiagent systems subjected to actuator faults. A new observer-based containment control structure is given in the scenario that only a small number of followers can access the knowledge of leaders. Firstly, prescribed-time distributed input, velocity, and position observers are designed to estimate the information of the convex hull that leaders have spanned. Then, the original practical prescribed-time fault-tolerant control issue is transformed into one with a deferred constraint on tracking errors by introducing a time-varying constraining function, and decentralized tracking controllers are designed based on the system’s fully actuated system model. With the prescribed-time prescribed performance function, the proposed method allows for the advance determination of the settling time and the final tracking accuracy as needed, as well as the reduction of the impact of actuator faults on the system without the need for actuator fault parameter estimations. The efficacy of the suggested approach is shown through simulation results. Note to Practitioners—The containment control issue of heterogeneous multiagent systems, as a popular topic in the control field, is crucial to practical engineering. It is worth noting that actuator faults often exist and they have the potential to spread throughout networks in practical applications. A novel observer-based containment control structure is developed and a robust fault-tolerant control algorithm is given to reduce the impact of actuator faults on the system without the need for actuator fault parameter estimations. What’s more, achieving containment control in a brief amount of time is highly desirable. Therefore, a practical prescribed-time control protocol is given to ensure containment errors converge to the predefined region within an assignable prescribed settling time interval. In summary, a practical prescribed-time fault-tolerant containment control technique is proposed, which promotes the advancement of containment control for MASs in practical applications.

This article investigates the fixed-time faulty parameter estimation problem for an interconnected fuzzy system with multiple time-varying delays. Based on the persistent excitation condition, an adaptive observer with a faulty parameter identification algorithm is constructed, to provide the accurate information of partial loss of actuator effectiveness within a fixed settling-time, and to guarantee the boundedness of state estimation error by mitigating the influence of external disturbance. Accordingly, several sufficient conditions for the existence of fuzzy observer gain, and the convergence proof of the input-to-state stability are also presented by utilizing the small-gain technique. Afterwards, an active fault-tolerant controller is synthesized to maintain the faulty interconnected system by compensating the actuator fault. Finally, simulation results on an inverted-pendulum system and a numerical example show the feasibility and advantage of the proposed approaches.

In rotating machinery, accurate fault diagnosis is crucial for efficiency and preventing failures. Traditional models often struggle with imbalanced datasets. This study introduces strategies that use feature fusion deep convolutional generative adversarial network (DCGAN) architectures to improve fault diagnosis accuracy. Initially, we pretrain the DCGAN using a comprehensive dataset encompassing various general faults to robustly capture the underlying features. Then, we use rare fault samples to refine the DCGAN, enhancing its capability to extract features from these minority classes. Random noise is input into the feature fusion deep convolutional generative adversarial network (FFDCGAN) model to obtain pseudosamples of the rare faults. The generated faults are then combined with the original dataset and analyzed by a convolutional neural network to classify fault types. Based on experimental results from the ZHS-2 and HIT aero-engine fault datasets, comparative analysis with existing studies shows that the proposed FFDCGAN method generates samples with significantly greater diversity. In addition, the proposed imbalanced fault diagnosis approach achieves higher accuracy, thereby validating its efficacy in handling imbalanced datasets.

Guaranteed system performance under various circumstances continues to be a challenge in technique and practice. Based on this, this article investigates the optimal fault-tolerant control strategy for a large-scale interconnected system with the intermittent actuator faults. Since the subsystem state is enforced to a restricted range, an asymmetric integral barrier Lyapunov function is incorporated into the principle of Bellman optimality to avoid the violation of state constraints. Also, it can conquer a conservative limitation that the bounds of the transformed error-constraints are known. Subsequently, the critic-actor–identifier framework is constructed in the backstepping step to evaluate the objective function, control behavior and unknown dynamic, respectively, wherein the decentralized controller derived from the learning process and the fault-tolerant controller are separated by introducing an intermediate controller. Meanwhile, it is illustrated that the trajectory tracking errors will approach to a small region nearby the origin, and the system states may not beyond the given asymmetric constraint bounds, even in the presence of faults. Finally, results are presented to exhibit the effectiveness and the advantage of the optimal approach through appropriate comparative simulations.

This study investigates the fixed-time and prescribed-time optimal formation control strategies for heterogeneous multiagent systems composed of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) unde actuator faults. In the proposed control framework, the critic-actor framework is designed to finish the optimization tracking. Radial basis function neural network (RBFNN) is implemented to derive the tracking control, in which the actor RBFNN is utilized to make up for the actuator faults and generate the formation control action, and the critic RBFNN is utilized to evaluate the execution cost. Then, a Lyapunov-based tracking technique is designed to ensure the fixed-time stability of the tracking error. Since the adaptive updating protocols are developed by deriving the gradient descent of the cost function, the optimized control algorithm can be obtained. In addition, a prescribed-time fault-tolerant optimal controller is further proposed, which renders the convergence time fully independent of any other parameter and the initial states, thus the convergence time can be uniformly prespecified. Finally, the validity of the proposed algorithms are demonstrated via the simulation experiments. Note to Practitioners—Actuator faults often occur in the operation of industrial automation equipment. Hence, it is of great practical significance for control systems to have faster fault-tolerant performance. In addition, the optimization effect of performance indicator often denotes the quality of the expected task completion. Therefore, this study proposes a faster optimal fault-tolerant formation strategy for heterogeneous unmanned formation system based on fixed-time and prescribed-time theorems under actuator faults. The effectiveness of the developed control approach is verified by designed simulation.

The fault-tolerant formation control problem for unmanned helicopters (UHs) with actuator faults under fixed and switching communication topologies is investigated in this paper. Firstly, the high-order fully actuated system model of the 6-DOF UH is established, which is divided into the position outer-loop subsystem and the attitude inner-loop subsystem. Secondly, a prescribed-time disturbance observer is constructed to rapidly and accurately estimate the composite disturbances composed of external disturbances and actuator faults. Then, with the aid of the fully actuated system approach, the formation fault-tolerant controller and attitude tracking fault-tolerant controller are designed for the inner and outer loops respectively, which can guarantee the prescribed-time stability of multiple UHs under fixed and switching topologies. Finally, the simulation results are provided to demonstrate the effectiveness of the proposed control strategy.

This article investigates the problem of fixed-time fault estimation and fault-tolerant control (FTC) for interconnected systems subject to both multiplicative and additive actuator faults. On the basis of the bilimit homogeneous theory, the proposed fault estimation observer can acquire the exact system state and fault information in a specified time, and such a time is determined by a constant upper bound, independent of the initial observation errors. Next, the prescribed performance function (PPF) is employed to impose the anticipant performance criterion on the trajectory tracking errors, for the purpose of preserving both desirable transient and steady-state responses. Afterward, we incorporate the recursive fast terminal sliding-mode technique into the active FTC (AFTC) design procedure to eliminate the influence of faults. In such a way, the fixed-time convergence property of tracking errors can be guaranteed without any restriction on the initial conditions. Finally, comparative simulation results are provided to illustrate the feasibility and superiority of the proposed strategy.

The leader-following cooperative problem in heterogeneous multiagent systems (HMASs) with unmodeled dynamics and actuator faults is investigated in this article. The HMASs, which include unmanned ground vehicles and unmanned aerial vehicles, are first described using a fully actuated system model (FASM). The FASM, as opposed to the first-order state-space model, preserves the physical significance of original systems and makes it feasible to apply the control rule entirely. In order to approximate unknown system dynamics, novel neuroadaptive laws with few learning parameters are then suggested. To counteract the negative effects of actuator faults, the Nussbaum function and adaptive approach are utilized. In addition, a cooperative fault-tolerant protocol is suggested, wherein consensus errors are uniformly ultimately bounded. The lack of virtual control variables in the proposed protocol reduces its complexity. The theoretical results are then validated by numerical simulations.

When cooperating through an intensive formation, the safe distancing of unmanned aerial vehicles (UAVs) is a delicate issue, especially if UAVs are subjected to actuator faults that cause rapid maneuvers. This article investigates the fixed-time fault-tolerant formation control of multiple quadrotor UAVs under actuator faults, which considers the collision avoidance among UAVs when faults occur, and the convenience of engineering application. First, an augmented fixed-time observer with measurement noise oppression is adopted to estimate and compensate actuator faults and disturbance in rotational and translational dynamics. Then, a baseline attitude controller, a command filter, and a velocity controller are proposed for each quadrotor UAV to track the desired velocity within a fixed time. Next, a distributed fixed-time sliding-mode controller that integrates the gradient of repulsive potential function into the sliding manifold is designed to achieve leader-follower formation control and collision avoidance simultaneously. The control scheme is proven to be fixed-time convergent via Lyapunov stability analysis and is normalized in accordance with the compatibility of hardware implementation. Finally, the designed algorithm is embedded into PX4 architecture to illustrate the effectiveness and practicality of the control strategy.

In this article, the distributed adaptive fixed-time output time-varying formation tracking issue of heterogeneous multiagent systems (MASs) with actuator faults is addressed, in which the followers suffer from loss-of-effectiveness actuator faults, and the leader has unknown bounded input. To solve the above issue, a distributed fixed-time observer is constructed with the leader's unknown input, by which each follower can obtain the leader's states in a predesigned time. Then, based on the observer and the desired formation vector, a local adaptive fixed-time fault-tolerant formation control algorithm is proposed for each follower with the help of time-varying gains to make up for the influence of actuator faults. Furthermore, it is proven that the designed controller can satisfactorily accomplish the considered task of the heterogeneous MASs by using the Lyapunov stability theory. Specifically, the obtained upper bound of the convergence time only depends on a few controller parameters. Finally, a simulation example is implemented to validate the efficiency of the analytical results.

This article studies the issue of distributed hierarchical fixed-time optimal fault-tolerant output formation for heterogeneous multiagent systems (MASs). A two-layer formation control framework is proposed by using distributed optimization and cooperative fault-tolerant output regulation approaches. The upper layer includes a virtual system and a distributed fixed-time optimization control algorithm to produce a global optimal reference signal, which minimizes the global objective function in a fixed time. The lower layer includes an actual agent system and an adaptive fixed-time fault-tolerant tracking control protocol to compensate for the actuator faults and ensure the fixed-time tracking of the optimal formation trajectory composed of the optimal reference signal and the expected time-varying formation vector. Different from the relevant works, this framework can avoid the phenomenon of fault propagation between neighboring agents by the interaction network. Furthermore, the convergence time of the formation error is not relied on the initial conditions of MASs. Finally, two simulation experiments are designed to prove the effectiveness of the developed theoretics.

This article investigates the fixed-time fault-tolerant formation control problem of a leader–follower heterogeneous multiagent system (HMAS), including multiple unmanned aerial vehicles (UAVs) and multiple unmanned ground vehicles (UGVs) under loss of effectiveness actuator faults and disturbances. Different from the existing fixed-time formation results, to realize the special application, a finite-time performance function (FTPF) is considered, which can guarantee that formation error converges to a prescribed arbitrarily small region within a known time. Then, based on sliding mode control and bi-limit homogeneity, distributed and decentralized fixed-time formation control algorithms are constructed for the HMAS in the$x$–$y$axis and$z$axis, respectively, which can steer the whole system achieving target formation configuration within a scheduled time. In addition, based on local state information, adaptive online updating strategies for unknown actuator efficiency factors and lumped uncertainties are proposed. Then, under the online updating parameters, two novel distributed and decentralized adaptive fault-tolerant formation control laws are presented using practical fixed-time stability theory, which not only achieves stable formation tracking with finite-time prescribed behavioral metrics but also ensures that the formation errors are uniformly bounded within a settling time. Finally, the effectiveness of the developed control schemes is verified by simulation examples.

The disturbance decoupling-based fixed-time and predefined-time fault estimation issues are addressed for complex networks. A distributed fixed-time fault estimation observer subject to two power functions is first constructed, which can not only eliminate the effect of external disturbances but also identify unknown faults in a fixed time. Then, a nonlinear fixed-time fault estimator with two power functions, including state residuals, is presented to enhance the convergence speed of fault estimation. Furthermore, the predefined-time design strategy is investigated to assure the convergence of fault estimation errors in the specified time in advance. Finally, simulation results of complex networks of chaotic systems are shown to verify the advantage of the presented fixed-time and predefined-time schemes.

In this article, a robust asymptotic fault estimation (RAFE) design is proposed for discrete-time interconnected systems with sensor faults. By constructing a singular augmented system, an equivalent description of the considered interconnected systems is presented. Then, a novel RAFE observer is proposed for the singular augmented system. Furthermore, gain matrices of the RAFE observer are calculated based on multiconstrained design. Simulation results are illustrated to show the feasibility of the presented approaches.

This study proposes a hierarchical structure-based fault-tolerant tracking control methodology for multiple 3-DOF helicopters in the presence of system nonlinearities, uncertainties and simultaneous actuator faults (partial loss of effectiveness, stuck, and saturation), and sensor faults (bias and drift). The hierarchical structure consists of the decentralized fault estimation hierarchy and distributed fault-tolerant tracking control hierarchy. The distributed constant gain-based, node-based, and edge-based adaptive fault-tolerant tracking control designs are developed to cope with bidirectional interactions and to guarantee the robust asymptotic stability and the good tracking property of multihelicopter systems, respectively. Simulation results validate the effectiveness of the proposed hierarchical structure-based tracking control algorithm.

This paper proposes a novel distributed fault-tolerant consensus tracking control design for multi-agent systems with abrupt and incipient actuator faults under fixed and switching topologies. The fault and state information of each individual agent is estimated by merging unknown input observer in the decentralized fault estimation hierarchy. Then, two kinds of distributed fault-tolerant consensus tracking control schemes with average dwelling time technique are developed to guarantee the mean-square exponential consensus convergence of multi-agent systems, respectively, on the basis of the relative neighboring output information as well as the estimated information in fault estimation. Simulation results demonstrate the effectiveness of the proposed fault-tolerant consensus tracking control algorithm.

This paper investigates the fixed-time time-varying formation control problems for heterogeneous multi-agent systems (MASs) composed of multiple Unmanned Ground Vehicles (UGVs) and multiple Unmanned Aerial Vehicles (UAVs) in the presence of actuator faults, parameter uncertainties, matched and mismatched disturbances. Besides achieving the desired formation configurations, each follower can also track the position trajectory produced by the virtual leader within fixed time simultaneously. The difference dynamic characteristics between the heterogeneous agents leads to unbalanced interaction of lumped uncertainties in the communication network, which increases the difficulty of collaborative control. To estimate the mismatched disturbances and lumped uncertainties, a fixed-time observer for each follower is designed, which can guarantee the estimation errors converge to the origin in fixed settling time. Subsequently, by utilizing the backstepping technique and the fixed-time stability theory, an observer-based distributed fixed-time formation controller for each follower in the X- Y axes and the observer-based decentralized fixed-time tracking controllers for follower-UAVs in the Z axes are presented, which are shown to be fixed-time stable even under the influence of actuator faults and mismatched disturbances. Moreover, the fixed-time results can ensure the convergence time is independent of initial conditions. Finally, numerical simulations demonstrate the effectiveness of the proposed algorithms.

This article studies the distributed fault estimation (DFE) and fault-tolerant control for continuous-time interconnected systems. Using associated information among subsystems to design the DFE observer can improve the accuracy of fault estimation of the interconnected systems. Based on the static output feedback (SOF), the global outputs of the interconnected systems are used to construct a distributed fault-tolerant control (DFTC). The multiconstrained methods are proposed to enhance the transient performance and ability to suppress the external disturbances simultaneously. The conditions of the presented design methods are expressed in terms of linear matrix inequalities. The simulation results are illustrated to show the feasibility of the presented approaches.

This paper proposes a novel decentralized output sliding-mode fault-tolerant control (FTC) design for heterogeneous multiagent systems (MASs) with matched disturbances, unmatched nonlinear interactions, and actuator faults. The respective iteration and iteration-free algorithms in the sliding-mode FTC scheme are designed with adaptive upper bounding laws to automatically compensate the matched and unmatched components. Then, a continuous fault-tolerant protocol in the observer-based integral sliding-mode design is developed to guarantee the asymptotic stability of MASs and the ultimate boundedness of the estimation errors. Simulation results validate the efficiency of the proposed FTC algorithm.

This paper investigates the attitude and position tracking control problem of the Lead–Wing close formation system with unknown multiplicative actuator faults. In close formation flight, the movement of the Wing unmanned aerial vehicle (UAV) is influenced by the vortex effects of the neighboring Lead UAV. This situation requires a modeling of the aerodynamic coupling vortex effects and linearization on the basis of optimal close formation geometry. Adaptive actuator fault parameters are identified by merging the improved unknown input observers, and adaptive laws with projection functions are presented for actuator fault tracking. The sufficient condition corresponding to the existence of unknown input observers is given. Then, an adaptive fault-tolerant H-infinity output feedback control scheme is developed to guarantee the asymptotic stability, H-infinity closed-loop system performance, and attitude and position tracking properties while the Lead UAV is being maneuvered. Simulation results of the Lead–Wing close formation flight validate the efficiency of the proposed fault-tolerant control algorithm.

In this paper, a new distributed fault estimation observer with adjustable parameters is designed for a class of nonlinear interconnected systems. The presented fault estimator consists of proportional and integral terms to improve the accuracy of fault estimation. The observer gain matrices of the proposed fault estimation scheme for the underlying systems are calculated based on robust${\mathcal {L}_{2}-\mathcal {L}_{2}}$and${\mathcal {L}_{2}-\mathcal {L}_\infty }$performance. The proposed method achieves a lower performance level in the aspect of quantitative analysis compared with existing fault estimation approaches. A simulation example is provided to demonstrate the effectiveness of the new design method.

In this paper, a novel adjustable parameter (AP)-based distributed fault estimation observer (DFEO) is proposed for multiagent systems (MASs) with the directed communication topology. First, a relative output estimation error is defined based on the communication topology of MASs. Then a DFEO with AP is constructed with the purpose of improving the accuracy of fault estimation. Based on${H} _{{\infty }}$and${H} _{{2}}$with pole placement, multiconstrained design is given to calculate the gain of DFEO. Finally, simulation results are presented to illustrate the feasibility and effectiveness of the proposed DFEO design with AP.

This paper addresses the problem of fault estimation observer design with finite-frequency specifications for discrete-time Takagi-Sugeno (T-S) fuzzy systems. First, for such T-S fuzzy models, an H∞ fault estimation observer with pole-placement constraint is proposed to achieve fault estimation. Based on the generalized Kalman-Yakubovich-Popov lemma, the given finite-frequency observer possesses less conservatism compared with the design of the entire-frequency domain. Furthermore, the performance of the presented fault estimation observer is further enhanced by adding the degree of freedom. Finally, two examples are presented to illustrate the effectiveness of the proposed strategy.

This paper studies the problem of robust fault estimation (FE) observer design for discrete-time Takagi–Sugeno (T–S) fuzzy systems via piecewise Lyapunov functions. Both the full-order FE observer (FFEO) and the reduced-order FE observer (RFEO) are presented. The objective of this paper is to establish a novel framework of the FE observer with less conservatism. First, under the multiconstrained design, an FFEO is proposed to achieve FE for discrete-time T–S fuzzy models. Then, using a specific coordinate transformation, an RFEO is constructed, which results in a new fault estimator to realize FE using current output information. Furthermore, by the piecewise Lyapunov function approach, less conservative results on both FFEO and RFEO are derived by introducing slack variables. Simulation results are presented to illustrate the advantages of the theoretic results that are obtained in this paper.

This paper addresses the problem of integrated robust fault estimation (FE) and accommodation for discrete-time Takagi–Sugeno (T–S) fuzzy systems. First, a multiconstrained reduced-order FE observer (RFEO) is proposed to achieve FE for discrete-time T–S fuzzy models with actuator faults. Based on the RFEO, a new fault estimator is constructed. Then, using the information of online FE, a new approach for fault accommodation based on fuzzy-dynamic output feedback is designed to compensate for the effect of faults by stabilizing the closed-loop systems. Moreover, the RFEO and the dynamic output feedback fault-tolerant controller are designed separately, such that their design parameters can be calculated readily. Simulation results are presented to illustrate our contributions.

This paper addresses the problem of robust fault estimation and fault tolerant control (FTC) for Takagi–Sugeno (T–S) fuzzy systems. A fuzzy-augmented fault estimation observer (AFEO) design is proposed to achieve fault estimation of T–S models with actuator faults. Furthermore, based on the information of online fault estimation, an observer-based dynamic output feedback-fault tolerant controller (DOFFTC) is designed to compensate for the effect of faults by stabilizing the closed-loop system. Sufficient conditions for the existence of both AFEO and DOFFTC are given in terms of linear matrix inequalities. Simulation results of an inverted pendulum system are presented to illustrate the effectiveness of the proposed method.