This paper addresses the adaptive finite-time fault-tolerant tracking control problem for nonlinear output feedback systems with actuator faults under multiplicative deception attacks. First, a composite observer is developed by integrating a fault compensation mechanism with the compromised output signal. Unlike conventional state observers, the proposed observer can simultaneously estimate unmeasured system states, actuator faults, and external disturbances. Second, a sig function, novel coordinate transformations, and an attack compensator are introduced to develop a nonsingular finite-time adaptive tracking controller under deception attacks. The proposed controller effectively eliminates the singularity problems inherent in traditional finite-time controllers and ensures the desired tracking performance. In addition, an improved finite-time adaptive filter is introduced to enhance control accuracy and relax constraints on design parameter selection, compared to existing filtering methods. To reduce communication burden, a dynamic event-triggered mechanism (DETM) is incorporated. The proposed control strategy guarantees practical finite-time stability of the closed-loop system while successfully avoiding the Zeno phenomenon. Simulation results further verify the effectiveness of proposed strategy.

This paper researches the adaptive fixed-time global prescribed performance tracking control (GPPTC) problem for a robotic manipulator (RM) under unknown backlash-like hysteresis and disturbance. In the control design of the RM, a novel global fixed-time prescribed performance function (FTPPF) is designed to achieve output tracking with arbitrarily prescribed transient performance. Moreover, fuzzy logic systems (FLSs) are used to handle the unknown robotic dynamics, and a hyperbolic tangent activation function is applied to deal with the hysteresis nonlinearity. The proposed prescribed performance control (PPC) method based on the FTPPF ensures that the tracking error converges to a predetermined range in a given time and remains within that range thereafter. Unlike the existing PPC methods, our control algorithm removes the limitation requiring the initial tracking error to satisfy the initial value of the PPF. Based on the fixed-time command-filtered (FTCF) technique, an adaptive fixed-time controller is designed, which enables the joint position to track the desired signal in a fixed time. Finally, the effectiveness of the proposed controller is demonstrated via the simulation.

This paper explores the security control problem of a class of hyperbolic partial differential equation (PDE) systems described by a set of nonlinear ordinary differential equation (ODE) under deception attacks. Compared with the control design process of traditional single ODE systems, the strong coupling characteristics of partial differential equation-ordinary differential equation (PDE-ODE) systems make the control design under deception attacks more difficult. By applying the infinite-dimensional backstepping transformation and its inverse transformation, the original PDE subsystem is transformed into a more tractable target system, thus effectively achieving control performance. The neural network approximation algorithm is adopted to separate the coupling effects caused by attacks, focusing on addressing the unknown nonlinear dynamics of the system. Deception attacks are modeled as time-varying weights with unknown control directions, and the Nussbaum function is employed to address the problem of unknown control directions. In addition, a dynamic event-triggered mechanism with a novel switching threshold is designed to alleviate the communication burden. The proposed control algorithm ensures that both the closed-loop system states and the actuator states are bounded. Finally, this conclusion is verified through numerical simulation.

In this paper, an adaptive time-varying formation optimal tracking control strategy is presented for nonlinear heterogeneous multi-agent systems (MASs) with performance constraints and unknown dynamics. A prescribed-time performance function is designed to quantify the tracking error constraints, while an error transformation function is introduced to eliminate initial value constraints and address singularity issues. Notably, the settling time and initial conditions of the performance function are independent of both the initial tracking error and system parameters. To facilitate reinforcement learning (RL)-based optimal formation control, a performance index function is formulated that incorporates the transformed tracking error, control input, and an exponentially discounted term. This design effectively avoids infinite integral values and ensures minimization of the index function. Moreover, stability analysis demonstrates that the time-varying formation tracking errors converge to the desired accuracy within a prescribed time, regulated by a sliding-mode control mechanism. Finally, numerical simulations on two practical examples validate the feasibility and effectiveness of the proposed control strategy.

This article investigates the adaptive tracking control strategy for a class of nonlinear systems subjected to false data injection (FDI) attacks, incorporating an improved event-triggered mechanism. A significant breakthrough of this study lies in the challenge that, after FDI, not all states of the system can be utilized for stability design, thereby making it more complicated to achieve tracking control. This article eliminates the restrictive assumption, required in some existing results, that the attack signal at the first step must be known. Instead, we propose to estimate the tracking error directly. This approach not only facilitates the tracking control of nonlinear systems but also enhances the generalizability and practical applicability of the solution. To conserve system resources, an improved event-triggered condition is proposed that utilizes the triggered attacked-output. Consequently, the controllers and adaptive laws are implemented using the sampled states rather than continuous real-time states, thereby minimizing unnecessary computations and communications. By constructing Lyapunov functions, the proposed control strategy ensures that all signals in the closed-loop system are globally bounded. Finally, the simulation results are displayed to validate the effectiveness of the proposed control strategy.

This article concentrates on the attack detection and active attack defense strategies for discrete-time linear cyber-physical systems (CPSs) with unknown but bounded (UBB) disturbance and noise in the presence of both actuator and sensor attacks. First, a novel zonotopic observer is constructed to estimate the set-valued state and actuator attack by introducing augmentation techniques. To mitigate the effects of uncertainty and enhance estimation accuracy, the $H_{\infty }$ technique is introduced to construct the observer. Unlike most existing works, the constructed observer simultaneously estimates the system state and actuator attacks. Then, by combining the designed observer with reachability analysis, a set-valued abnormal detector and a residual-based abnormal detector are designed to detect actuator and sensor attacks, respectively. In addition, by incorporating the obtained state reachable sets and the $H_{\infty }$ technique, an active attack defense mechanism is designed to mitigate the impact of attacks on system performance. The proposed defense strategy does not introduce any performance loss in the absence of attacks. Finally, the superiority of the developed method is demonstrated by its application to a numerical simulation and an autonomous aircraft system.

This article proposes an adaptive fixed-time control strategy for uncertain high-order nonlinear cyber-physical system subject to deception attacks on both the sensor-to-controller (S-C) and controller-to-actuator (C-A) communication channels. First, to mitigate the impact of dual-channel attacks, mathematical tools are employed to decouple the high-order term induced by C-A channel attacks, and a robust controller is designed based on the compromised state information. Second, novel Lyapunov functions and an adaptive mechanism are constructed to transform nonlinear uncertainties into a linearly parameterized form with unknown parameters. This transformation effectively compensates for unknown control coefficients and mitigates the severe nonlinear growth caused by high-order dynamics under attacks. Third, a control strategy independent of the system's powers is developed, which relaxes the requirement for prior knowledge of system powers and avoids singularities. Finally, the effectiveness and feasibility of the proposed strategy are confirmed via simulation results.

This article addresses the problem of prescribed-time fault-tolerant tracking control for a class of nonlinear multiagent systems (MASs) subject to parameter uncertainties and external disturbances. To improve tracking precision, the trajectory reconstruction approach based on cubic spline interpolation is proposed, which effectively reconstructs the discrete reference signals. Then, a class of prescribed-time regulators is meticulously designed to formulate the fault-tolerant tracking controller, ensuring that the outputs of the controlled system converge to the reconstructed trajectory with arbitrary accuracy within the prescribed tracking time. Finally, stability analyses and a simulation example are presented to demonstrate the effectiveness of the proposed prescribed-time fault-tolerant tracking control strategy, validating its theoretical significance and practical applicability in engineering systems.

Robust multi-object tracking (MOT) is hindered by the instability of appearance features under visual corruptions such as occlusion and motion blur. These perturbations introduce high-variance noise into feature trajectories, weakening temporal representations and causing identity switches. We address this challenge by learning more stable appearance representations under feature corruption. To this end, we propose the Causal Interaction Module (CIM), a causal architecture that follows a filter then reconstruct design for online tracking. A temporal filtering stage summarizes the historical feature trajectory into a stable anchor, and a contextual enhancement stage uses that anchor to refine frame-level features before association. Integrated into standard trackers, CIM improves association robustness while preserving the host tracking formulation. Experiments on multiple MOT benchmarks and corruption stress tests show consistent gains, especially on association-related metrics.

This article investigates the problem of observer-based prescribed-time tracking control (OPTC) for a class of nonlinear systems with uncertain nonvanishing disturbances. First, a prescribed-time observer (PTO) with a well-designed time-varying high gain is constructed to achieve zero-error observation of the uncertain nonvanishing disturbances within the prescribed observation time. Subsequently, a two-stage controller design framework is proposed to construct the desired control input, which consists of two distinct components: the first-stage controller and the second-stage controller. The first-stage controller is established to compensate for the effects of the system’s nonlinear dynamics, thereby providing a relatively satisfactory tracking performance. The second-stage controller, on the other hand, is constructed based on a sophisticated switching mechanism of the control gains, which not only ensures that the tracking error converges to zero within the prescribed tracking time but also guarantees a smooth transition between the two-stage controllers. Finally, the simulation example involving a disturbed single-link flexible-joint robotic manipulator is presented to demonstrate the effectiveness of the proposed control strategy.

This article addresses the security-based practical fixed-time adaptive stabilization problem for nonlinear cyber-physical systems (CPSs) with higher powers under deception attacks. First, a novel practical fixed-time stability criterion is proposed based on Nussbaum functions. The criterion introduces a relaxed convergence condition, facilitating the analysis of practical fixed-time stability for high-power nonlinear systems. Second, to compensate for the compromised states, a dual coordinate transformation structure consisting of a virtual coordinate transformation and an available coordinate transformation is proposed. This structure is applicable to both low- and high-power systems. Moreover, a security-based fixed-time control strategy is developed by combining adaptive methods with Nussbaum functions to mitigate the influence of unknown attack gains. The proposed strategy also effectively overcomes the singularity problem. Finally, the effectiveness of the designed control strategy is validated through simulations.

This article proposes a decentralized resilient adaptive intermittent output feedback fault-tolerant control (FTC) method for interconnected nonlinear systems with sensor deception attacks, multiple actuator faults, and input saturation. First, we constructed a new composite observer using intermittent compromised output signals and fuzzy logic systems (FLSs) to estimate the state variables in the face of deception attacks and unknown external disturbances. On this basis, the reasonable adaptive laws are cleverly devised to handle multiple unpredictable actuator faults. Then, in order to deal with unknown gains caused by deception attacks, a projection operator-based compensation mechanism is proposed. In addition, the “explosion of complexity” in the traditional backstepping design process is solved through command filtering technology. At the same time, an error compensation system and an auxiliary system are designed to reduce the errors caused by command filtering and solve the input saturation problem, respectively. The results indicate that the proposed control scheme can ensure the boundedness of all signals in the closed-loop system, and the tracking errors converge to a bounded compact set. Finally, the effectiveness of the proposed strategy was verified through numerical simulation.

This article investigates the prescribed-time containment control problem for multiple wheeled mobile robots (MWMRs) with unknown control gains. A novel and generalized prescribed-time stability theorem is established, significantly advancing existing frameworks and facilitating controller design. For each follower, a distributed containment observer is developed to ensure that the observer state converges precisely to the convex hull formed by multiple leaders within a prescribed time. This approach effectively transforms the containment control problem into a more tractable tracking control problem, meanwhile enabling local reconstruction of unmeasured neighbor states using available observer outputs. Then, the type-B Nussbaum function is employed to eliminate the effects of the time-varying unknown control coefficient. Based on the developed prescribed-time theorem and the time-varying parametric Lyapunov equation (PLE), the fully actuated controllers are designed for the MWMRs. It can guarantee that the containment errors converge to zero within the prescribed time. Finally, simulation results validate the effectiveness of the proposed method.

This work concentrates on the predefined-time and predefined-accuracy tracking controller design problem for a nonstrict-feedback nonlinear system under asymmetric output constraints. Unlike finite-time or fixed-time control strategies in related literature, the great advantage of our presented controller design algorithm is that the algorithm can specify the convergence time and the accuracy of the system in advance, depending on the user’s requirements. First, an extremely important performance of RBF NNs is employed to handle the design obstacle caused by nonstrict-feedback structure. Then, a time-varying nonlinear transformation function is introduced to handle the asymmetric output constraints problems. Second, under the framework of adaptive backstepping design, we propose the predefined-time controller and the asymptotic tracking controller simultaneously, and a continuous switching function is used to transition the predefined-time controller to the asymptotic tracking controller when the resulting tracking error arrives at the specified accuracy. Under our control scheme, it is rigorously demonstrated that all signals of the studied system remain bounded and the tracking error achieves a predefined accuracy within a preset time. Finally, two practical simulation experiments are given to validate the effectiveness of the controller.

This article addresses the real-time security reachable set (RS) control problem for nonlinear semi-Markov jump cyber–physical systems (s-MJCPSs) subject to multiple time-varying delays and actuator attacks. Then, based on the neural network (NN) approximation approach and employing a sliding mode control (SMC) strategy, an adaptive NN SMC scheme is proposed to tackle challenges arising from nonlinear attack functions and mode jumps. The proposed strategy ensures s-MJCPSs stability and mean-square boundedness of system states within a predefined RS. Sufficient conditions for real-time security RS control are derived. Finally, an example is presented to demonstrate the effectiveness of the proposed strategy in realizing adaptive real-time RS control.

This paper proposes a zonotopic secure estimation framework for discrete-time cyber-physical systems (CPSs) subject to unknown-but-bounded (UBB) disturbances and false data injection (FDI) attacks. A decentralized dynamic event-triggered mechanism (DETM) is developed, allowing each sensor to adapt its triggering threshold using local output deviations, thereby reducing communication while preserving estimation accuracy. Subsequently, a zonotopic interval observer is developed to estimate the system state under DETM. The observer propagates zonotopic error bounds and is designed via LMIs to ensure stability and l1 performance. Furthermore, a zonotope-based attack reconstruction approach is formulated. The attack signal is conservatively enclosed in a residual-based zonotope, and a threshold test is used to isolate attacked channels. Finally, simulation results confirm that the method reduces communication significantly while maintaining reliable estimation, validating its use in resource-constrained CPSs.

This article addresses the problem of distributed adaptive bipartite containment control for nonlinear multiagent systems under deception attacks and actuator faults. By constructing a modified coordinate transformation and designing a Lyapunov function based on predefined accuracy functions, a control scheme is developed that ensures bipartite containment errors converge to a user-defined value, even under deception attacks. To handle unknown time-varying attack signals and actuator faults, a two-step approach is employed in controller design. This guarantees that 1) the outputs of the followers converge to the convex hull formed by the leaders with cooperative relationships, and 2) all closed-loop signals remain bounded. Finally, the effectiveness of the proposed method is demonstrated through a simulation of an RLC circuit system.

This article studies the attack detection and reconstruction problem for autonomous underwater vehicles (AUVs) subject to unknown but bounded disturbances and measurement noise. First, a Takagi-Sugeno (T-S) fuzzy model is utilized to address the nonlinearity of AUVs. Then, a$H_{\infty }$T-N-L observer is introduced to estimate system state. Subsequently, to improve the accuracy of attack detection, an improved attack detection method within the T-S fuzzy system framework is obtained by the reachability analysis of the residual. Afterwards, the effect of disturbances and measurement noise on attack reconstruction and isolation is analyzed. The accuracy of attack reconstruction and isolation for T-S fuzzy systems is improved by zonotopic analysis. Finally, the effectiveness and advantages of the proposed method are verified through simulation results.

This paper investigates the fault detection and isolation problem of a class of leader-follower multi-agent systems subject to unknown-but-bounded disturbances under an event-triggered communication mechanism (ETCM). Firstly, an adaptive ETCM is proposed to avoid the continuous acquisition of outputs from neighboring agents, thereby reducing the communication burden. Secondly, a joint state and fault observer is designed, and H∞ analysis is utilized to improve the robustness of the observer against external disturbances and event-triggered errors. Next, zonotopic reachability analysis is utilized to derive the estimated intervals of the system state and fault signal, based on which a fault detection and isolation method is developed to determine both when the system is faulty and which agent is at fault. Finally, a fighter formation model is employed to verify the effectiveness of the proposed approach.

This paper focuses on the adaptive neural network output feedback control problem for heterogeneous vehicle platoon system (HVPS) under the condition of sensor deception attack. Firstly, an event-triggered mechanism by double-channel transmissions is constructed, which considers both controller triggering and output triggering, effectively reducing the waste of communication resources and unnecessary data transmission. Secondly, in order to estimate the unmeasured states in the system, a neural network state observer is designed. It takes the output signals caused by output triggering and sensor failures as input to generate usable state estimates and ensure the smooth operation of the backstepping method. In addition, barrier Lyapunov functions (BLFs) are used to impose constraints on vehicle spacing errors to ensure that the errors will not expand infinitely. Combined with dynamic surface control (DSC) technology, an adaptive event-triggered output feedback control scheme based on backstepping is proposed in this paper. It guarantees both individual vehicle stability and weak string stability of HVPS. Through Lyapunov stability analysis, it is proved that all signals remain bounded. Finally, a simulation example verifies the effectiveness of the proposed method.

It is difficult to ensure tracking performance even for general nonlinear systems under the condition that only intermittent output signals are used. This paper studies the problem of adaptive fuzzy consensus tracking for a class of mismatched nonlinear strict-feedback multi-agent systems (MASs) by using intermittent output signals. Firstly, a novel fuzzy state observer using intermittent output states and fuzzy-logic systems is constructed to estimate the unknown state variables of the system. Secondly, dynamic filtering technology is applied to address the issue of virtual controller non-differentiability caused by intermittent output feedback during the backstepping design process. Furthermore, for the situation where the controller is non-differentiable in stability analysis, an alternative solution can be proposed: initially, a distributed continuous control strategy is developed using conventional continuous output signals, and then the output signals in the previous scheme are replaced with event-triggered signals to design a distributed event-triggered control scheme. It is demonstrated that the designed event-triggered control scheme guarantees that all closed-loop system signals remain semi-globally uniformly ultimately bounded (SGUUB), and the distributed consensus tracking errors can converge to a neighborhood of zero. Finally, the effectiveness of the proposed scheme is verified through simulations involving a group of single-link robots.

This paper investigates the practical fixed-time distributed optimization problem (DOP) in nonlinear multi-agent networks, where the optimization decision of each agent is subject to global consensus and local set-inclusion constraints. Unlike existing distributed optimization results, this work considers high-order nonlinear multi-agent systems with unknown nonlinearities and mismatched disturbances. To address the challenges arising from the complex high-order structures, a novel disturbance-rejection distributed optimization control framework is proposed, which integrates fixed-time control theory based on the sign function and consensus-based optimality conditions. The proposed algorithm is implemented through an active disturbance rejection backstepping design procedure, consisting of two key stages: first, a fixed-time extended state observer is developed to estimate the unknown nonlinear terms and mismatched disturbances in the system; second, a distributed fixed-time optimization controller is constructed based on fixed-time state and gradient observers, which eliminates the need for an optimal signal generator and thus avoids additional tracking errors. Furthermore, rigorous Lyapunov stability analysis guarantees the practical fixed-time stability of the proposed method, namely, the system error converges to a bounded neighborhood of the origin within a fixed time. Finally, numerical simulations validate the effectiveness and robustness of the proposed framework.

This paper focuses on the distributed event-triggered adaptive neural resilient time-varying formation control problem for a class of multiple-input multiple-output nonlinear multi-agent systems, where all network communication links between agents are subjected to denial-of-service (DoS) attacks simultaneously. A second-order resilient time-varying formation estimator is designed to obtain the unknown leader information in DoS attack active intervals. Meanwhile, a state-triggering mechanism (STM) is designed to save system communication resources. Nevertheless, the STM can lead to virtual control laws being non-differentiable. To circumvent the problem, we first design an adaptive neural resilient formation control scheme. Then, based on the adaptive neural resilient formation control scheme, we replace continuous states with intermittent ones. By utilizing a dynamic filtering technique, an event-based adaptive neural resilient formation control scheme is designed. The key technology of control scheme design is to establish an improved first-order auxiliary system to deal with the negative impact of actuator saturation. It is proved that formation tracking errors can converge to a residual set around zero, and all signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, simulation results are presented to show the effectiveness of the control scheme.

In this article, in the occurrence of load disturbances and internal actuator faults, exact performance compensation problem for nonlinear interconnected power systems (NIPSs) integrated with wind farms is solved by presenting an observer-based sliding mode control strategy. Concretely, a dynamic event condition in the sensor channel is designed by virtue of triggered output error and a dynamic threshold. With the help of event outputs and neural networks (NNs) technology, a composite observer is proposed to perform state, disturbance, and fault estimations of the power system simultaneously. By utilizing the variable estimations, a novel sliding mode manifold is designed and an observer-based controller is derived directly. Intuitively, the compensation action is triggered once the unknown variables of the NIPSs are estimated, thereby the disturbance rejection and fault tolerance can be achieved. A prominent benefit of the presented strategy is that the estimation convergence ability of the observer is proved independently, then the relationship between the observer and controller for the NIPSs can be relaxed. The control ability is analyzed within aH∞performance through the Lyapunov theory. Simulation results for the two area NIPSs and comparisons on the recent achievements of the NIPSs are made, the results show that more than ten percent improvements can be realized compared with the recent control methods, which in return demonstrate the compensation performance of the presented control strategy.

This work considers the adaptive output feedback consensus asymptotic tracking control problem for full-state-constrained nonlinear multiagent systems (MASs) under the denial-of-service (DoS) attacks and the actuator faults. Since MASs are regardered as a network, where each agent is considered as a network node, the DoS attacks that cut network communication links between agents are studied in this paper. Moreover, to compensate the unknown actuator fault signal, the Nussbaum function method is introduced into the controller design process for each agent. Due to the researched nonlinear MASs contain unknown nonlinearities and the system states of each agent are unmeasurable, an estimator based on fuzzy logic systems (FLSs) is constructed for each agent. Further, the secure control strategy based on the barrier Lyapunov functions (BLFs) is proposed for the researched nonlinear MASs, which guarantees the consensus tracking errors asymptotically converge to zero, all closed-loop signals remain bounded and the full-state constraint requirements are not broken. In the illustrative example, the proposed secure control strategy is applied to the MASs composed of multiple forced damped pendulums (FDPs).Note to Practitioners— In the framework of network communication, how to eliminate the impact of cyber attacks on nonlinear MASs that rely on communication links to transmit information is critical. Furthermore, due to practical systems are inevitably subject to multiple physical and environmental constraints, the problem of dealing with system constraints can not be ignored. Therefore, a secure control algorithm based on the BLFs is proposed to eliminate the effects of the DoS attacks on the researched nonlinear MASs and ensure that the full-state constraints are not broken. To realize the output feedback control and approximate the unknown nonlinearities of the studied system, the estimators combining with the intelligent approximation techniques based on FLSs are developed. The Nussbaum function is introduced into controller to solve the actuator faults problems for each agent.

This paper investigates the adaptive finite-time containment control problem for a class of nonlinear multiagent systems (MASs) under false data injection (FDI) attacks. On account of the fact that instability is inevitable when the false datas are injected into the researched system, the backstepping technique based on the modified coordinate transformation is applied to eliminate the impact of the FDI attacks. Furthermore, the “dynamic surface control”(DSC) approach is utilized to overcome the issue of “explosion of complexity” caused by repeatedly taking derivatives for the virtual control laws. Then, by designing an observer to refactor the immeasurable states of the MASs, a finite-time adaptive output-feedback tracking containment controller is constructed. It is shown that all the signals in the closed-loop systems are semi-globally practical finite-time stability(SGPFS), and the outputs of all the followers converge to the convex hull spanned by the multiple leaders’s outputs. Besides, the observer errors and the containment errors can converge to a small neighborhood of the origin in finite time. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed containment control protocol.

This paper investigates the problem of adaptive output feedback control for uncertain nonlinear systems with input/output quantization subject to intermittent denial-of-service (DoS) attacks. When a DoS attack becomes active, the system is unable to obtain output signal. In order to address this challenge, we compensate the output signal by introducing an attack compensator. At the same time, a novel quantization compensator-based (QC) state observer is designed, which uses only the quantized compensated signal to reconstruct the system states. In addition, the problem of over-parameterisation is avoided by using parameter projection technique to design the parameter estimator. By combining Lyapunov stability theory and a modified average dwell time (ADT) approach, the stability of the closed-loop system is ensured. Furthermore, the proposed controller ensures that all closed-loop signals are bounded, and the control performance of mean-square error can be adjusted by appropriately selecting certain design parameters. Finally, the effectiveness of the proposed control strategy is validated through a single-link robot simulation results.Note to Practitioners—Considering that resources are limited, the DoS attacks mentioned in this paper are aperiodic, which means that attackers engage in frequent attacks within a relatively short time frame. This aligns more closely with real-world scenarios of network attacks. When the attack is active, the output signal is not available for the system. In this paper, a new QC state observer is designed, which in turn enables the estimation of the system state signals. Furthermore, this paper considers both input and output quantization, which reduces duplicate transmission of samples and improves the use of communication resources. This makes the work in this paper more relevant to the practical engineering context.

This article investigates the adaptive prescribed-time consensus tracking control problem for nonlinear multi-agent systems (MASs), where the states of systems are unmeasured and the actuators suffer from the deception attacks. Firstly, a novel coordinate transformation technology is developed by introducing a time-varying constraint function, such that the prescribed-time tracking control problem of nonlinear MASs is converted into the constraint problem of the error variables. Then, a new attack compensator is proposed to address the unknown time-varying attack gains caused by the actuator deception attacks. Further, the state observers are designed to estimate the unavailable state variables and fuzzy-logic systems (FLSs) are employed to handle the unknown functions that exist within the systems. In addition, the attack compensator-based controller ensures the boundedness of all signals, while the error variables converge to the predefined region in a specified time. The upper bound of the whole tracking errors in the mean square sense can be decreased by selecting the appropriate design parameters. At last, the simulation example illustrates the availability of the developed control method. Note to Practitioners—In the industry, consensus tracking control of nonlinear MASs exists in many different systems, such as mobile robot networks, intelligent transportation management, surveillance and monitoring. Since the above systems operate in a network environment, the security problems of the systems cannot be ignored. Hence, considering the unmeasured states, the unknown functions, and the unknown time-varying attack gains existing simultaneously in the studied systems, it is a challenging and meaningful task to achieve the desired security control objectives. On the other hand, based on a time-varying constraint function, this article presents an adaptive prescribed-time consensus tracking control scheme for the nonlinear MASs under the deception attacks. It provides a viable strategy for industrial applications.

This paper studies the adaptive fuzzy resilient fixed-time bipartite consensus tracking control problem for a class of nonlinear multi-agent systems (MASs) under sensor deception attacks. Firstly, in order to reduce the impact of unknown sensor deception attacks on the nonlinear MASs, a novel coordinate transformation technique is proposed, which is composed of the states after being attacked. Then, in the case of unbalanced directed topological graph, a partition algorithm (PA) is utilized to implement the bipartite consensus tracking control, which is more widely applicable than the previous control strategies that only apply to balanced directed topological graph. Moreover, the fixed-time control strategy is extended to nonlinear MASs under sensor deception attacks, and the singularity problem that exists in fixed-time control is successfully avoided by employing a novel switching function. The developed distributed adaptive resilient fixed-time control strategy ensures that all the signals in the closed-loop system are bounded and the bipartite consensus tracking control is achieved in fixed time. Finally, the designed control strategy’s validity is demonstrated by means of a simulation experiment.Note to Practitioners—Currently, there are many practical application scenarios for nonlinear MASs, such as intelligent transportation, unmanned aerial vehicle cluster formation, etc. This paper investigates the adaptive fuzzy resilient fixed-time bipartite consensus tracking control problem for a class of nonlinear MASs under sensor deception attacks. In practice, these two situations are common: 1) The topology graph describing the communication relationship of nonlinear MASs is unbalanced 2) The nonlinear MASs is subjected to external malicious cyber attacks. Therefore, a novel coordinate transformation technique is proposed to reduce the impact of sensor deception attacks on the nonlinear MASs, and a partition algorithm is employed to implement bipartite consensus tracking control based on the unbalanced communication topology graph. At the same time, the nonsingular fixed-time control strategy can significantly improve the convergence of the studied nonlinear MASs. Furthermore, the nonlinear nonstrict-feedback model and backstepping design method used in this paper are general and practical.

This paper addresses the problem of adaptive tracking control of high-order nonlinear systems with time-varying delays under asymmetric output constraints. Unlike the existing researches, the studied system exhibits constantly changing unknown powers, which makes the existing Lyapunov Functionals invalid. Therefore, the Lyapunov Functionals are carefully designed to be suitable for the changing powers, where the changing powers include low power ($0 1$). Besides, we also incorporate the well-constructed dynamic gain signals into the Lyapunov Functionals to enhance the robustness, accuracy, and response speed of the system. Further, we cleverly deal with the time-varying delays by combining the novel dynamic gain signals and Lyapunov-Krasovskii (L-K) Functionals in the controller design process. For the system performance requirement, the asymmetric output constraints are considered by introducing a nonlinear transformation for the output signal$x_1$and the reference signal$y_r$. While the derivative of this nonlinear transformation generates a gain term in the form of function, which makes the controller design more difficult. We utilize the adding one power integrator technique to design the desired controller and solve the design difficulty caused by the gain term. Under the proposed controller, all the signals in the closed-loop system remain bounded, the asymmetric output constraints are not violated as well as the tracking error stays in a small neighborhood of the origin. Finally, a simulation example is given to demonstrate the effectiveness of the present strategyNote to Practitioners—In the article, we consider a class of high-order nonlinear systems with time-varying delays under asymmetric output constraints, and their models are widely utilized in the engineering field, such as transportation, manufacturing sector and so on. Further, the tracking problem is regarded as a popular topic in the control field, so designing a desired tracking controller for high-order nonlinear systems is a significant research topic. Since the considered system has the changing powers and time-varying delays, the existing methods cannot be applied to the studied problem, so we provide some new strategies by the introduction of the well-constructed dynamic gain signals, the improved L-K functionals and the nonlinear transformation. From what has been mentioned above, an effective adaptive tracking control strategy is developed for the studied system, where the proposed strategy has great application prospect.

This paper focuses on the prescribed performance adaptive containment control problem for a class of nonlinear nonstrict-feedback multiagent systems (MASs) with unknown disturbances and full-state constraints. First, the radial basis function neural networks (RBF NNs) technology is employed to approximate the unknown nonlinear functions in the system, and the problem of “explosion of complexity” caused by repeated derivation of virtual controls is solved by using the dynamic surface control (DSC) technology. Then, the nonlinear disturbance observers are designed to estimate the external disturbance, and the barrier Lyapunov functions (BLFs) and the prescribed performance function (PPF) are combined to achieve the control objective of prescribed performance without violating the full-state constraints. The theoretical result shows that all signals in the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB), and the local neighborhood containment errors can converge to the specified boundary. Finally, two simulation examples show the effectiveness of the proposed method.Note to Practitioners—The containment control problem is a hot topic in the field of control, which plays an important role in practical engineering. Especially for this problem of nonlinear MASs, the mathematical models are difficult to be obtained accurately. This paper investigates the prescribed performance adaptive containment control problem for the nonlinear nonstrict-feedback MASs, whose model can be extended to more complex engineering applications, such as unmanned aerial vehicle formations and intelligent traffic management. It is worth noting that external disturbances and state constraint problems often exist in practical applications. Therefore, the disturance observers are designed to compensate for the system disturbances, which can eliminate the impacts of disturbances on the systems. By introducing BLFs, it is ensured that all states of the system are constrained within the specified regions. To sum up, the paper proposes a prescribed performance adaptive containment control strategy, which contributes to the development of containment control for MASs in practical applications.

Adaptive Takagi-Sugeno (T-S) fuzzy control was a real-time control method without off-line input and output data, but the approximate error between this T-S fuzzy model and the actual system model was rarely considered in the existing methods. This problem can lead to the degradation of controller accuracy in practical engineering. In order to solve this problem, the mathematical expression of the upper bound for the approximate error between adaptive T-S fuzzy logic system and the actual system was derived for the first time under any number of rules. This achievement was the key to the design of robust fuzzy controller based on Lyapunov synthesis method under finite number of rules, and this controller can achieve predictability of accuracy. Compared with existing T-S fuzzy control methods, the proposed method can realize the self-adjusting accuracy control for the unknown-structure system without the off-line input and output data. The unknown non-affine control system simulation and 3-DOF robotic arm experiment were carried out to verify the effectiveness of proposed method.Note to Practitioners—Due to the wide application of T-S fuzzy model in practice control system, such as the robot control, the unmanned vehicle control and so on, the actual control accuracy of T-S fuzzy controller was concerned by many scholars. However, the actual precision degradation of the controller was a difficult problem in on-line T-S fuzzy control. In order to solve this problem, a novel adaptive T-S fuzzy control method was proposed in this paper. In practical application, T-S fuzzy model often had a large approximate error with the actual model because of structure uncertainty, and this approximate error was the key factor affecting the actual accuracy of T-S fuzzy controller. Hence, the mathematical expression of the upper bound for the approximate error between adaptive T-S fuzzy logic system and the actual system was derived for the first time under any number of rules. Based on this mathematical expression, we can design a self-adjusting accuracy robust fuzzy controller based on Lyapunov synthesis method. 3-DOF robotic arm experiment verified that the proposed method can achieve the predefined control error with or without the feedforward of robot dynamics. 3-DOF robotic arm comparison experiments verified that the advantages of proposed method.

This paper studies the asymptotic consensus tracking control problem for a class of stochastic nonlinear multiagent systems (MASs) with output constraints and unknown control gains. Firstly, the Nussbaum technique is introduced to solve the difficulty of the unknown control gains in the stochastic nonlinear MASs. Meanwhile, a$ tan$-type nonlinear mapping (NM) function is used to ensure that the output of each agent satisfies the predefined output constraints. Furthermore, the “explosion of complexity” problem caused by the traditional backstepping design methods is handled by using the command filter technique. The developed distributed adaptive asymptotic consensus tracking control strategy ensures that all the signals in the closed-loop system are bounded in probability and the consensus tracking errors of all agents converge to zero in probability. Finally, a simulation example proves the effectiveness of the proposed control strategy.Note to Practitioners—In this paper, the asymptotic consensus tracking control problem is studied for a class of the stochastic nonlinear MASs. In nature, there are many meaningful movements of multi-agents with stochastic disturbances. It is particularly challenging to achieve the asymptotic consensus tracking control problem for stochastic nonlinear MASs, which involves the unknown control gains and output constraints. Therefore, the Nussbaum technique is used to solve the difficulty of the unknown control gains, meanwhile the command filter technique is introduce to solve the “explosion of complexity” problem in the backstepping design process. Moreover, the designed control strategy and stability analysis for the studied system is based on the nonlinear mapping technique and Lyapunov method, which makes the developed methodology more engineering-oriented.

In this paper, we propose a new noise-tolerant neurodynamic algorithm with fixed-time convergence to solve mixed variational inequality problems (MVIPs) and design the circuit framework for its hardware implementation. We prove that the proposed neurodynamic algorithm converges to a unique solution within fixed-time under some conditions and give its convergence time upper bound, which is independent of the initial states. Meanwhile, the robustness of the neurodynamic algorithm under additive perturbations is also demonstrated. In addition, the proposed neurodynamic algorithm is implemented using numerical simulation, analog circuits, and field-programmable gate array (FPGA) respectively. Finally, the superiority of the proposed algorithm is verified by two applications of image reconstruction and elastic net logistic regression.

The practical fixed-time resource allocation problem is investigated for multi-input-multi-output nonlinear uncertain multiagent systems with disturbed dynamics, subject to global equality and local inequality constraints. Due to the coexistence of distributed high-order dynamics system within agents and decision-making constraints, decision variables in resource allocation optimization problems cannot be directly obtained from the system. Existing strategies are insufficient to solve such complex fixed-time optimization control problems with coupled decision-making constraints. To address these challenges, a novel integrated framework is proposed, fusing symbolic-function-based fixed-time control theory with gradient consistency. The proposed algorithm is implemented through an output-feedback backstepping design process, which involves two stages. First, in the output-feedback design stage, a fixed-time high-order extended state observer estimates the uncertain dynamics and disturbances. Second, in the backstepping design stage, a time-switching controller is developed. This controller's virtual control law has two components: the first employs the proportional-integral control method to satisfy the equality constraints, while the second uses gradient information from the $\epsilon $ -exact penalty function to address the inequality constraints. Using the Lyapunov stability criterion, the proposed algorithm can ensure that all signals remain practical fixed-time stable, and that the error between the outputs of all agents and the optimal solution is maintained within a neighborhood of the origin. Finally, simulations are presented to demonstrate the effectiveness of the approach.

Presents corrections to the paper, (Erratum to "Distributed Practical Fixed-Time Resource Allocation Algorithm for Disturbed Multiagent Systems: An Integrated Framework").

This article studies the dynamic event-triggered adaptive finite-time tracking control issue for a robotic manipulator (RM) system with disturbances. First, a new global prescribed performance function (PPF) is designed based on a scaling function such that the tracking error evolves within the constrained bounds and the restriction related to the initial conditions is removed. Then, the finite-time command filter (FTCF) is used to avoid the direct derivations of virtual controllers and the singularity issue of the conventional backstepping technique. Moreover, the filtering errors caused by the FTCF are removed by the designed error compensation mechanism. A novel dynamic event-triggered mechanism (DETM) using the dynamic auxiliary variable is designed to save communication resources. The proposed control scheme can guarantee that all signals of the RM are globally bounded within a finite time, and the tracking error can asymptotically reach zero. Finally, a simulation example and several comparative simulations show the validity of the proposed scheme.

This article primarily studies the adaptive output-feedback consensus tracking control issue for nonlinear multiagent systems (MASs) with unknown control directions against deception attacks. First, a composite observer combining the state observer and the disturbance observer is developed to concurrently estimate the states of confronting deception attacks and unmeasurable disturbances. Moreover, to resolve the unknown gains resulting from deception attacks, the adaptive attack compensator is proposed. Furthermore, in view of the logarithm Lyapunov function in the final step of the design process and the intelligent approximation technique, a new composite-observer-based adaptive consensus tracking control strategy is constructed. The suggested control strategy ensures the boundedness of all the closed-loop signals while also achieving synchronous tracking of the leader's output by the followers. Last but not least, the effectiveness of the suggested control strategy is validated through two simulation examples.

This article presents several adaptive event-triggered control (ETC) strategies for a class of uncertain nonlinear cyber-physical systems (CPSs) under constant or time-varying full-state constraints, as well as deception attacks via the senior network. Initially, the system under investigation is reformulated into a new system that encompasses both the original system state and the compromised state, enabling the use of compromised states for feedback control. Subsequently, two innovative asymptotic integral barrier Lyapunov functions (IBLFs) are developed by directly imposing constraints on the compromised state, thereby eliminating the necessity to convert state constraints into error constraints as required by traditional BLFs-based methods. Furthermore, controllers designed using relative/switched threshold event-triggered strategies ensure that all signals within the entire closed-loop system remain bounded, that the constant or time-varying full-state constraints are not breached, and that asymptotic stability is attained without Zeno behavior. Ultimately, simulation results validate the efficacy of the proposed strategies through a practical example.

In this article, the problem of adaptive dynamic event-triggered nonsingular predefined-time (PT) tracking control for a third-order fully heterogeneous vehicle platoon system is investigated. First, an improved nonsingular PT adaptive tracking controller is constructed by introducing a piecewise continuous function within the control signal in each step of the backstepping procedure, which avoids the singularity problem of the traditional PT control signals in the existing literature and guarantees the existence of the values for all the terms within the control signals in the real number field. Second, a class of universal barrier Lyapunov function (UBLF) is adopted to set restrictions on distance, which ensures that collisions are avoided and communication connectivity is maintained. In addition, based on a dynamic auxiliary variable, the communication resources are saved with the use of the dynamic event-triggered control scheme. Finally, through the PT stability criterion, it is proven that the PT stability of the whole vehicle platoon is ensured, and the effectiveness of the control algorithm is verified by the simulation results.

This article principally presents the adaptive fuzzy dynamic event-triggered output-feedback consensus tracking control problem for constrained nonlinear multiagent systems encountering false data injection attacks, using monotone tube boundary functions (MTBFs). First, the composite observer is designed to concurrently estimate the unpredictable system states and disturbances. Then, a novel parameter integration approach is constructed via the fuzzy approximation technique to reduce the computational burden, where the uncertainty terms (state errors, composite errors, fuzzy weights, and injection attacks) can be converted into a linear parameterized form with merely one unknown scalar. In addition, a set of MTBFs is designed to prevent the excessive overshoot or jitter of system errors in the transient-state performance. Furthermore, an adaptive dynamic event-triggered control strategy is constructed on the basis of the auxiliary dynamic variable. All the closed-loop signals are shown to be bounded, and the followers can achieve the synchronous tracking of the leader's output. In the end, the simulation results demonstrate the efficiency of the proposed control strategy.

In this article, the adaptive fuzzy fixed-time bipartite consensus tracking control problem is studied for stochastic nonlinear multi-agent systems with unknown control gains and time-varying output constraints. First, in order to address the difficulties arising from the unknown control gains, the Nussbaum technique is employed. In the meantime, the$tan$-type nonlinear mapping function is introduced, which guarantees the predefined output constraints are not violated. Then, different from the previous control strategies in which they only focused on the balanced directed topology, the classification optimization algorithm is presented to accomplish the bipartite consensus tracking control according to the structurally unbalanced directed topology. Besides, by combining the adaptive backstepping technique with the adding power integration methodology, the nonsingular fixed-time control strategy is proposed. The proposed adaptive fuzzy fixed-time control strategy ensures that the bipartite consensus tracking errors converge to a region near zero in fixed time and all the signals in the closed-loop system are bounded in probability. Last, the effectiveness of the presented control scheme is demonstrated with a simulation example.

In this article, we propose a dynamic event-triggered adaptive prescribed-time output feedback tracking control strategy for nonlinear systems with unknown external disturbances under denial-of-service (DoS) attacks. The presence of malicious intermittent DoS attacks makes the output signal and states of the system unavailable, which in turn leads to more difficulty in the design of the controller. To overcome the above difficulty, we construct a novel composite observer based on the attack compensator, whereby the system states can be reconstructed. Moreover, with the help of the time-varying constraint function, the prescribed-time tracking control problem for nonlinear systems is transformed into the constraint problem of tracking error. At the same time, a new dynamic event-triggered adaptive prescribed-time safety fuzzy controller is built and remains applicable in the systems that operate continuously after the predefined time. The adaptive fuzzy safety control method proposed in this article ensures that the tracking error converges to the user-specified region in the predefined time, all signals of the closed-loop system remain bounded under intermittent DoS attacks, and the repeated transmission of samples from the controller to the actuator can be further reduced, generating fewer events and saving communication resources. Finally, the simulation results of the single-link robotic arm demonstrate the rationality and effectiveness of the developed control algorithm.

An adaptive event-triggered consensus control strategy for nonlinear multiagent systems without leaders against deception attacks is presented, where a more general deception attacks is considered in this article. The impact of deception attacks on systems cannot be ignored and the most significant difficulty for researchers is the exact state variables are unavailable. Therefore, a new observer that can observe the unavailable real states of the system is designed. Furthermore, this article presents an unusual coordinate transformation technology, where the states of the observer and the compromised states are considered simultaneously, to remove the effect of the malicious deception attacks. The event-triggered mechanism is introduced to construct a controller can ensure that resource waste is minimized and the utilization is improved as much as possible. Under the proposed control strategy, all signals in the closed-loop system are proven to be semi-global bounded and the stability for the studied systems under deception attacks is ensured. Conclusively, we conduct simulation experiments using the MATLAB software to verify the effectiveness of the proposed strategy.

In this article, we propose an event-triggered unified fault-tolerant control strategy for continuum robots with prescribed performance, considering multiple levels of actuator failures. First, by integrating a Kelvin–Voigt model, this article introduces an improved constant curvature model for continuum robots accounting for dissipative effects. Second, a comprehensive fault-handling framework is established, which combines extreme fault detection, dynamic actuator redundancy, and asymmetric performance recovery within the context of a unified prescribed performance. Third, by taking advantage of the dynamic characteristic of auxiliary variable and designing suitable event-triggering conditions, a dual-channel event-triggering mechanism is introduced to effectively reduce the number of triggers and optimize the utilization of communication resources. The proposed unified fault-tolerant control strategy ensures the boundedness of all signals in the closed-loop system and multiple kinds of prescribed performance behaviors under actuator failures. Simulation results validate the effectiveness of the proposed control strategy.

This article addresses the practical prescribed-time fault-tolerant tracking control (PFTC) problem for a class of nonlinear systems characterized by uncertain control gains and external disturbances. A novel prescribed-time regulator (PTR) is proposed to construct the controller, thereby achieving the tracking control objective with arbitrary accuracy within the prescribed tracking time. The phenomenon of complete actuator faults is also considered, and a fault-tolerant control strategy with immediate actuator switching is designed to mitigate their impact. Furthermore, a self-regulating control gain based on an error-feedback mechanism is introduced to restrain the control input while improving the overall control performance. To overcome the issue of “complexity explosion” arising from the derivation of virtual controllers, a class of nonlinear filters is designed to estimate the values of the virtual controllers. The PFTC strategy proposed in this article ensures the following: 1) all the signals in the closed-loop system remain bounded; 2) the tracking error is practical prescribed-time tracking stable; and 3) after detection of actuator faults, the tracking error reconverges to the desired range within the prescribed recovery time. Lastly, a simulation example is provided to demonstrate the effectiveness of the proposed control strategy.

In this article, an adaptive fixed-time event-triggered consensus tracking control strategy is proposed for the robotic multiagent systems (MASs). First, this article considers the robotic MASs rather than the single robotic manipulator system, which is of great research significance in practical applications. Then, the adaptive fixed-time control method within the backstepping technique is developed such that each robotic manipulator can track the ideal signal more quickly. Moreover, in the face of complex tasks, the communication resources of the robotic MASs are in short supply. By sampling the data from the original controller, the relative threshold event-triggered control (RTETC) strategy is adopted for each robotic manipulator system, which can ensure that all signals in the closed-loop system are bounded without the Zeno phenomenon. In the end, a simulation example is presented to demonstrate the validity of the proposed control strategy.

Based on output triggering, an adaptive prescribed-time tracking control strategy is proposed for a class of uncertain strict-feedback nonlinear systems with unknown control gains in this article. The nondifferentiability of the virtual control signals is identified as the most prominent design difficulty in this research. In order to solve the above difficulty, a new fuzzy state observer is built by using triggered output signal and fuzzy logic systems (FLSs), which in turn generates alternative continuous states. Simultaneously, the estimated signals are utilized to design virtual control signals, making certain that the virtual control signals have a well-defined first derivative. On this basis, by introducing a time-varying constraint function, a new adaptive prescribed-time fuzzy controller is constructed, so that the controller can still be applied to continuously operating systems after the predefined time. Additionally, we introduce the command filtering technique to mitigate repeated differentiation of virtual control signals during the backstepping design process. Combining the constructed logarithmic Lyapunov functions and bounded control technique with backstepping design, it is possible to guarantee that the established adaptive prescirbed-time event-triggered control method satisfies the following: 1) within the predefined time, the tracking error converges to the user-specified region and 2) the full range of signals involved in the closed-loop system is kept bounded. At last, the results of the single-link arm simulation example verify the reasonableness and effectiveness of the established control scheme.

This article introduces a finite-time adaptive bipartite consensus tracking control algorithm leveraging an improved nonlinear mapping (NM), capable of implementing the prescribed asymmetric full-state constraint requirements for nonlinear heterogeneous multiagent systems (MASs) under actuator deception attacks. First, a locally optimal bipartition strategy is proposed in this article to enable bipartite consensus tracking control within unbalanced directed graph. Unlike most previous full-state-constrained controls employing the barrier Lyapunov function (BLF), the proposed algorithm is derived from building a state-dependent NM function that can achieve one-to-one mapping for the original function and constructing a new coordinate transformation, leading to the solution of full-state-constrained performance control without the feasibility conditions on the control signals. By means of the proposed practical finite-time stability criterion, the novel design aims at constructing finite-time controllers that can ensure the existence and nonsingularity of the finite-time term in each control signal, which are oblivious in the existing results on finite time control. What’s more, the designed controller even under actuator deception attack achieves that:1)the bipartite consensus tracking errors converge to a small area containing zero in a finite time;2)the prescribed asymmetric full-state constraints are obeyed. At last, the availability of the proposed design solution is clarified by virtue of single-link robot systems.

This article investigates an adaptive bipartite consensus tracking control algorithm for a class of heterogeneous nonaffine nonlinear multiagent systems (MASs) with prescribed finite-time tracking performance under an unbalanced communication topology. In the case of an unbalanced digraph, a novel locally optimal bipartition strategy is proposed to transform the unbalanced communication topology into a structurally balanced one, thereby enabling the implementation of bipartite consensus tracking control. To achieve the expected tracking performance, the design philosophy focuses on developing a prescribed finite-time performance function (PFTPF), capable of preassigning the convergence time and accuracy precisely beforehand. The explored adaptive control algorithm can ensure that the whole signals concerning the closed-loop MASs remain bounded while the bipartite consensus errors converge to a predetermined range around zero within the prescribed finite time. Ultimately, the simulation results on robotic systems prove the availability of the developed design solution.

In this work, via proposing a novel$\tan $-type asymmetric barrier Lyapunov function (ABLF), we developed a command filtered adaptive fault tolerant control scheme for a class of uncertain nonlinear systems with predefined-time asymmetric and time-varying output constraints. First, such a class of constraints under interest is more practical. Unlike most of the existing constraints that need to be addressed at the moment of inception, the initial value requirement of the constrained object in this work is released. A predefined setting time can be installed in advance through the implementation of a shifting function embedded within the proposed ABLF. Second, the problem of unknown actuator faults is considered where the actuator faults can be both multiplicative and additive. Third, by combining the command filter and backstepping techniques, a twice-transformation design method is presented to construct the desired controller, under which the errors between the virtual control laws and the outputs of the command filters can be compensated thoroughly. Aside from avoiding the “explosion of complexity” issue, the designed controller also achieves the requisite tracking performance. Meanwhile, under such controller, the effect of the actuator faults can be estimated. Finally, the validity of the given scheme is evaluated through the use of a practice example.

This article mainly considers the adaptive secure bipartite consensus tracking control (BCTC) problem for nonlinear multiagent systems (MASs) under false data injection (FDI) attacks with predefined accuracy. Since FDI attacks produce unknown attack gains, which increases the difficulty of the controller design, an adaptive secure control strategy is given based on the essential property of Nussbaum functions. By improving the traditional coordinate transformation in the current literatures that can only achieve unilateral consensus control, a backstepping-based control algorithm is put forward attaining bilateral consensus control. In addition, the appropriate Lyapunov functions are generated by a class of non-negative functions to construct the adaptive secure bipartite consensus controllers, which not only makes certain that the bilateral errors ultimately converge to a predefined interval, but also guarantees that all the closed-loop signals within the investigated system are bounded. Conclusively, a practical example is provided to validate the effectiveness of the proposed control strategy.

In this article, the problem of reachable set (RS) synthesis for a class of nonlinear delayed hidden semi-Markov jump systems with actuator saturation and multiple cyberattacks is addressed. First, a dynamic-event-triggered mechanism (DETM) with a time-varying additional threshold is introduced, which can save communication resources more effectively. However, due to the introduction of DETM, the modes of the controller and the system exhibit asynchronous behavior. On the other hand, while network communication facilitates signal transmission, it also exposes the system to an open environment vulnerable to cyberattacks. To address these issues, we devise a security asynchronous controller based on the hidden Markov model. In addition, this article also considers a class of actuator saturation problem. After that, the sufficient conditions for RSs are obtained by applying the stability theory of Lyapunov functional and linear matrix inequalities. The controller gains are obtained by the matrix decoupling method. Finally, the feasibility and practicability of the method are verified by the circuit model and a numerical simulation.

A practical fixed-time adaptive fuzzy control strategy is investigated for uncertain nonlinear systems with time-varying asymmetric constraints and input quantization. To overcome the difficulties of designing controllers under the state constraints, a unified barrier function approach is employed to construct a coordinate transformation that maps the original constrained system to an equivalent unconstrained one, thus relaxing the time-varying asymmetric constraints upon system states and avoiding the feasibility check condition typically required in the traditional barrier Lyapunov function based control approach. Meanwhile, the “explosion of complexity” problem in the traditional backstepping approach arising from repeatedly derivatives of virtual controllers is solved by using the command filter method. It is verified via the fixed-time Lyapunov stability criterion that the system output can track a desired signal within a small error range in a predetermined time, and that all system states remain in the constraint range. Finally, two simulation examples are offered to demonstrate the effectiveness of the proposed strategy.

An adaptive event-triggered control strategy for non-strict feedback nonlinear cyber-physical systems with time delays against deception attacks and actuator faults is presented. The most prominent difficulty lies in after the system signals are damaged by malicious deception attacks, all the exact states in the system are unavailable. Another design difficulty is the common existence of unknown nonlinearities and time-varying time delays, which makes it difficult to get the desired controller. Thus, to stabilize the studied cyber-physical systems, an unusual coordinate transformation is presented, where the attack gains and the problem of unavailability of states are considered simultaneously. Furthermore, the effect of the malicious deception attacks on the studied system is tackled by using Nussbaum technology and designing the Lyapunov functions with the attack gains. The unknown nonlinear functions, the mismatch problem for the control input caused by the nonlinearities of time-varying time delays are processed by neural networks technology and Lyapunov-Krasovskii functions. As a result, a controller based on event-triggered mechanism is constructed to reduce the waste of communication resources. The presented control strategy can ensure the signals in the closed-loop system are bounded. Finally, the Matlab simulation experiments are showed to verify the effectiveness of the developed strategy.Note to Practitioners—This paper studies the adaptive event-triggered control strategy for non-strict feedback nonlinear cyber-physical systems with time delay under deception attacks and actuator faults. Cyber-physical systems are widely used in power system, aviation system and other practical systems. However, due to the openness of network communication channels, attackers are prone to transmitting incorrect data to controllers and actuators, resulting in unusable system states, which is a challenging problem to ensure system stability by only using the compromised system states. In addition, the safety control problem of cyber-physical systems with time delays and actuator faults is investigated simultaneously, which poses significant challenges to the design of an desired controller. Therefore, by constructing Lyapunov functions and designing adaptive laws, not only the system under deception attacks is stabilized, but also the control strategy studied is made more practical.

This paper investigates the attack-compensated output control problem for a class of Markov jump cyber-physical systems (MJCPSs) subject to mismatched modes. A sub-domain-awareness adaptive probabilistic event-triggered mechanism (APETM) is innovatively developed to fully enhance the control performance of the networked control system. Here, sub-domain-awareness means the network’s communication ability, which may be affected by time delay and network resource. To defend against the cyber-attacks imposed on the communication channel, a predictor-based compensator is constructed to mitigate the impact of attacks on the control performance. Different from the existing works, the mismatch degree between the controller and the system, governed by a random variable obeying any discrete-time distribution over$[0, 1]$, is changing dynamically. A mismatched output feedback controller is designed based on the APETM and attack-compensator, and an augmented closed-loop system is obtained. Both time delay-and triggering threshold-dependent Lyapunov functionals are introduced to perform the asymptotical stability analysis. With a separation technique, a solving algorithm is provided which converts the non-convex analysis conditions into traceable ones. Finally, simulations are conducted to validate the proposed results through a mass-spring-damping system model.Note to Practitioners—Cyber-physical systems (CPSs) have found many applications in the fields such as smart grid, gas distribution systems, and automated manufacturing systems. The open communication network deployed in CPSs face two main challenges including the security of data transmission and the efficiency of resource utilization. Owing to the practical environment and other factors, system parameters may change abruptly, which can be well defined by a Markov model. In the resultant Markov jump system, it is typically assumed that the mode mismatch degree between the controller and the system remains the same, which is unrealistic in a time-varying network environment. Motivated by these observations, this paper investigates the secure output control of Markov jump CPSs (MJCPSs) subject to mismatched modes and unknown cyber-attacks. An adaptive probabilistic event-triggered mechanism is innovatively proposed, which compared with the existing mechanisms strikes a higher level balance between the communication burden and the control performance. And attack-compensated mismatched output controllers are developed to stabilize MJCPSs and meanwhile preserve the security level. Finally, a mass-spring-damping system is adopted to verify the application effectiveness of the proposed results. Note that communication traffic control and secure control are finely involved based on CPSs, making our proposed results more applicable to practical systems.

In this paper, for a class of uncertain nonlinear systems, a low-computation design scheme for fault detection and performance recovery based on deferred replacement actuators is proposed. Different from the existing two mainstream adaptive fault-tolerant control schemes, the proposed method does not require prior knowledge of fault models, nor does it require multiple actuators working in parallel simultaneously to mitigate the impact of faults. The disadvantage of the former is that most of the considered fault models cannot cover all fault types, while the latter adds unnecessary wear and tear to actuators that do not generate faults. In order to overcome the shortcomings of the existing fault-tolerant control, a method with deferred actuator replacement is proposed. By designing a fault detection function and a shifting function, new error variables are reconstructed to achieve performance recovery. In addition, a computationally efficient design scheme is established through the idea of constraint control. Unlike the existing advanced technology, firstly, dealing with the problem of complexity explosion from a new perspective and ensuring the rationality of assumptions; secondly, analyze the controllability of system states during the deferred replacement stage. Finally, simulation results on a twin otter aircraft system verify the effectiveness of the proposed scheme.Note to Practitioners—For widely used modern control systems such as aircraft systems, self-driving systems, etc., it is extremely difficult to diagnose and repair the sudden fault behavior in a short time, and in this process, the adverse impact caused by the serious decline of the system performance is huge. Inspired by the practical application of airbus states in the flight control system, a fault-tolerant control scheme of deferred replacement actuators is designed in this paper. In addition, by designing a low-computation control scheme, the assumptions that are difficult to achieve in practice are relaxed, and the structure of the controller is very simple without the help of any auxiliary design. After fault detection, the replacement actuators strategy successfully realizes the recovery of the system performance within the specified time.

In this article, a novel distributed prescribed-time consensus tracking control strategy is presented for heterogeneous nonlinear multi-agent systems (MASs) under deception attacks and actuator faults. Since the original states of the studied system are unavailable under deception attacks, we present a new coordinate transformation technique considering the compromised states and the outputs of command filters to design the corresponding controller. Then, to handle the unknown control gains caused by actuator faults, the rational adaptive laws are cleverly designed for the upper bounds involving the unknown control gains. Besides, by introducing a time-varying constraint function in the backstepping design process, a new adaptive prescribed-time controller is constructed in this paper, such that the prescribed-time tracking control problem of the heterogeneous nonlinear MASs is converted into the constraint problem of the tracking errors. Through the Lyapunov stability analysis, the final results prove that the whole signals in the closed-loop MASs remain bounded and the tracking errors can converge to the pre-set region in the predefined time. Finally, the simulation results demonstrate the availability of the developed control method.Note to Practitioners—This paper investigates the distributed prescribed-time consensus tracking control problem for heterogeneous nonlinear MASs, whose models can be extended to more complex industrial applications, such as flexible manipulators, series elastic actuators and electric systems. In certain practical scenarios, security and fault problems are inevitable. Hence, it is challenging to design a control strategy that achieves distributed consensus tracking control in an insecure network environment. Furthermore, the proposed approach based on the time-varying constraint function ensures the system stability within the predefined time, which provides a viable strategy for engineering applications.

A distributed adaptive secure control algorithm is proposed for asynchronous switching nonlinear multi-agent systems (MASs) in pure-feedback form while considering the sensor attacks and actuator faults, which eliminates the effect of attack signals, actuator faults and uncertainties without knowing the sign of the control gain functions. Since the system states measured by the sensors are corrupted by the malicious attacker, only the post-attack system states can be obtained. Thus, an improved coordinate transformation is constructed by using the post-attack system states and a backstepping method based on the improved coordinate transformation is developed to solve the consensus tracking control problem of the researched systems under sensor attacks. The common Lyapunov function is designed to ensure the stability of all asynchronous switching subsystems of each agent. In the end, a simulation example is presented to illustrate the theoretical results’ validity.Note to Practitioners—This paper deal with the distributed adaptive secure consensus tracking control problem for asynchronous switching nonlinear MASs, whose models can describe many phenomena in nature such as biological processes, robot team formation and sensor networks. It is extremely challenging to achieve the tracking control problem of the researched asynchronous switching nonlinear system in an unsafe network environment, where the unknown sensor attacks signals, actuator faults coefficients, and randomly switched non-affine nonlinearities exist together for the followers. Furthermore, the control design and stability analysis of the researched system is based on the common Lyapunov approach, which makes the developed approach more engineering oriented.

This paper investigates the deferred output constraint (DOC) issues of high-order random nonlinear systems. The DOC indicates that the system output is constrained within a given range after the system running for a period of time, rather than being constrained at the beginning. This leads to an obstacle that the well used barrier Lyapunov function method is invalid because it is not defined at the initial stage. For this reason, a prescribed-time scaling function and a barrier function are introduced. Then, to more accurately describe the disturbances in nature, this paper considers a more common stochastic process than white noise, which is called colored noise. In addition, a dynamic-memory event-triggered mechanism (DMETM) that takes into account the influence of historical information of internal dynamic variables on trigger conditions is proposed to reduce the waste of communication resources. With the assistance of Lyapunov stability theory and backstepping approach, it is shown that our developed DMETM-based control scheme can guarantee that all signals are bounded in the presence of colored noises. Ultimately, two simulation examples are included to demonstrate the effectiveness of the proposed theory.Note to Practitioners—Since higher-order nonlinear systems can describe nonlinear features in system dynamics, some complex actual systems such as induction motorcycles and space vehicles can be modeled as such systems. In engineering applications, controlled systems are usually affected by random noises from external environment, thus colored noises are introduced in this paper. Compared with white noises, colored noises can describe disturbances in nature more accurately and reasonably. In addition, to ensure that practical systems such as car operation systems and robotic arm systems can work safely, their DOC issues need to be considered. However, the traditional barrier Lyapunov functions (BLFs) cannot solve the DOC problems because they are not defined in the initial stage, hence the prescribed-time scaling and barrier functions are proposed. Meanwhile, to circumvent the problem of limited communication bandwidth, a DMETM with delay terms of internal variables is devised.

Combining with the reinforcement learning (RL) strategy and adaptive backstepping method, an event-triggered-based adaptive optimized bipartite consensus control protocol is constructed for heterogeneous nonlinear strict-feedback multi-agent systems (MASs). The control objective is to synchronize the state variables of the MASs and obtain the optimized bipartite tracking performance. In order to finish the control objective, a fuzzy logic system (FLS) based RL method is employed in the critic-actor structure. Different with the exist RL methods, the RL updating laws in this article is stemmed from a simple positive function which is derived by Hamilton-Jacobi-Bellman (HJB) equation. The FLSs are used to release the persistence excitation condition and the switching threshold event-triggered strategy is designed to reduce the calculation and communication frequency. It is shown that the developed control protocol not only achieves the bipartite consensus tracking performance of the studied heterogeneous MASs but also maintains the stability of the whole closed-loop system. Finally, the simulation results are provided to demonstrate the effectiveness of proposed control protocol.Note to Practitioners—Nowadays, energy conservation and environmental protection have become the current trend. Therefor, it is imperative to consider efficiency improvement as the fundamental principle of modern control design. In this paper, an optimal control method is employed to find a control protocol for considered MASs to accomplish the control task with the minimum utilization of control resources. In some practical application scenarios such as sea voyage for deep-sea exploitation or ocean transportation, the designed optimal control protocol can not only reduce the massive energy consumption for surface vessels but also eliminate the persistence of excitation assumption in Zhang and Feng (2021), Tang and Lau (2022), and Ren et al. (2022). The developed switching threshold event-triggered strategy and bipartite control design can effectively reduce the call frequency of channel resources in practical and divide all agents into two groups in surface vessels collaboration. Thus, our control algorithm can be easily applied in practical engineering.

In this paper, the robust consensus tracking problem is investigated for the heterogeneous nonlinear multi-agent systems (MASs) with weighted communication graph and time-varying input delays. Different from other existing works, the heterogeneous MASs have more general topology graph which contains a spanning tree. Further, the assumption of leader system is relaxed to contain the disturbance term. Hence, the intelligent technologies are used to approximate the unknown quantities from neighbor systems and leader system. To deal with the difficulties caused by the input delays, the compensation system, double integral type and novel constructed exponential type Lyapunov-Krasovskii (L-K) functionals are proposed to design the adaptive controllers. It should be known that the novel constructed exponential type L-K functional is simpler to design, and not only can satisfy the stability requirements but also can counteract the input delay. Besides, the uniform hysteretic quantizer is used to save the communication costs, and the dynamic surface filter is considered to optimize the controller structure for each agent. Under the proposed control protocol, the tracking errors are shown to achieve satisfactory control accuracy. Finally, the numerical example is provided to verify our strategies.Note to Practitioners—This paper considers the consensus tracking problem for the heterogeneous nonlinear MASs with weighted communication graph and time-varying input delay. The model is widely applied in the flocking control field, such as transportation, communication, manufacturing sector and so on. As the delay causes system performance degradation, it is more meaningful for realistic scene to consider the continuous and non-differentiable controller with unknown time-varying delay. Furthermore, the designed controller can keep the control accuracy, and the computation and communication costs are efficiently reduced.

This paper investigates the event-triggered-based adaptive bipartite finite-time tracking control problem of nonlinear nonstrict-feedback coopetition multi-agent systems (MASs) with the time-varying disturbances. First, the major design difficulties generated by the entirely unknown nonlinear functions containing all states are solved by utilizing the approximation property of radial basis function neural networks (RBF NNs) and the structural feature of Gaussian functions. Then in the backstepping procedure, the issue of “explosion of complexity” is handled by combining the adaptive neural approach and the command filter technique, which simplified the complexity of the controllers for all the agents. Meanwhile, the novel compensation signals are designed, which skillfully eliminate the error influence caused by the filters. Moreover, to save the communication resources, the relative threshold event-triggered control (ETC) scheme is presented for the designed controllers, and there is no Zeno phenomenon. Overall, it is shown that the new proposed control approach drives the tracking errors to the desired neighborhood of the origin in an almost fast finite time, and all the signals in the closed-loop systems are almost fast finite-time bounded. Finally, the numerical and practical simulation results are both given to show the validity of the obtained design methodNote to Practitioners—This paper presents the event-triggered adaptive bipartite finite-time tracking control scheme for the nonlinear nonstrict-feedback coopetition MASs with the time-varying disturbances, which can be used to model most practical systems such as sensor network, submarine underwater robot and space satellites. Although the bipartite control problem has been studied a lot, the bipartite finite-time tracking control problem for nonlinear nonstrict-feedback coopetition MASs with the time-varying disturbances is still open and challenging. The proposed approach guarantees that the tracking errors can converge to the desired neighborhood of the origin in an almost fast finite time. In addition, the ETC strategy is proposed to address the limited power consumption. A remarkable point for this paper is that the obtained results are demonstrated by the simulation examples, which shows the validity of the proposed approach.

In this paper, an adaptive finite-time bipartite consensus tracking control strategy is presented for a class of heterogeneous nonlinear nonstrict-feedback multi-agent systems (MASs) with output constraints. Firstly, to deal with the time-varying output constraints problem, an improved tan-type nonlinear mapping (NM) function is presented for the first time. And based on the improved NM function, a novel tracking error is constructed to design controller for each agent, which guarantees the bipartite consensus tracking is achieved while constraints requirement is not violated. Then, a state observer is designed to estimate the unmeasurable states of each agent. Moreover, in the case of unbalanced directed topological graph, a partition algorithm (PA) is employed to implement bipartite consensus tracking control. The developed distributed adaptive finite-time control strategy ensures that all the signals in the closed-loop system are bounded and the bipartite consensus tracking control is achieved in finite time. Finally, the validity of the designed control strategy is demonstrated by a simulation experiment.Note to Practitioners—At present, nonlinear MASs are widely used in practice, such as robots formation control, vehicular platoon systems control, etc. This paper investigated the adaptive finite-time bipartite consensus tracking control problem for a class of heterogeneous nonlinear nonstrict-feedback MASs with output constraints. In the scenarios of practical application, these two situations are common: 1) The communication topology graph of nonlinear MASs is unbalanced. 2) The output of each agent is constrained. Therefore, this paper presents an improved tan-type NM method to deal with the time-varying output constraints problem, and a partition algorithm is employed to implement bipartite consensus tracking control based on the unbalanced communication topology graph. Meanwhile, the nonsingular finite-time control strategy effectively improves the convergence of the studied nonlinear MASs. In addition, the system model and backstepping technology used in this paper are general and practical.

This paper investigates the adaptive finite-time consensus tracking control problem for a class of nonlinear nonstrict-feedback multi-agent systems (MASs) with output constraints. Firstly, to deal with the output constraints problem, an improved tan-type nonlinear mapping (NM) function is presented for the first time. Then, the singularity problem that exists in finite-time control is successfully avoided by employing a novel switching function. A modified tracking error involving the dependent variable of the designed NM function is constructed to guarantee that the outputs of all agnets achieve consensus tracking simultaneously and satisfy the constraints requirement. In addition, a switching threshold event-triggered control (ETC) strategy is applied to design controller for each agent, which combines the advantages of fixed threshold strategy and relative threshold strategy, and saves system communication resources well. The developed distributed adaptive finite-time control protocol ensures that all the signals in the closed-loop system are bounded and the consensus tracking control is achieved in finite time. Finally, the effectiveness of the designed control strategy is verified by a simulation experimentNote to Practitioners—Due to the wide application of nonlinear MASs in practice, such as unmanned aerial vehicles (UAVs) formation control, robots formation control and so on, the adaptive finite-time consensus tracking control problem for a class of nonlinear nonstrict-feedback MASs is studied in this paper. In practical applications, the practical fast finite-time strategy can effectively increase the system convergence, the NM method not only solves the output constraints problem well, but also overcomes the conservativeness of traditional barrier Lyapunov functions. Then, in order to reduce the communication burden of the nonlinear MASs, a switching threshold ETC is considered. In addition, the system model and backstepping technology used in this paper are general and practical.

This paper investigates event-triggered based finite-time bipartite consensus tracking control problem for multi-agent systems (MASs) over signed directed graphs. Compared with the existing related results, the main features of the results presented in this paper are as follows: (i) The strict limitation for nonlinear MASs with a structurally balanced digraph is removed by introducing a prioritized strategy. (ii) A state estimator is constructed by combining neural networks (NNs), which reconstructs the immeasurable system states of each agent in nonstrict-feedback form for the first time and approximates the completely unknown nonlinearities that exist in the system. (iii) A new distributed control algorithm, named finite-time distributed control strategy is designed by introducing a novel first-order filter, which ensures that the consensus errors can obtain a fast convergence. (iv) The results are successfully extended to the event-based bipartite tracking control for MASs by using relative threshold strategy. Moreover, the proposed control algorithm is applied to the consensus problem of a group of forced damped pendulums (FDPs). Based on backstepping method and Lyapunov stability theory, the distributed consensus tracking errors can converge to a small neighborhood of the origin at a finite-time under the proposed protocol, and all the signals of the closed-loop system remain bounded. Finally, the simulation results illustrate the validity of the proposed schemes.Note to Practitioners—The studies of the bipartite consensus problems of multi-agent systems (MASs) have gained great attention due to its applications in multi-spacecraft systems, natural networks, and biological communities, and a new event-triggered based finite time bipartite tracking consensus control method for multi-agent systems (MASs) is studied in this paper. In practical applications, the finite time method can obtain the optimal control performance in time. Then, in order to save the communication and computation resources for the nonlinear MASs, this paper extends the proposed control strategy to the event-based bipartite tracking control problem for MASs by using the relative threshold event-triggered rules, which greatly conserves the communication resources between the control signal and the actuator. In addition, the dynamic model and backstepping technology used in this paper are general and practical.

This paper proposes an adaptive bipartite secure consensus asymptotic tracking control scheme based on event-triggered strategy for the nonlinear multi-agent systems (MASs) under denial-of-service (DoS) attacks. First, by incorporating the concept of shortest path into the hierarchical algorithm, the bipartite consensus control problem in the presence of unbalanced communication topology is successfully addressed. Further, an anti-attack bipartite control strategy by designing the improved forms of the tracking errors and virtual controllers is proposed under DoS attacks. Then, a modified event-triggered mechanism based on the relative threshold strategy is proposed, which can ensure that the bipartite consensus tracking errors converge to zero asymptotically by utilizing the Barbalat’s Lemma. Under the Lyapunov stability theory, it is guaranteed that the outputs of all agents can reach agreement with an identical magnitude but opposite signs and all the signals of the closed-loop MASs are bounded. Finally, the simulation results on the model of damping pendulums are given to verify the efficiency of the proposed secure controller.Note to Practitioners—In this paper, the adaptive bipartite secure consensus asymptotic tracking control problem is considered for nonlinear MASs subject to DoS attacks, whose models can describe many critical applications, such as bidirectional formation of unmanned vehicles and robots. The research on the secure tracking control problem will be rather complicated yet challenging if the DoS attacks of the communication channels are taken into account in the insecure complex network environment. In addition, the event-triggered mechanism is used to reduce the usage of communication resources, which makes the proposed control scheme more easier to implement and more friendly for control engineers.

The majority of the results on constrained nonlinear multi-agent systems (MASs) control focused on output or state constraints without considering the saving of communication resources. In this paper, for a class of uncertain nonlinear MASs, we first present a new adaptive bounded consensus tracking control scheme in which the asymmetric and full-state constraints are jointly synthesized with a switching threshold event-triggered strategy, such that the communication resources are effectively utilized. The key to accomplishing the asymmetric and full-state constraints is that a kind of improved$tan$-type barrier Lyapunov functions are constructed. The controller constructed for each agent by the switching threshold event-triggered strategy guarantees that the asymmetric and full-state constraints are not violated and the output of each agent can track the leader’s trajectory with an adjustable bounded tracking error. Furthermore, to achieve the asymptotic consensus tracking control, we give another kind of novel$tan$-type barrier Lyapunov functions to design the desired controller for each agent. A simulation example of five single-link robots is proposed to illustrate the effectiveness of our control scheme.Note to Practitioners—In this paper, the adaptive bounded consensus tracking control problem is considered for nonlinear MASs subject to full-state constraints, whose models are capable of describing a multitude of critical applications, including the formation of unmanned vehicles and robots. The research on the tracking control problem will be rather complicated yet challenging if the asymmetric and full-state constraints are taken into account in a complex environment. Additionally, the incorporation of an event-triggered mechanism aids in the reduction of communication resource usage, enhancing the ease of implementation and improving the user-friendliness of the proposed control scheme.

This paper investigates the consensusability for a class of nonlinear pure-feedback multiagent systems (MASs) with delayed full-state constraints. First, by using a novel state-shifting transformation (SST), the constrained states are encapsulated into some barrier functions such that the new converted state variables and their dynamic model are generated. Then, the essential relationship between the post-transformation tracking errors and the pre-transformation tracking errors are further explained. By employing the radial basis function neural networks (RBF NNs) to deal with the unknown nonlinearities for each agent and introducing a relative threshold method to overcome the waste problem of system transmission resources, an event-triggered control protocol is developed for the considered system. The proposed protocol has its own advantages: 1) This is the first work to consider the pure-feedback MASs with delayed full-state constraints. By transforming the constrained states into unconstrained variables, the states of the MASs can be converged into ideal ranges within a predefined time$T$; 2) Under this control protocol, only one adaptive law is necessary to be updated online in each follower and the use efficiency of system resources is improved by using reasonable event triggering mechanism. Finally, the effectiveness of the suggested consensus control protocol is demonstrated by the simulation results.Note to Practitioners—Delayed constraints often encountered in practical applications, which represent a type of constraints that may be violated initially but required to be satisfied sometime after system operation, so it is very necessary and important to converge states into ideal ranges within a predefined time when delayed constraints required. What’s more, considering the requirement of high control accuracy in practical application and the current Barrier Lyapunov Function (BLF) methods need to restrict the virtual control signals within some given regions, such restrictive conditions make the design and implementation of the traditional controllers particularly difficult. In this article, the control protocol for a class of nonlinear pure-feedback MASs with delayed full-state constraints and event-triggered communication are constructed to promote the development of asymptotic tracking control methods, and a novel state-shifting transformation is used to ensure the system states could be converged into the ideal constrained intervals in a predefined time.

Under a directed graph, a distributed nonsingular finite time adaptive control algorithm is proposed in this paper for a class of nonlinear multiagent systems (MASs) with parametric uncertainties and completely unknown non-identical control directions. Firstly, a modified coordinate transformation is proposed by introducing the dynamic surface control (DSC) technique, which avoids the massive use of neighbor informations and overcomes the “explosion of complexity” challenge arising from iterative differentiation concerning the virtual controls. Secondly, we adopt a set of Nussbaum functions with different frequencies for each agent to deal with the unknown control directions and make the effects of the multiple Nussbaum functions enhance each other instead of counteracting. In addition, by introducing a piecewise continuous function in each step of the backstepping procedure, a novel nonsingular finite time adaptive tracking controller is designed, which eliminates the possible singularity problems resulting from the presence of negative fractional powers. Based on the finite time stability criterion, it is proved that all closed-loop signals are bounded and the tracking errors can converge to a small residual set in a finite time. Finally, a simulation example of four DC motors is provided to demonstrate the effectiveness of the proposed algorithm.Note to Practitioners—This paper investigates the distributed nonsingular finite time adaptive consensus tracking control problem for the nonlinear MASs with parametric uncertainties and completely unknown non-identical control directions, whose models can describe many critical applications, such as unmanned vehicle formation and robot formation. The proposed algorithm provides an intuitive design paradigm for the consensus tracking control of uncertain nonlinear MASs with completely unknown non-identical control directions. In addition, the developed finite time control method can effectively increase the system convergence, which makes the designed algorithm more engineering oriented.

This article addresses the dynamic memory event-triggered anti-disturbance (DMETAD) control problem for switched cyber-physical systems (SCPSs) under the scenario of multiple disturbances and periodic Denial-of-Service (DoS) attacks. The multiple disturbances are composed by modeled disturbance and unmodeled disturbance. The control objective is to mitigate the impact of multiple disturbances and periodic DoS attacks. Firstly, the dynamic memory event-triggered (DMET) mechanism is introduced. Then, the disturbance observer is designed to estimate the modeled disturbance. Further, the controller based on the disturbance observer and DMET protocol is constructed to compensate the modeled disturbance and suppress the unmodeled disturbance. Next, by virtue of the multiple Lyapunov functions strategy, constraints are established for the SCPSs to force the solvability of the DMETAD control issue. Finally, a switched RLC circuit system simulation case is implemented, validating the reasonability of the established DMETAD control technique.

In this article, two novel adaptive fault-tolerant control schemes for a class of nonlinear strict-feedback cyber-physical systems (CPSs) with deception attacks are presented. Deception attacks, such as false data-injection attacks, which destroy sensor networks, make the outputs and states of the CPSs unavailable. It is very difficult and challenging for a designer to achieve the tracking control under the circumstance of cyberattacks. To realize the tracking control for the studied CPSs, we propose a new coordinate transformation technology without precedent, where it takes the attack gains into account and uses the compromised states to design the corresponding controllers. In the backstepping design process, Nussbaum functions are presented to alleviate the influence of the unknown attack gains. Furthermore, we consider the actuator faults problem, which includes the loss of effectiveness and the bias fault. By skillfully designing the adaptive laws, the effect of actuator faults is completely eliminated. It is theoretically proved that the first proposed tracking control scheme can guarantee all signals in the closed-loop system are bounded and the output can track the desired reference signal. In addition, the second adaptive control scheme is also developed for the CPSs under the actuator faults and a more general assumption on the deception attacks is proposed simultaneously. Finally, the feasibility of the new proposed methods is verified by MATLAB simulation analysis.

This article presents a new event-triggered adaptive finite-time control strategy using a fuzzy state observer for a class of nonlinear cyber-physical systems (CPSs) under malicious deception attacks with a more general form. Compared with the traditional assumptions on the deception attacks in the existing results, a more general assumption on deception attacks is given in this article. During the design process, real system states are initially estimated by developing an improved state observer, which effectively addresses the problem of state unavailability. Then, a coordinate transformation technology, in which the estimated states of observer are considered, is presented to stabilize the studied system. By constructing the singularity-free finite time virtual controls, the singularity problem in the traditional finite time design algorithms is cleverly avoided. Furthermore, to minimize communication overhead, a final finite-time controller is established by using a relative threshold event-triggered scheme. The developed event-triggered adaptive finite-time control strategy guarantees that all signals in the closed-loop system are semi-globally bounded in finite time without Zeno behavior. Finally, the correctness of the proposed control strategy is validated through two simulation results.

This article proposes an adaptive fixed-time output feedback tracking control scheme for a class of nonstrict- feedback stochastic nonlinear systems subjected to unmodeled dynamics and dynamic disturbances. To address the uncertainty arising from nonlinear terms, fuzzy logic systems (FLSs) are used as a universal approximator. Moreover, a state observer is utilized to estimate the unmeasured states. Then, the dynamic signal is introduced into the design process of the controller to solve unmodeled dynamics. Through stability analysis, the proposed new output feedback tracking controller guarantees the boundedness of all the signals, and the tracking error converges to a small residual set within a fixed time. The results of the simulation illustrate the effectiveness of the developed controller.

In this paper, an adaptive fuzzy bipartite formation tracking control strategy of nonlinear multi-agent systems (MASs) is developed under a directed communication topology. Fuzzy logic systems are utilized to approximate the unknown nonlinear dynamics. Then, considering MASs with both cooperative and competitive relationships, the proposed bipartite formation tracking strategy allows each agent to operate according to their specific advantages. By employing a nonlinear state transformation function, the original constrained outputs of the MASs are converted into unconstrained ones. Meanwhile, a prescribed-time shifting function is introduced to handle the deferred output constraints, by which the singularity problem generated from the denominator of nonlinear state transformation functions is avoided. In addition, considering the communication bandwidth is limited, a distributed dynamic self-triggered control (DSTC) mechanism is constructed to improve the transmission efficiency. Different from the traditional self-triggered control strategy, the proposed DSTC strategy allows triggered intervals to be adjusted dynamically according to bipartite formation tracking errors, which enables the DSTC strategy to compromise communication burdern and system performances dynamically. Finally, two simulation examples are given to illustrate the validity of the proposed control scheme.

This paper focuses on the adaptive fuzzy practical predefined-time (PT) bipartite consensus tracking control (BCTC) problem for heterogeneous nonlinear multi-agent systems (HNMASs) with actuator faults. First, the fuzzy logic systems (FLSs) are used to approximate the unknown nonlinear functions. Then, the partial loss of effectiveness and bias fault of actuator are considered simultaneously in the HNMASs, which is effectively handled by using adaptive compensation technology. In addition, the developed bipartite consensus tracking control protocol based on a practical predefined-time strategy not only ensures the fast convergence of the studied systems, but also predetermines the convergence time not relied on the initial conditions. The theoretical result shows that all signals of the closed-loop system are semiglobally uniformly predefined-time bounded (SGUPTB), and the BCTC performance is guaranteed within the predefined time. Finally, the simulation example based on the agents of different orders shows the validity of the obtained results.

This article explores a novel singularity-free command-filtered adaptive fuzzy finite-time tracking control algorithm for the flexible robotic manipulator with dead-zone input. First, by considering the influence of the residual term in two cases, a novel practical finite-time stability criterion is presented, and the settling time is more accurately characterized, which is applied to the design of the flexible robotic manipulator. The unknown nonlinear function in the robotic manipulator is handled by employing an intelligent estimation technique based on fuzzy logic systems. Unlike the related finite-time work, a new adaptive command-filtered finite-time controller is constructed by fusing a piecewise continuous function in each step of the backstepping process, such that the singularity of the control signal of the finite-time results is completely circumvented. Further, the mathematical model of the dead zone is delicately reconstructed such that the dead-zone input can be rigorously designed using effective mathematical techniques. Finally, the robotic manipulator system demonstrates the validity of the designed finite-time algorithm.

This article proposes a bumpless tracking switching control method for the interval type-2 (IT2) switched positive Takagi–Sugeno (T–S) fuzzy systems (SPTSFSs). The IT2 SPTSF model is employed to adeptly transform the nonlinear positive system into a linear form with inherent uncertainties addressed by IT2 fuzzy sets. First, the conservativeness of the system model is relaxed by refining the IT2 membership function. Then, by the multiple Lyapunov functions technique, the condition is developed to derive the solvability of the bumpless tracking switching control issue for the IT2 SPTSFSs. By employing the matrix transformation method, the condition is convex. Furthermore, controller and switching logic are established to force the IT2 SPTSFSs to obtain the bumpless tracking switching performance. Finally, an elaborate simulation case on the turbine engine is given to verify the validity of the introduced bumpless tracking switching control strategy.

In this article, the asymptotic tracking control problem for a class of nonlinear multi-agent systems (MASs) is researched by the combination of radial basis function neural networks (RBF NNs) and an improved dynamic surface control (DSC) technology. It's important to emphasize that the MASs studied in this article are nonlinear and nonstrict-feedback systems, where the nonlinear functions are unknown. In order to satisfy the requirement that all items in the controller must be available, the unknown nonlinearities in the system are flexibly approximated by utilizing RBF NNs technique. Moreover, the issue of ``complexity explosion'' in the backstepping procedure is handled by improving the traditional DSC technology, and meanwhile, the influences of the boundary layers caused by the filters in the DSC procedure are eliminated skillfully through the compensation terms. In addition, the relative threshold event-triggered strategy is developed for the designed controllers to reduce the waste of communication resources, where Zeno phenomenon is successfully avoided. It is observed that the new presented control strategy ensures that all the closed-loop systems variables are uniformly ultimately bounded (UUB), and furthermore all the outputs of followers are able to track the output of the leader with zero tracking errors. Finally, the simulation results are presented to show the effectiveness of the obtained design scheme.

This article solves the cooperative adaptive tracking control problem for nonlinear pure-feedback multi-agent systems (MASs). Compared with the previous achievements of adaptive control of pure-feedback MASs, the partial derivative of the nonaffine function may not exist by using decoupling technology. In the controller design framework based on the backstepping technique, the additional state variables are processed using the special properties of the radial basis function neural networks (RBF NNs). A special-shaped Laplacian matrix is proposed to unify the leader gain form in the tracking error design process (the coefficient in the second term of tracking error). Furthermore, an event trigger mechanism (ETM) is introduced to save resources. The constructed controller under the ETM can not only stabilize the system states but also make the tracking error reach a small accuracy. Finally, the simulation results demonstrated the feasibility of the proposed method.

This article explores the practical finite/fixed-time consensus control algorithms for nonlinear multiagent systems (MASs) using an initial-value-free nonlinear mapping (NM) approach. By integrating a piecewise continuous function into each virtual control, the novel control signal can effectively avoid the singularity problem inherent in finite-time and fixed-time work. Compared with the previous constrained papers, we reconstruct the nonlinear MASs by introducing boundary performance functions into the NM method to release the initial-value conditions. Then, a command-filtered technique is provided to tackle the issue of the “explosion of complexity” stemming from iterative differentiation regarding the virtual controls, while a twice-transformation design technique is used to compensate for the filtered error. The adaptive controllers utilizing radial basis function neural networks (RBF NNs) can effectively address the effects of the unknown control gains and system uncertainties. The explored control strategies ensure that all signals of the closed-loop system converge into a compact set near zero within a practical finite/fixed time without violating the imposed constraints. Ultimately, the simulation outcomes on robotic systems illustrate the availability of the designed algorithms.

In this article, the resilient adaptive intermittent output feedback control is investigated for a class of uncertain strict-feedback nonlinear systems under unknown sensor deception attack. The underlying problem is rather challenging not only because the system contains mismatched uncertainties, the output information is corrupted by an additional attack signal, and only the intermittent false output is available for control design, but also because the virtual control terms are nondifferentiable due to the utilization of event triggering. To circumvent these obstacles, we construct a new fuzzy state estimator via intermittent false output and fuzzy-logic systems (FLSs), which, in conjunction with a new set of error surfaces employing the false and estimated state information, allows a novel observer-based resilient adaptive intermittent control strategy to be developed. The results of the proposed resilient adaptive output event-triggered control shown that the stabilization errors converge to a vicinity of the origin, and all the signals of the overall system remain bounded. Numerical simulations confirm the efficiency of the proposed methodology.

In this article, for the single-input–single-output (SISO) nonlinear strict-feedback system, optimized backstepping (OB) control combined with the dynamic surface (DS) technique is developed. OB is to make every subsystem control of backstepping as the optimized one so as to ensure the entire backstepping control being optimized. However, the original design of OB still needs to repeatedly calculate the derivative of virtual controls, as a result, it will inevitably cause the problem of “differential explosion.” In order to alleviate the phenomenon, the OB control is combined with the DS technique. Furthermore, OB control needs to conduct with reinforcement learning (RL) in every backstepping step, hence simplifying the algorithm of RL is very necessary and substantive for achieving the combination. In this work, because the optimized control derives both critic and actor training laws by utilizing a simple positive function instead of the square of approximation of Hamilton–Jacobi–Bellman (HJB) equation, it can obviously simplify the RL algorithm to compare with the traditional optimizing methods. Finally, the feasibility is illustrated via both theory and simulation.

A new state estimation method is proposed in this manuscript for a class of linear cyber-physical systems (CPSs) with sparse sensor attacks, unknown input and output disturbances. The sensor attack will make part of the measurement signal received by the remote observer inaccurate. In order to achieve the secure state estimation (SSE) for the investigated linear CPSs, an unknown input observer (UIO) with adaptive switching mechanism is designed. Inspired by the existing results, a set of sub-observers is designed which can exclude the influence of unknown input and output disturbances. To achieve switching between different sub-observers, the adaptive switching mechanism is designed according to the switching adversarial principle. Some parameters of the observer are obtained by designing a set of linear matrix inequalities (LMIs). The sufficient condition for the existence of the observer and the proof of its effectiveness are respectively given by theoretical analysis. Finally, the effectiveness of the proposed method is proved by two Matlab simulation experiments.

This work concentrates on the adaptive resilient dynamic surface controller design problem for uncertain nonlinear lower triangular stochastic cyber-physical systems (CPSs) subject to unknown deception attacks based on a switching threshold event-triggered mechanism. The adverse effect of deception attacks on the stochastic CPSs is that the exact system state variables become unavailable. Furthermore, it should be emphasized that the coexistence of unknown nonlinearities, stochastic perturbations, and unknown sensor and actuator attacks makes it a very difficult and challenging event to implement the control design. To get the desired controller, radial basis function (RBF) neural networks (NNs) are introduced so that the design obstacle caused from the unknown nonlinearities can be easily solved. On this basis, in order to save resources and effectively transmit, the event-triggered control scheme based on a switching threshold strategy is further considered. In the backstepping design process, the dynamic surface control (DSC) technique is presented to deal with the issue of "explosion of complexity." By skillfully designing a new coordinate transformation and the attack compensators, the problem of unknown deception attacks is successfully handled. Under our proposed control scheme, all the closed-loop signals are bounded in probability and the stabilization errors converge to an adjustable neighborhood of the origin in probability. Finally, the simulation results on the double chemical reactor show the validity of the proposed design scheme.

This article investigates the adaptive event-triggered output-feedback control problem for a class of switched stochastic nonlinear systems with actuator faults. In the existing works, the developed results on adaptive control for switched stochastic nonlinear systems are almost based on the average dwell-time method, and how to construct a desired adaptive controller in the frame of the mode-dependent average dwell time (MDADT) remains a control dilemma. By presenting a general adaptive control rule based on the MDADT, this article implements the adaptive output-feedback control for the switched stochastic system under interest. In the process of controller design, fuzzy-logic systems, a flexible approximator, are utilized to approximate the unknown nonlinear functions. The dynamic surface design approach is employed to avoid taking derivatives of the constructed virtual controls to decrease the difficulty of complex calculation greatly. Meanwhile, a switched observer is designed to estimate the unknown states. In the frame of backstepping design, an event-triggered-based adaptive output-feedback controller is constructed such that all signals existing in the closed-loop system are ultimately bounded under a class of switching signals with MDADT property. Finally, the simulation results show the validity of the proposed control strategy.

This work focuses on the problem of predefined-time bipartite consensus tracking control for a class of nonlinear MASs with asymmetric full-state constraints. A predefined-time bipartite consensus tracking framework is developed, where both cooperative communication and adversarial communication among neighbor agents are implemented. Different from the finite-time and the fixed-time controller design methods for MASs, the prominent advantage of the controller design algorithm presented in this work is that our algorithm can make the followers track either the output or the opposite output of the leader within the predefined time in accordance to the user requirements. In order to obtain the desired control performance, an improved time-varying nonlinear transformed function is skillfully introduced for the first time to handle the asymmetric full-state constraints and radial basis function neural networks (RBF NNs) are employed to deal with the unknown nonlinear functions. Then, the predefined-time adaptive neural virtual control laws are constructed by using the backstepping technique, while their derivatives are estimated by the first-order sliding-mode differentiators. It is theoretically testified that the proposed control algorithm not only guarantees the bipartite consensus tracking performance of the constrained nonlinear MASs in the predefined time but also remains the boundedness of all the resulting closed-loop signals. Finally, the simulation research on a practical example shows the validity of the presented control algorithm.

This article presents a novel adaptive bipartite consensus tracking strategy for multiagent systems (MASs) under sensor deception attacks. The fundamental design philosophy is to develop a hierarchical algorithm based on shortest route technology that recasts the bipartite consensus tracking problem for MASs into the tracking problem for a single agent and eliminates the need for any global information of the Laplacian matrix. As the sensors suffer from malicious deception attacks, the states cannot be measured accurately, we thus construct a novel dynamic estimator to estimate the actual states, which, together with a new coordinate transformation involving the attacked and estimated state variables, allows a distributed security control scheme to be developed, in which the singularity of the adaptive iterative process involved in existing works is completely avoided. Furthermore, the Nussbaum functions are included in the controller to account for the influence of the unknown control gains caused by sensor deception attacks. It is shown that the distributed consensus tracking errors converge to a small neighborhood of the origin, and all the signals in the closed-loop system remain bounded. Simulation on a forced damped pendulums (FDPs) is conducted to demonstrate and verify the effectiveness of the proposed strategy.

This article investigates the neural-network-based adaptive predefined-time tracking control problem for switched nonlinear systems. Neural networks are employed to approximate the unknown part of nonlinear functions. The finite-time differentiators are introduced to estimate the first derivative of the virtual controllers. Then, a novel adaptive predefined-time controller is proposed by utilizing the backstepping control technique and the common Lyapunov function (CLF) method. It is explained by the theoretical analysis that the developed controller guarantees that all signals of the switched closed-loop systems are bounded under arbitrary switchings and the tracking error converges to zero within the predefined time. A simulation is shown to verify the validity of the developed predefined-time control approach.

In this article, the finite-time observer-based sliding-mode control (SMC) problem is considered for stochastic Markovian jump systems (MJSs) with a deterministic switching chain (DSC) subject to time-varying delay and packet losses (PLs). First, the stochastic MJSs with DSC are appropriately modeled and the PLs case is characterized by using some Bernoulli random variables. Then, a nonfragile finite-time bounded sliding-mode observer is designed. Our objective is to propose a finite-time observer-based SMC approach such that for the above addressed system, the finite-time boundedness in a certain time interval can be guaranteed by giving sufficient criteria via the stochastic analysis skills and average dwell time (ADT) method. Moreover, a new robust finite-time sliding-mode controller can be designed to ensure reachability of the common sliding surface in the estimation space. Finally, a numerical example is provided to illustrate our theoretical results.

In this article, an adaptive fuzzy fixed-time fault-tolerant tracking control problem for high-order nonlinear systems (HONSs) with sensor and actuator faults is considered. The fuzzy logic systems are introduced to approximate the unknown nonlinear functions of the HONS. In addition, based on backstepping technology and fixed-time theory, an adaptive fuzzy fixed-time fault-tolerant controller is developed to ensure that all the signals of the closed-loop HONS are bounded. Eventually, a numerical example can be shown to prove the rationality of the developed method

This article proposes two adaptive asymptotic tracking control schemes for a class of interconnected systems with unmodeled dynamics and prescribed performance. By applying an inherent property of radial basis function (RBF) neural networks (NNs), the design difficulties aroused from the unknown interactions among subsystems and unmodeled dynamics are overcome. Then, in order to ensure that the tracking errors can be suppressed in the specified range, the constrained control problem is transformed into the stabilization problem by using an auxiliary function. Based on the adaptive backstepping method, a time-triggered controller is constructed. It is proven that under the framework of Barbalat's lemma, all the variables in the closed-loop system are bounded and the tracking errors are further ensured to converge to zero asymptotically. Furthermore, the event-triggered strategy with a variable threshold is adopted to make more precise control such that the better system performance can be obtained, which reduces the system communication burden under the condition of limited communication resources. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed control scheme.

In this work, a neural-networks (NNs)-based adaptive asymptotic tracking control scheme is presented for a class of uncertain nonstrict feedback nonlinear systems with time-varying full-state constraints. First, we construct a novel exponentially decaying nonlinear mapping to map the constrained system states to new system states without constraints. Instead of the traditional barrier Lyapunov function methods, the feasible conditions which require the virtual control signals satisfying the constraint requirements are removed. By employing the Nussbaum design method to eliminate the effect of unknown control gains, the general assumption about the signs of the unknown control gains is relaxed. Then, the nonstrict feedback form of the system can be pulled back to the strict feedback form through the basic properties of radial basis function NNs. Simultaneously, the intermediate control signals and the desired controller are constructed by the backstepping process and the Nussbaum design method. The designed controller can ensure that all signals in the whole closed-loop system are bounded without the violation of the constraints and hold the asymptotic tracking performance. In the end, a practical example about a brush dc motor driving a one-link robot manipulator is given to illustrate the effectiveness of the proposed design scheme.

This article presents a global adaptive neural-network-based control algorithm for disturbed pure-feedback nonlinear systems to achieve zero tracking error in a predefined time. Different from the traditional works that only solve the semiglobal bounded tracking problem for pure-feedback systems, this work not only achieves that the tracking error globally converges to zero but also guarantees that the convergence time can be predefined according to the user specification. In order to get the desired predefined-time controller, first, a mild semibound assumption for nonaffine functions is skillfully proposed so that the design difficulty caused by the structure of pure feedback can be easily solved. Then, we apply the property of radial basis function (RBF) neural networks (NNs) and Young's inequality to derive the upper bound of the term that contains the unknown nonlinear function and external disturbances, and the designed adaptive parameters decide the derived upper and robust control gain. Finally, the predefined-time virtual control inputs are presented whose derivatives are further estimated by utilizing finite-time differentiators. It is strictly proved that the proposed novel predefined-time controller can guarantee that the tracking error globally converges to zero within predefined time and a practical example is shown to verify the effectiveness and practicability of the proposed predefined-time control method.

This article studies a security issue in remote distributed consensus estimation where sensors transmit their measurements to remote estimators via a wireless communication network. The relative entropy is utilized as a stealthiness metric to detect whether the data transmitted through the wireless network are attacked. The performance degradation induced by an attacker that attempts to be stealthy or undetected is analyzed, and the corresponding false-data attack strategy is characterized, which can achieve the maximal integrated mean-square error (IMSE). Finally, the tradeoff between the performance degradation and attack stealthiness level is evaluated through an example.

In this article, a fuzzy logic system (FLS)-based adaptive optimized backstepping control is developed by employing reinforcement learning (RL) strategy for a class of nonlinear strict feedback systems with unmeasured states. For making the virtual and actual controls are optimized solution of the corresponding subsystem, RL of observer-critic-actor architecture based on FLS approximations is constructed in every backstepping step, where the observer aims to estimate the unmeasurable states, and the critic and actor aim to evaluate control performance and perform control behavior, respectively. In the proposed optimized control, on the one hand, the state observer method can avoid to require the design constants making its characteristic polynomial Hurwitz, which is universally demanded in the existing observer methods; on the other hand, the RL is significantly simple in algorithm, because the critic and actor training laws are derived from the negative gradient of a simple positive function, which is produced from the partial derivative of Hamilton–Jacobi–Bellman (HJB) equation, instead of the square of approximated HJB equation. Therefore this optimized scheme can be more easily applied and widely extended. Finally, from two aspects of theory and simulation, it is demonstrated that the desired objective can be fulfilled.

This study proposes the time-/event-triggered adaptive neural control strategies for the asymptotic tracking problem of a class of uncertain nonlinear systems with full-state constraints. First, we design a time-triggered strategy. The effect caused by the residuals of the estimation via radial basis function (RBF) neural networks (NNs), and the reasonable upper bounds on the first derivative of the reference signal and the derivative of each virtual control, can be eliminated by designing appropriate adaptive laws and utilizing the basic properties of RBF NNs. Moreover, the construction of the barrier Lyapunov functions (BLFs) in this work ensures the compliance of the full-state constraints and also holds the asymptotic output tracking performance. Then, based on the time-triggered strategy, we further design a relative threshold event-triggered strategy. The proposed event-triggered adaptive neural controller can solve the main control objective of this work, that is: 1) the full-state constraint requirements of the system are not violated and 2) the output signal asymptotically tracks the reference signal. Compared with the traditional method, the event-triggered strategy can improve the utilization of communication channels and resources and has greater practical significance. Finally, an example of single-link robot under the proposed two strategies illustrates the validity of the constructed controllers.

This article addresses the problem of adaptive finite-time neural tracking control for nonstrict-feedback nonlinear systems via dynamic surface (DS) technique. First, a new quasi-fast finite-time practical stability (QFPS) criterion is proposed for a class of general nonlinear systems. Then, the presented QFPS criterion is applied to design the desired adaptive finite-time neural tracking controller for a class of nonstrict-feedback nonlinear systems. The presented design scheme for the nonstrict-feedback nonlinear system has the following two features: 1) the “explosion of complexity” issue of the backstepping design is addressed by utilizing the DS technique and 2) the structural feature of Gaussian functions is applied to solve the design difficulties caused by the nonstrict-feedback form. It is proved that the designed controller for the nonstrict-feedback nonlinear system can make the resulting closed-loop system stabilizable in a quasi-fast finite time and the tracking error converges to a sufficiently small neighborhood of the origin. Finally, the simulation results are given to show the validity and practicability of the proposed design scheme.

This article proposes a novel attack detection approach based on zonotopes for linear parameter-varying (LPV) systems with unknown-but-bounded (UBB) noises. The following three types of attacks are considered: 1) denial-of-service (DoS) attacks; 2) replay attacks (RAs); and 3) false-data-injection (FDI) attacks. In order to reduce the conservativeness, a free-weighting matrix is introduced, which can be computed by solving an optimization problem. Moreover, the radius of the intersection zonotope can be guaranteed to be limited as well. Furthermore, it is not necessary to acquire the knowledge about the specific type of attack in advance. Finally, a numerical example is given to illustrate the validity of the given method.

This article addresses the asynchronous event-triggered control problem for switched Takagi–Sugeno (T–S) fuzzy systems under data injection attacks. In reducing communication data update frequency, event-triggered control is an effective control method. The periodic sampling-based adaptive event-triggering schemes with switching structure are first proposed, which can dynamically adjust triggered conditions based on system performance. It is assumed that only the event-triggered and quantized data of the system state and the event-triggered switching signal are available for controllers. However, since the switching signal is sampled and triggered, asynchronous switching may occur between subsystems and subcontrollers. Furthermore, the data injection attacks are considered in the communication network of the system. A time-delay closed-loop switched T–S fuzzy system model is obtained by using a model transformation technique. The resulting criterion provides sufficient conditions to ensure that the closed-loop system subject to data injection attacks is exponential stability with an$H_{\infty }$performance. Moreover, a set of conditions for the co-design of controllers and adaptive event-triggering schemes is presented. Finally, simulations are given to verify the effectiveness of the asynchronous event-triggered control design.

In this paper, we propose an optimal event-triggered tracking control scheme for completely unknown nonlinear systems under the adaptive dynamic programming (ADP) framework. A data-driven model based on recurrent neural networks (RNNs) is first constructed to model the system uncertainties including the drift dynamics and the input gain matrix, and the modeling error caused by NN approximation is well eliminated through adding a compensation term in the data-driven model such that the model state can asymptotically track the system state. Apart from the traditional construction of optimal tracking controllers, in this paper, an augmented system is developed and a discounted performance function is considered to achieve the optimality. By employing the Bellman optimal principle, an event-triggered tracking Hamilton–Jacobi–Bellman (HJB) equation is then formulated. The approximate solution of the HJB equation can be obtained by virtue of a critic NN, which significantly simplifies the implementation architecture of ADP. Both the historical state data and the current state data are incorporated into the updating of the weight vector in the critic NN, in this circumstance, the persistence of excitation assumption is not needed anymore. It is strictly proven via Lyapunov stability theory that the tracking error state and the critic NN weight are uniformly ultimately bounded. Simulation results examine the validity of the design scheme.

This article investigates the observer-based finite-time H∞control problem for interconnected fuzzy systems with quantization and random network attacks, where two types of network attacks including denial-of-service (DoS) and fault data injection (FDI) attacks are considered. In order to achieve the occupancy reduction of network resources, the measured outputs of interconnected systems are quantized through a logarithmic quantizer before being transmitted by the communication channel. Combining the effects of quantization and random network attacks, an observer-based control model is first constructed. Then, based on Lyapunov functional approach and stochastic analysis technique, some sufficient conditions are presented such that the considered closed-loop interconnected system is stochastically finite-time bounded with a prescribed disturbance attenuation level, and the gain matrices of fuzzy observer and fuzzy controller can be found by solving an optimization algorithm with linear matrix inequalities constraints. Finally, two simulation examples are given to illustrate the validity of the proposed approach.

In this article, a decentralized adaptive finite-time tracking control scheme is proposed for a class of nonstrict feedback large-scale nonlinear interconnected systems with disturbances. First, a practical almost fast finite-time stability framework is established for a general nonlinear system, which is then applied to the design of the large-scale system under consideration. By fusing command filter technique and adaptive neural control and introducing two smooth functions, the "singular" and "explosion of complex" problems in the backstepping procedure are circumvented, while the obstacles caused by unknown interconnections are overcome. Moreover, according to the framework of practical almost fast finite-time stability, it is shown that all the closed-loop signals of the large-scale system are almost fast finite-time bounded, and the tracking errors can converge to arbitrarily small residual sets predefined in an almost fast finite time. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed finite-time decentralized control scheme.

In this paper, we address the adaptive neural tracking control problem for a class of uncertain switched stochastic nonlinear pure-feedback systems with nonlower triangular form. The significant design difficulty is the completely unknown nonlinear functions with all state variables that can neither be directly estimated by radial basis function (RBF) neural networks (NNs) nor be eliminated by the traditional backstepping technique. To achieve the control objective of this paper, a common state-feedback controller for all subsystems is first systematically constructed by using the common coordinate transformation, the variable separation technique, and the universal approximation capability of RBF NNs. Then the stability analysis shows that the semi-global bounded in probability of the whole closed-loop switched system can be obtained and the desired tracking performance can also be insured under a class of switching signals with the average dwell time property. Finally, simulation results are given to demonstrate the effectiveness of the obtained control scheme.

In this article, an adaptive approximation-based output-feedback tracking control scheme is presented for a class of stochastic switched lower-triangular nonlinear systems with input saturation and unmeasurable state variables. First, to overcome the design obstacle caused by the nondifferential saturation nonlinearity, a carefully selected nonlinear function of the control input signal is applied to estimate the saturation function. Then, a reduced-order state observer is designed to model the unmeasured system states, which also means the error system can be established. Furthermore, the fuzzy-logic systems are utilized to approximate the unknown system nonlinearities in the adaptive backstepping-based controller design procedure. It is ensured that all the closed-loop system variables are bounded in probability and the error signal belongs to a compact set in the mean square sense. Finally, the effectiveness and the practicability of the proposed control scheme are shown by two examples.

This paper deals with event-triggered H∞filtering problem for switched continuous-time systems with quantization. A multiple periodic sampling-based event-triggering strategy is adopted to select those “necessary” sampled signals to be transmitted. As a result, the amount of communication and the frequency of signal updates can be reduced significantly. Regarding the nonideal communication network, we consider network-induced delays and packet disorders, which are common during packet transmission through networks. In order to cope with packet disorders, an active packet loss approach is introduced. As such, a new time-delay system model is established, by which the filtering error system is modeled as a switched system with an interval time-varying delay. Then, by employing piecewise Lyapunov functional method and average dwell time technique, some criteria are derived to ensure that the filtering error system can achieve a prescribed level of H∞performance. Moreover, the relationship between switching instants and the data updating instants in filter is discussed in detail, and the filter gains and event-triggering parameters can be jointly designed in terms of solutions to some linear matrix inequalities. Finally, numerical simulation is provided to verify the effectiveness of the proposed method.

In this paper, the problem of adaptive neural tracking control for a type of uncertain switched nonlinear nonlower-triangular system is considered. The innovations of this paper are summarized as follows: 1) input to state stability of unmodeled dynamics is removed, which is an indispensable assumption for the design of nonswitched unmodeled dynamic systems; 2) the design difficulties caused by the nonlower-triangular structure is handled by applying the universal approximation ability of radial basis function neural networks and the inherent properties of Gaussian functions, which avoids the restriction that the monotonously increasing bounding functions of the nonlower-triangular system functions must exist; and 3) multiple Lyapunov functions are utilized to develop a backstepping-like recursive design procedure such that the solvability of the adaptive neural tracking control issue of all subsystems is unnecessary. Based on the proposed controller design methods, it can be obtained that all signals in the closed-loop switched system remain bounded and the tracking error can eventually converge to a small neighborhood of the origin. In the simulation study, two examples are supplied to prove the practicability and feasibility of the developed design schemes.

In this article, we study the issue of adaptive neural output-feedback controller design for a class of uncertain switched time-delay nonlinear systems with nonlower triangular structure. The prominent contribution of this article is that the delay-dependent stability criterion of nonswitched nonlinear systems is successfully extended to that of switched nonlower triangular nonlinear systems. The design algorithm is listed as follows. First, a switched state observer is designed such that the error dynamic system can be generated. Second, neural networks, adaptive backstepping technique, and variable separation method are, respectively, applied to construct a common controller for all subsystems, in which the Lyapunov-Krasovskii functionals are deliberately constructed such that the average dwell-time scheme can be employed to guarantee the stability and performance of the closed-loop system, despite the existence of time delays. Third, the stability analysis process confirms in detail that all the variables of the closed-loop system are semiglobally uniformly ultimately bounded. Finally, simulation study is given to show the validity of the proposed control approach.

In this paper, the problem of adaptive neural state-feedback tracking control is considered for a class of stochastic nonstrict-feedback nonlinear switched systems with completely unknown nonlinearities. In the design procedure, the universal approximation capability of radial basis function neural networks is used for identifying the unknown compounded nonlinear functions, and a variable separation technique is employed to overcome the design difficulty caused by the nonstrict-feedback structure. The most outstanding novelty of this paper is that individual Lyapunov function of each subsystem is constructed by flexibly adopting the upper and lower bounds of the control gain functions of each subsystem. Furthermore, by combining the average dwell-time scheme and the adaptive backstepping design, a valid adaptive neural state-feedback controller design algorithm is presented such that all the signals of the switched closed-loop system are in probability semiglobally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood of the origin in probability. Finally, the availability of the developed control scheme is verified by two simulation examples.

In this paper, an adaptive neural-network-based dynamic surface control (DSC) method is proposed for a class of stochastic interconnected nonlinear nonstrict-feedback systems with unmeasurable states and dead zone input. First, an appropriate state observer is constructed to estimate the unmeasured state variables of the stochastic interconnected system. Then radial basis function neural networks combined with adaptive backstepping technique are applied to model the unknown nonlinear system functions of the stochastic interconnected system; and the DSC method is adopted to ensure the computation burden is greatly reduced. Furthermore, the proposed controllers guarantee that the closed-loop stochastic interconnected system is semi-globally bounded stable in probability. In the end, two simulation examples are provided to show the effectiveness and practicability of the proposed control scheme.

In this paper, a novel neural-network (NN)-based adaptive tracking controller design method is presented for the single-input/single-output nonlinear stochastic switched systems in lower triangular structures with an output constraint. First, a well-designed nonlinear mapping is introduced to transform the switched stochastic system to a new system without constraints, which implies the controller design of the transformed system is equivalent to that of the stochastic switched system. Then radial basis function NNs are applied to model the unknown nonlinearities and the adaptive backstepping technique is employed to construct two classes of adaptive neural controllers under different adaptive laws. It is proved that both controllers can assure all the signals in the closed-loop remain bounded in probability, and the tracking error finally converges to a neighborhood of the origin without violating the constraint. Furthermore, the use of the nonlinear mapping to deal with the asymmetric output constraint is also studied as a generalization result. Two illustrative examples with numerical data and simulation results are given to show the validity and performance of the proposed control schemes.

This paper is concerned with the trajectory tracking control problem of a class of nonaffine stochastic nonlinear switched systems with the nonlower triangular form under arbitrary switching. Fuzzy systems are employed to tackle the problem from packaged unknown nonlinearities, and the backstepping and robust adaptive control techniques are applied to design the controller by adopting the structural characteristics of fuzzy systems and the common Lyapunov function approach. By using Lyapunov stability theory, the semiglobally uniformly ultimate boundness in the fourth-moment of all closed-loop signals is guaranteed, and the system output is ensured to converge to a small neighborhood of the given trajectory. The main advantages of this paper lie in the fact that both the completely nonaffine form and nonlower triangular structure are taken into account for the controlled systems, and the increasing property of whole state functions is removed by using the structural characteristics of fuzzy systems. The developed control method is verified through a numerical example.

This brief proposes a new neural-network (NN)-based adaptive output tracking control scheme for a class of disturbed multiple-input multiple-output uncertain nonlinear switched systems with input delays. By combining the universal approximation ability of radial basis function NNs and adaptive backstepping recursive design with an improved multiple Lyapunov function (MLF) scheme, a novel adaptive neural output tracking controller design method is presented for the switched system. The feature of the developed design is that different coordinate transformations are adopted to overcome the conservativeness caused by adopting a common coordinate transformation for all subsystems. It is shown that all the variables of the resulting closed-loop system are semiglobally uniformly ultimately bounded under a class of switching signals in the presence of MLF and that the system output can follow the desired reference signal. To demonstrate the practicability of the obtained result, an adaptive neural output tracking controller is designed for a mass-spring-damper system.

This paper deals with the issue of adaptive observer-based stabilization for a more general class of uncertain switched stochastic nonlower triangular nonlinear systems with average dwell-time (ADT) switching. The completely unknown nonlinear functions possessing the entire states are handled using the neural networks universal approximation property and the variable separation technique. The main novelty of this paper is that it presents a universal formula for constructing an adaptive output-feedback controller of the considered system with only one adaptive parameter by designing a switched state observer. The theoretical analysis shows that the Lyapunov stability of the overall closed-loop system is ensured in the presence of ADT switching. Finally, the effectiveness and practicability of the obtained design scheme are illustrated by two simulation examples.

This paper deals with the problem of robust stabilization for a class of uncertain nonlinear pure-feedback switched time-delay systems with quantized input signal. In order to overcome the design difficulty caused by the quantization and unpredictable switchings, a nonlinear decomposition strategy for quantizer is employed in advance. In the controller design procedure, the unknown time-delay terms are compensated by utilizing Lyapunov-Krasovskii functionals, the desired virtual stabilizing functions and desired actual control input are approximated by applying radial basis function neural networks, and dynamic surface control technology are used to handle the issue of “explosion of complexity” in the traditional backstepping procedure. Furthermore, it is shown that the resulting closed-loop system are stable in the sense of semi-global uniformly ultimately bounded. Finally, to verify the effectiveness and applicability of the presented control scheme, an example is given to construct an adaptive neural controller for an electromechanical system.

In this paper, a new adaptive approximation-based tracking controller design approach is developed for a class of uncertain nonlinear switched lower-triangular systems with an output constraint using neural networks (NNs). By introducing a novel barrier Lyapunov function (BLF), the constrained switched system is first transformed into a new system without any constraint, which means the control objectives of the both systems are equivalent. Then command filter technique is applied to solve the so-called "explosion of complexity" problem in traditional backstepping procedure, and radial basis function NNs are directly employed to model the unknown nonlinear functions. The designed controller ensures that all the closed-loop variables are ultimately boundedness, while the output limit is not transgressed and the output tracking error can be reduced arbitrarily small. Furthermore, the use of an asymmetric BLF is also explored to handle the case of asymmetric output constraint as a generalization result. Finally, the control performance of the presented control schemes is illustrated via two examples.

This paper considers the problem of adaptive fuzzy backstepping-based output-feedback controller design for a class of uncertain switched nonlinear stochastic systems in lower-triangular form without the measurements of the system states. By combining fuzzy logic systems' universal approximation ability and dynamic surface control technique in the adaptive backstepping recursive design with a modified average dwell-time scheme, a new adaptive fuzzy control approach is presented for the switched system. More specifically, a switched observer is constructed to reduce the conservativeness aroused by the employ of a common observer, and individual coordinate transformations for subsystems are given up by adopting a common coordinate transformation of all subsystems. It is proved that the overall closed-loop system is stable in the sense of semi-globally uniformly ultimately bounded in mean square, and the output of the switched system converges to a small neighborhood of the origin with appropriate choice of design parameters. Finally, simulation studies are provided to demonstrate the validity of the proposed control method.

In this paper, the problem of switching stabilization for a class of switched nonlinear systems is studied by using average dwell time (ADT) switching, where the subsystems are possibly all unstable. First, a new concept of ADT is given, which is different from the traditional definition of ADT. Based on the new proposed switching signals, a sufficient condition of stabilization for switched nonlinear systems with unstable subsystems is derived. Then, the T-S fuzzy modeling approach is applied to represent the underlying nonlinear system to make the obtained condition easily verified. A novel multiple quadratic Lyapunov function approach is also proposed, by which some conditions are provided in terms of a set of linear matrix inequalities to guarantee the derived T-S fuzzy system to be asymptotically stable. Finally, a numerical example is given to demonstrate the effectiveness of our developed results.

This paper aims to discuss the H∞control problem of nonlinear stochastic switched systems in case where both global asymptotically stable in the mean (GASiM) subsystems and unstable subsystems coexist. An average dwell time (ADT) scheme is established to show us that the system is GASiM, if the activation time of GASiM subsystems is comparatively longer than that of unstable ones. Further, some conditions upon the H∞performance of the stochastic switched system are provided. The effectiveness of the proposed result is illustrated by a simulation example.