This paper concentrates on a fault detection-based performance recovery control scheme using an actuator replacing method. The main procedure includes: 1) an integral sliding-mode (ISM) based event-triggered nominal controller; 2) a shifting-function-assisted fault detection design; and 3) an event-triggered reconfigurable controller. Unlike existing FTC schemes, no prior fault model is required. Minor actuator faults are directly attenuated via ISM, whereas significant faults are handled by switching to a backup actuator. For both nominal and reconfigurable phases, a modified Hamilton-Jacobi-Bellman (HJB) equation is solved with a single critic neural network, and an experience replay mechanism mitigates the persistence of excitation requirement while reducing computational complexity. A shifting function guarantees that post-replacement reconstructed states re-enter the prescribed performance bound within a finite window, and an actuator-oriented event-triggered strategy lowers update frequency while ensuring single-actuator operation. The effectiveness of the proposed scheme is validated by two simulation examples.

Combining reinforcement learning (RL) and quantization methods, this article addresses the formation control problem for a class of multi-input multi-output (MIMO) nonlinear multi-agent systems (MASs) subject to denial-of-service (DoS) attacks. Since the information exchange between agents is destroyed by DoS attacks, the leader’s information becomes unavailable. Thus, a distributed formation estimator is designed to obtain the leader’s state. Next, by constructing an logarithmic quantizer, a new dynamic event-triggered quantized control strategy is studied to save communication resources. In order to satisfy both transient and steady-state performances, an improved funnel function is embedded in controller design. In addition, based on optimized backstepping technique, an actor-critic architecture is established to achieve optimized secure formation control by RL method. Finally, the simulation results verify the effectiveness of proposed control scheme.

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.

This paper studies the transient-state control of linear switched aero-engines with input saturation. Firstly, by formulating the problem as an input-to-state stability (ISS) property investigation of switched linear aero-engine models with saturated control input, a saturated controller coupled with an event-triggered mechanism (ETM) avoiding Zeno and asynchronous phenomena is developed. It shows that the ISS property of switched linear aero-engine models can be guaranteed utilizing the designed strategy. Then, in order to estimate the disturbance bound and the initial value domain, an optimization problem is proposed. Finally, an application study based on the GE-90K aero-engine is carried out to reveal the effectiveness of the proposed strategy. Simulation results show that the aero-engine can be transitioned to a desired steady-state point under the designed controller. In addition, comparisons and discussions demonstrate the advantages and potential significance of the work in practice.Note to Practitioners—Transient-state control is one of the most important problems in aero-engine control and affects the maneuverability of aircrafts. In addition, the saturation of controllers may lead to bad control performance. Thus, this paper is devoted to proposing a new control method for linear switched aero-engine models subject to input saturation. By designing a new controller coupled with an event-triggered mechanism, better transient-state performance compared with some existing methods, can be guaranteed.

This paper addresses the active disturbance rejection predefined-time consensus tracking problem for non-affine nonlinear multiagent systems (MASs) with self-triggered communication. With the active disturbance rejection strategy, the uncertainty of the system can be estimated and the issue of explosion of complexity under the backstepping framework is handled. To improve the utilization of network resources, a self-triggered mechanism that the next trigger moment is calculated from the current information is adopted, for communication of each follower. The advantage of this triggered mechanism is that the triggering conditions are not required to be continuously monitored. Meanwhile, a time-varying tuning function-based predefined-time method is designed to achieve convergence within the predetermined time. Compared with existing finite/fixed-time convergence consensus schemes, its biggest advantage is that the upper bound of convergence time can be a positive constant arbitrarily selected by users. Additionally, the problem of input saturation is considered in the controller design to improve the generality of our scheme. Finally, the effectiveness of the proposed scheme is verified via simulation example. Note to Practitioners—In this paper, the active disturbance rejection predefined-time consensus tracking control problem for MASs with non-affine properties is discussed, which is embodied in numerous applications, such as sensor networks, space satellites and robot formations. The convergence time required for all agents to conclude consensus is used as an important indicator to evaluate the control performance in the consensus control of MASs. The existing control methods including finite and fixed time methods can only achieve the system to converge in a preset time. Based on this, it is a challenging topic to achieve predefined-time convergence by setting the accurate convergence time t. Meanwhile, to improve the utilisation of network resources, a self-triggered mechanism is designed. The advantage of this triggered mechanism is that the triggering conditions are not required to be continuously monitored, which greatly reduces the control cost. Additionally, the problem of input saturation is considered in the controller design to improve the generality of our scheme.

This article focuses on a dynamic event-triggered adaptive neural networks backstepping control for a class of uncertain strict-feedback systems with communication constraints. The uncertain terms including external disturbances and unknown nonlinear functions are approximated by radial basis function neural networks, in which the weight update laws are obtained via the gradient descent algorithm, ensuring the local boundedness of the approximation error of neural networks. Then, to enhance the transmission efficiency of control signals, a dynamic event-triggered mechanism is introduced, which enables the dynamic adjustment of threshold parameters in response to the actual tracking performance. It is strictly proved via the Lyapunov stability criterion that the tracking error can converge to a desired small neighborhood of the origin, and all signals in the closed-loop system are bounded. Finally, the validity of the control strategy is demonstrated through a simulation example.Note to Practitioners— In practical network control systems, control signals are typically transmitted continuously or periodically to devices through the communication network in the form of data packets. As communication networks are usually shared by various system nodes, and resources such as communication channel bandwidth and computational capabilities are limited, improving the transmission efficiency of control signals becomes a crucial design problem for controllers in network control systems. Therefore, This study introduces a control method via event-triggered sampling, aiming to enhance sampling efficiency while ensuring the stability and reliability of the system. The proposed control method is suitable for a broad category of strict-feedback nonlinear systems with communication constraints, offering notable advantages such as low-complexity design and straightforward implementation.

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.

For the existing tracking control schemes of flexible-joint robots, precise sensor measurement is an implicit premise. However, idealized sensors are difficult to achieve due to manufacturing technology or other external factors. To this end, this paper further investigates the tracking control problem for flexible-joint robots with unknown measurement sensitivity. Specifically, for such multi-input multi-output Euler-Lagrange systems with completely unknown system dynamics, a novel measurement values-based adaptive control method is proposed by fusing sensitivity information and system variables into Lyapunov function candidates, where the restriction on system states in other the approximation lemma-based results is removed, since unknown nonlinearities are scaled by the structural characteristics of system variables. Above all, even if there are measurement errors, satisfactory tracking performance can be obtained by adjusting the design parameters, which is proved by rigorous theoretical analysis. Finally, hardware experiments further verify the effectiveness of the proposed method.Note to Practitioners—This work is motivated by the trajectory tracking control problem for flexible-joint robots under imprecise sensor measurements. Due to manufacturing technology limitations and component aging, there is inevitably a deviation between the measured values of sensors and real values, and this problem may become more prominent as the working environment of flexible-joint robots tends to become more complex. To our knowledge, most of the existing solutions for flexible-joint robots are developed based on precise sensor measurements, and they may fail to achieve satisfactory performance when real state information is not available. Moreover, the prior knowledge about model parameters and measurement sensitivity is difficult or impossible to exactly obtain in practice, which seriously hinders the further application of control methods that are dependent on system dynamics. To this end, this paper proposes a novel tracking control scheme based on measurement information for flexible-joint robots with unknown measurement sensitivity, where the dependence on model information is eliminated with the elaborately constructed Lyapunov function candidates, and the real tracking error is still adjusted to an acceptable range even if there are measurement errors. Preliminary experiments on a flexible-joint robot developed by Quanser company demonstrate the feasibility and effectiveness of the proposed method. In future studies, designing an effective scheme to achieve direct preset tracking control is the focus of the work.

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.

This paper investigates a zero-sum game (ZSG)-based fault-tolerant tracking control problem for a class of interconnected nonlinear systems, in which the faults of each subsystem can affect the other subsystems through couplings. First, a static control policy is developed to transform the fault-tolerant tracking control problem into a ZSG problem of a deduced error system, where the controllers and the faults are regarded as players with opposite interests. Then, based on the sliding mode control technology and the concept of hierarchical design, a novel robust control policy is proposed to regulate the tracking error while minimizing a special cost function. Subsequently, a critic neural network (NN) is trained online to derive the solution of the coupling HJI equation. The critic NN weights are tuned on the basis of the gradient descent approach as well as the historical stored data, such that the persistence of excitation conditions are no longer required. Finally, a simulation example is presented to demonstrate the validity of the proposed control strategy.Note to Practitioners—Since complex modern engineering systems are difficult to be controlled by a single component, the research on adaptive control of interconnected nonlinear systems has become the mainstream trend. In addition, for the practical applications of interconnected systems, fault problems are becoming more common. These faults may make the system difficult to operate normally. Hence, how to guarantee the normal work of the control system when subject to faults has become a hot topic. Furthermore, several engineering applications often take production cost as an important index, and thus it is necessary to design a control strategy that can achieve control objectives with the minimum cost. This paper discusses the optimal fault-tolerant control problem for interconnected nonlinear systems. Meanwhile, a hierarchical sliding-mode control mechanism is designed to improve system robustness.

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 article focuses on the problem of resilient event-triggered$H_{\infty }$filtering for networked switched Takagi–Sugeno (T-S) fuzzy systems in the presence of Denial-of-Service (DoS) attacks. To improve the utilization efficiency of communication resources and resist the influence of attacks, the resilient mode-dependent event-triggered strategy (ETS) is proposed to determine the necessary data transmission. Different from the existing ETSs for the switching linear systems, the proposed strategy not only removes the two adjacent trigger instants that are strictly less than the average dwell time constraint but also releases data immediately at the end of the attack to mitigate its side effects. Based on the transmitted switching signal and measurable output, the switching fuzzy filter is constructed to estimate the target signal. Unlike the traditional switching filter design, the transmission signals are affected by intermittent interruption of DoS attacks and ETS leads to the asynchronous behavior of system mode and filter mode, which increases the difficulty of filtering error system analysis and filter design. To overcome this challenge, a novel multiple Lyapunov function related to attack signals, system modes, and filter modes is established to analyze the exponential stability and$H_{\infty }$performance of the estimation error system. Furthermore, co-design methods regarding filter gains and event-triggered parameters are given. Finally, simulation results are carried out to substantiate the feasibility of the proposed approach.

This article studies the hierarchical sliding-mode surface (HSMS)-based adaptive optimal control problem for a class of switched continuous-time (CT) nonlinear systems with unknown perturbation under an actor-critic (AC) neural networks (NNs) architecture. First, a novel perturbation observer with a nested parameter adaptive law is designed to estimate the unknown perturbation. Then, by constructing an especial cost function related to HSMS, the original control issue is further converted into the problem of finding a series of optimal control policies. The solution to the HJB equation is identified by the HSMS-based AC NNs, where the actor and critic updating laws are developed to implement the reinforcement learning (RL) strategy simultaneously. The critic update law is designed via the gradient descent approach and the principle of standardization, such that the persistence of excitation (PE) condition is no longer needed. Based on the Lyapunov stability theory, all the signals of the closed-loop switched nonlinear systems are strictly proved to be bounded in the sense of uniformly ultimate boundedness (UUB). Finally, the simulation results are presented to verify the validity of the proposed adaptive optimal control scheme.

An adaptive neural bipartite tracking control approach is proposed for nonlinear multi-agent systems in this article. In contrast to previous results, it is worth noting that this paper considers a cooperative-competitive relationship in multi-agent systems, which stands for a more common situation. In this paper, a distributed self-triggered communication strategy is designed to improve the transmission efficiency of the whole system. In addition, the designed controller can compensate the actuator failure and dead-zone nonlinearity, and increases the system fault-tolerance. The proposed method ensures the boundedness of all signals of the closed-loop system and the bipartite tracking performance. The effectiveness of the proposed method is verified by two simulation examples.Note to Practitioners—Since complex modern engineering systems are difficult to be controlled by a single component, the cooperative control mode of multi-agent systems has become the mainstream trend. For multi-agent systems with cooperative-competitive relationships, the unique bipartite consensus will allow each agent to better complete the control objectives according to their respective advantages. In addition, for engineering systems such as automated manufacturing systems and transportation systems, fault problems are becoming more commonplace. These faults may make the system difficult to operate normally, and then affect the project progress. Therefore, how to guarantee the normal work of the control system when subject to faults has become a key topic. On the other hand, the channel bandwidth of the actual communication system is limited, and frequent updating of control signals will produce huge communication pressure in the traditional control scheme. Hence, it is challenging to design a control strategy that can achieve system stability and reduce communication resources simultaneously. This paper discusses the bipartite fault-tolerant control problem for nonlinear multi-agent systems. Meanwhile, a distributed adaptive self-triggered mechanism is designed to save communication resources.

This article investigates the hierarchical sliding-mode surface (HSMS)-based adaptive critic tracking control problem for nonlinear multiplayer zero-sum games (ZSGs). First, a generalized fuzzy hyperbolic model-based identifier is employed to approximate the unknown nonlinear functions. According to the derived data-driven model, a static control policy is proposed to transform the considered optimal tracking control problem into an optimal regulation control problem of an induced error system. Subsequently, based on sliding mode control technology and the concept of hierarchical design, a novel optimal feedback control policy is developed to regulate the tracking error by minimizing a performance index function related to the HSMS. The solution to the Hamilton–Jacobi–Isaacs equation of nonlinear multiplayer ZSGs is obtained via the HSMS-based critic neural network. Furthermore, the historical stored data are utilized to conquer the difficulty associated with the persistence of excitation conditions. Based on Lyapunov stability theory, it is strictly proven that the tracking error and the critic neural network weight are uniformly ultimately bounded. Finally, two examples are presented to demonstrate the effectiveness of the proposed control scheme.

This article proposes an adaptive neural-network command-filtered tracking control scheme of nonlinear systems with multiple actuator constraints. An equivalent transformation method is introduced to address the impediment from actuator nonlinearity. By utilizing the command filter method, the explosion of complexity problem is addressed. With the help of neural-network approximation, an adaptive neural-network tracking backstepping control strategy via the command filter technique and the backstepping design algorithm is proposed. Based on this scheme, the boundedness of all variables is guaranteed and the output tracking error fluctuates near the origin within a small bounded area. Simulations testify the availability of the designed control strategy.

This article presents an effective method to address the tracking control problem arising in uncertain switched high-order nonlinear system in strict-feedback form. The system under consideration contains unknown functions, which causally make the asymptotic tracking performance difficult to be achieved. By adopting the adding a power integrator approach in the framework of backstepping, a novel tracking controller is developed to guarantee an asymptotic tracking performance in the presence of the approximation error cased by neural networks (NNs) under arbitrary switching. The main contributions lie in: 1) the article for the first time embeds the backstepping technique in designing a kind of discontinuous controller with proportional integral (PI) compensation and 2) with the help of Filippov’s theory, a new defined system described by differential inclusions can be first obtained by taking some transformations, and then a novel nonsmooth Lyapunov function approach along with its upper right Dini derivative technique is applied to complete the construction of the discontinuous controller. Finally, two simulation examples are exhibited to verify the validity of the proposed design techniques.

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 considers the problem of event-triggered optimal control for discrete-time switched nonlinear systems with constrained control input. First, an event-triggered condition is given to make the closed-loop switched system asymptotically stable. Second, a novel method, event-triggered heuristic dynamic programming (ETHDP), is applied to derive the optimal control policy. Two neural networks (NNs) are utilized to approximate the value function and control law, respectively. When the event-triggered condition is violated, the weights of the two NNs are updated, which can decrease the networks calculation and transmission load notably. A proof of the convergence of the ETHDP is also carried out. Finally, the effectiveness of the proposed method is verified by an example.

In this article, the issue of adaptive neural fault-tolerant control (FTC) is addressed for a class of uncertain switched nonstrict-feedback nonlinear systems with unmodeled dynamics and unmeasurable states. In such a system, the uncertain nonlinear parts are identified by radial basis function (RBF) neural networks (NNs). Also, with the help of the structural characteristics of RBF NNs, the violation between the nontsrict-feedback form and backstepping method is tackled. Then, based on the small-gain technique, input-to-state practical stability (ISpS) theory, and common Lyapunov function (CLF) approach, an adaptive fault-tolerant tracking controller with only three adaptive laws is developed by designing an observer. It is shown that the designed controller can ensure that all the closed-loop signals are bounded under arbitrary switching, while the tracking error can converge to a small area of the origin. Finally, two simulation examples are provided to demonstrate the feasibility of the suggested control approach.