This article aims to investigate the neural network (NN) nonsingular fixed-time adaptive consensus control issue for nonlinear multiagent systems (MASs) with parameter uncertainties. By introducing a generalized intermediate-variable-based disturbance observer (IVBDO), a novel distributed fixed-time NN adaptive controller is constructed based on the quartic Lyapunov function method. Under this protocol, the mismatched external disturbances of each agent are real-time online estimated; meanwhile, the singularity phenomenon during the fixed-time design process can be effectively eliminated. The presented control algorithm not only guarantees that the controlled system is semi-globally uniformly ultimately bounded (SGUUB) but also that the distributed output tracking errors converge to an adjustable compact set of the origin within a fixed-time interval. Simulation results are displayed to check the effectiveness of the suggested approach.

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 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 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.

In this paper, an observer-assisted model free adaptive predictive control algorithm is designed for nonlinear heterogeneous multi-agent systems under denial-of-service (DoS) attacks. To begin with, consensus error of the system is transformed into an equivalent linear data model at the operating point by means of a dynamic linearisation technique. Thereafter, in order to conserve network communication resources, a dynamic event-triggering mechanism is devised for the consensus error and an observer is incorporated to facilitate the acquisition of a time-varying parameter called "pseudo partial derivative" in the linear data model. Subsequently, to mitigate impact of random DoS attacks, we introduce an attack compensation strategy that allows each agent’s output to swiftly revert to the neighbourhood of leaderless consensus objective in DoS-free intervals. Finally, the pseudo partial derivative parameter estimates, observation errors, and consensus errors are rigorously proved to be bounded in mean using the contraction mapping principle. Simulation results on heterogeneous nonlinear multi-agent systems demonstrate that, compared with conventional event-triggered model free control, the proposed approach improves the convergence rate by 33.82%, reduces steady-state consensus error by 93.80%, and decreases pre-convergence fluctuations by 21.91%. Furthermore, it achieves a 64.00% faster recovery speed and a 95.98% higher recovery accuracy after DoS attacks. Meanwhile, the average communication load is reduced by 59.79%.

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.

Inspired by backstepping method, this paper proposes a novel adaptive stabilizing control method for a class of uncertain underactuated nonlinear systems, which is named as underactuated adaptive backstepping. Firstly, based on a virtual controller and a partial differential equation (PDE), a residual system is constructed. Then, a novel coordinate transformation is introduced to analyse the adaptive stabilizing control problem of the residual system, which breaks through the restriction of strict feedback form and achieves the estimation of unknown parameters. The proposed method first applies backstepping to form a residual system, and then uses backstepping again to design an adaptive controller for the residual system. The stability of the proposed method is proven based on Lyapunov’s theorems. Finally, two actual underactuated examples with physical damping are provided to demonstrate the effectiveness of the proposed underactuated adaptive backstepping.Note to Practitioners—This paper aims to develop a novel underactuated adaptive scheme called underactuated adaptive backstepping for underactuated mechanical systems. This scheme can effectively address the parameter uncertainty problem and achieve good control effect, even if there is uncertain physical damping which may change the equilibrium point in the system. Compared with existing methods, this scheme provides a novel design approach without linearization and approximation, which fully promotes the development of backstepping in the underactuated field. Moreover, the simulation experiments are carried out on the inertia wheel pendulum and ball and beam system with physical damping, thus effectively proving the feasibility of this scheme. In the future, the scheme will be applied to practical mechanical systems.

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.

Tower cranes play an important role in construction, whose performance can determine the efficiency and safety of building construction. Payloads (end-effectors) must be transported along desired paths to ensure work efficiency and obstacle avoidance, rather than point to point. In this paper, an end-effector tracking controller is designed for 5-DOF underactuated tower cranes. Based on the proposed system transformation, tower cranes can be described as cascade systems including actuated and unactuated subsystems. A novel nonlinear coupling variable is defined between actuated (positions and speeds of jibs, trolleys and rope lengths) and unactuated (positions and speeds of payload swing angles) states according to position of end-effectors. The developed control strategy is constructed by block backstepping and the stability analysis is given based on approximate linearization to ensure its mathematical rigor. Finally, the developed end-effector tracking controller is applied to an actual laboratorial tower crane to demonstrate its superiority by comparing to the existing control strategies. The experimental results show that the tracking accuracy of payloads is 35.3% and the maximum swing angle of payloads is 62.65% of the existing controllers.

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 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 paper studies the event-triggered time-varying formation control problem for nonlinear multi-agent systems with actuator faults. Based on the neural network approximation technique, a neural observer is constructed to estimate the unmeasured states of systems. Then, a distributed adaptive event-triggered time-varying formation control manner is proposed utilizing the intermittent estimated states information from the agent and its neighbors. To overcome the problem that estimated states triggering leads to virtual control laws is non-differentiable, a distributed continuous control scheme under regular output-feedback is designed firstly, upon which a distributed event-triggered controller is constructed by replacing estimated states with intermittent estimated ones. It is shown that the designed event-triggered output-feedback time-varying formation fault-tolerant controller can compensate for actuator faults, and all signals in closed-loop systems are semi-globally uniformly ultimately bounded. Finally, simulation results of a practical example are given to verify the effectiveness of the proposed control manner.Note to Practitioners—Formation control has broad application prospects in modern military and civilian fields, such as combat aircraft flying formation, satellite formation, autonomous vehicle formation, etc. In formation control systems, when agents occur actuator faults, it may break the original formation and even cause collision between agents. As a result, the security of formation control systems is facing great challenges in practical engineering applications. On the other hand, communication bandwidth is limited in practical engineering systems, and how to make systems quickly form formation under the limited communication bandwidth has become a key topic. Inspired by the above discussions, a distributed state-triggered output-feedback time-varying formation fault-tolerant control scheme is designed in this paper, in which actuator faults are compensated by using adaptive technology. Meanwhile, to sufficiently save the usage of system communication resources, a dual-channel event-triggered mechanism is designed.

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.

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.

This article focuses on an observer-based adaptive sensor fault compensation fixed-time tracking control problem for uncertain nonlinear systems. A sixth-power Lyapunov function is designed for the first time which lays the foundation to construct the effective adaptive fixed-time fault compensation mechanism. Meanwhile, in the controller design procedure, owing to the existence of the sensor fault, only the actual output can be measured, unlike existing results, an improved state observer is constructed to estimate the unmeasured states effectively. Under our developed control mechanism, all closed-loop signals are bounded within fixed-time interval, observation errors and tracking error can converge into a small domain around zero. Simulation verifies the availability of the presented approach further.

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.

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.

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.

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.

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.

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.

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.

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.

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 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.

This article considers the issue of adaptive fuzzy predefined-time control for nonlinear systems. Fuzzy logic systems (FLSs) are introduced to estimate the uncertain nonlinear functions. The command filter technology is applied to overcome the difficulty of “explosion of complexity”. The error compensation mechanism is adopted to compensate the error generated via command filter. Based on the backstepping technique, a fuzzy adaptive predefined-time command filter control scheme is presented. The presented control strategy demonstrates that all the signals in closed-loop system are bounded and the tracking error can converge to a small area near zero within predefined time. The simulation results illustrate the validity of the developed control strategy.

Fractional-order chaotic systems show great potential in secure communications because of their unique properties. In order to improve their encryption and anti-attack capabilities, a new compounding mechanism is developed for fractional-order multidrive and response chaotic systems. Rather than using simple addition, which is often employed in existing work, the compounding is based on multiplication, making the system topology much more complex and difficult to predict. A synchronization method is thus developed for the compounded system using a projective approach and the synchronization error is able to converge to zero within the range defined by a prescribed performance function. In addition, the developed synchronization controller represents a general form, and it can be easily transformed into other methods by choosing different design parameters. Simulation results and comparative analysis are also carried out between the proposed and prior control techniques to illustrate the effectiveness of the presented scheme.

In this article, the adaptive tracking control problem is considered for high-order stochastic nonlinear time-delay systems in fixed-time. Being different from existing results, an improved Lyapunov-Krasovskii function is designed, which can not only compensate for the time-delay term but also remove the obstacle from the high-order term. Due to the introduction of the Lyapunov-Krasovskii function into the total Lyapunov function, it makes it difficult to stabilize the controlled system within a fixed-time interval. L'Hopital's rule is used to determine the boundedness of the Lyapunov-Krasovskii function, and the fixed-time boundedness of the integral functions can be inferred. By utilizing the fixed-time Lyapunov stability theorem, it is proved that the controlled system is semi-globally practical fixed-time stable (SGPFS), all the closed-loop signals (CLSs) are bounded within the fixed-time interval, and the tracking error converges into a small region around zero. The validity of the designed scheme is substantiated via 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.

This research studies the adaptive fast finite-time tracking control problem for switched nonlinear systems with full-state constraints. In this design procedure, the barrier Lyapunov function is used to solve the difficulty from state constraints. The uncertain nonlinear functions in the original system are identified by applying the approximation of fuzzy logic systems. A linear common state observer is designed to estimate the unknown states. Based on adaptive backstepping technique and barrier Lyapunov functions, a fast finite-time adaptive tracking control scheme is proposed via the common Lyapunov function method. The designed controller enables that all the signals in the resulting system remain bounded and all the states do not suffer from violation in fast finite time. At last, a simulation example proves the effectiveness of the proposed control strategy.

This article considers the predefined-time composite adaptive attitude control problem for nonlinear multiple six-rotor unmanned aerial vehicles (UAVs) with external disturbance. The multiple six-rotor UAVs considered are regarded as nonlinear multiagent systems, and each subsystem has multiple inputs. Via the backstepping recursive algorithm, a valid adaptive predefined-time control method is proposed by combining fuzzy logic systems (FLSs) and predefined-time theory. FLSs are utilized to handle unknown nonlinearity and unmodeled parts in attitude systems. By constructing a serial-parallel estimation model, the accuracy of approximating the unknown functions is ameliorated. Moreover, taking into account the prediction error of the serial-parallel estimation model, a novel composite adaptive fuzzy control scheme is developed. Unlike some existing control schemes for multi-UAVs, the developed control scheme allows one to shun the chattering phenomenon and ameliorate the approximation performance. The developed controller assures that all signals of the multiple six-rotor UAV attitude systems are bounded and the tracking errors converge to a small neighborhood of the origin within an expected settling time. Eventually, with the help of simulation results, the effectiveness of the proposed control scheme was illustrated.

In this research, the adaptive neural network consensus control problem is addressed for a class of non-affine multiagent systems (MASs) with actuator faults and stochastic disturbances. To overcome difficulties associated with actuator faults and uncertain functions of the designed MAS, a neural network fault-tolerant control scheme is developed. Moreover, an adaptive backstepping controller is developed to solve the non-affine appearance in multiagent stochastic non-affine systems using the mean value theorem. Being different from the existing control methods, the developed adaptive fixed-time control approach can ensure that the outputs of all followers track the reference signal synchronously in the fixed time, and all signals of the controlled system are semi-globally uniformly fixed-time stable. The simulation results confirm that the presented control strategy is effective in achieving control goals.

The problem of adaptive neural fixed-time tracking control for high-order systems is addressed in this article. In order to handle the difficulties from the uncertain nonlinearities within the original systems, the radial basis function neural networks (RBF NNs) are introduced to approximate the unknown nonlinear functions, and the adding a power integrator is applied to overcome the obstacle from high-order terms. It is proven that all signals in the closed-loop system are bounded and the output signal can eventually converge to a small neighborhood of the reference signal. Simulation results further verify the approaches developed.

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 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.

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.

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 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 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 research addresses the finite-time control problem for nonaffine stochastic nonlinear systems with actuator faults and input saturation. Specifically, a new finite-time control scheme is constructed based on the adaptive backstepping framework, with the usage of a state observer and taking advantage of the universal approximation capability of the fuzzy-logic system (FLS). The novelty of this work is that it considers the output feedback problem of a completely nonaffine stochastic system and incorporates the idea of the dynamic surface control (DSC) design. By using the Lyapunov stability theory, all the signals of the controlled system can be semiglobal finite-time stable in probability (SGFSP) while the system is imposed with multiple actuator constraints. In the meantime, the problem of "complexity explosion" is avoided. Two simulation examples are given to demonstrate the validity of the presented 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.

This article takes into account the problem of adaptive fixed-time control for nonlinear systems in a strict form via finite-time command-filtered backstepping. Our presented control scheme gives consideration to rapidity by using fixed-time control and finite-time command filter, and its prime control objective is to ensure that the system output can be guided from any initial conditions to go after an ideal variable. Meanwhile, this control strategy makes sure that all the system states and other signals are bounded at finite time, and its convergence time does not have any connection with the system initial conditions and is determined by the design parameters. At every step in the design process, a fuzzy logic system is introduced to approximate the unknown part, and a finite-time command filter is also utilized so as to avoid the issue of derivation of virtual control laws and complex calculation. At last, we verify that the presented scheme is viable through a simulation example.

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 investigates the problem of adaptive fuzzy fixed-time control for a class of nonlinear systems subject to time-varying full-state constraints and actuator hysteresis. The fuzzy logic systems (FLSs) are employed to approximate the unknown nonlinear dynamics. A tan-type nonlinear mapping (NM) approach is used to solve the control problem of nonlinear systems with full-state constraints. The actuator hysteresis nonlinearities are expressed by differential equations with unknown parameters and combining the adaptive backstepping control technique with the fixed-time stability theory, an adaptive fuzzy fixed-time control method is presented. The proposed control scheme can guarantee the boundedness of all signals in the closed-loop system without violating the state constraints, and the output can accurately track the desired signals in a fixed time. Finally, the feasibility of the presented algorithm is verified by simulation results.

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.

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.

In this article, an adaptive nonlinear controller is developed for a class of stochastic systems, whose inputs are uncertainly nonlinear and virtual control gains (simplified as VCGs) include unknown and known items. A novel auxiliary function of boundedness and smoothness is constructed for handling the unknown items of VCGs. Aiming at the challenges of control laws without enough differentiability and uncertainties caused by deadzone and saturation of inputs, the novel control signals are proposed, which are tested on a nonsmooth system, SISO robot and MIMO quadrotor. The superiority and effectiveness of the designed control strategy are proved via the strict stability analysis and simulation comparisons.

This article is devoted to an adaptive tracking control problem for nonlinear systems with input deadzone and saturation, whose virtual control coefficients include the known and unknown terms. A novel smooth function is first introduced to approximate the input nonlinearities. By utilizing an auxiliary variable and the Nussbaum gain technique, an improved real control signal is constructed to handle the uncertainties of the virtual control coefficients and input nonlinearities. Furthermore, an adaptive tracking controller is constructed and applied to the attitude control of a quadrotor, which guarantees the boundedness of all the signals in the resulting closed-loop system. Finally, both stability analysis and simulation results validate the effectiveness of the developed control strategy.

In this article, finite-time-prescribed performance-based adaptive fuzzy control is considered for a class of strict-feedback systems in the presence of actuator faults and dynamic disturbances. To deal with the difficulties associated with the actuator faults and external disturbance, an adaptive fuzzy fault-tolerant control strategy is introduced. Different from the existing controller design methods, a modified performance function, which is called the finite-time performance function (FTPF), is presented. It is proved that the presented controller can ensure all the signals of the closed-loop system are bounded and the tracking error converges to a predetermined region in finite time. The effectiveness of the presented control scheme is verified through the simulation results.

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 considers the problem of prescribed performance control for a class of affine nonlinear systems with state constraints. Fuzzy logic systems (FLSs) are employed to cope with unknown nonlinear functions. In addition, an additive transformation and one-to-one mapping method are introduced to handle the control problem of nonlinear systems with full-state constraints. Then, based on adaptive backstepping control, we develop a new prescribed performance adaptive fuzzy control method, which not only makes the tracking error be constrained within the prescribed range but also ensures the other state variables do not violate the predefined constraints. The simulation example verify the feasibility of the control method.

This article presents a fuzzy finite-time command filtering output feedback control method for a class of nonlinear systems. A fast convergent output feedback control algorithm based on backstepping finite-time command filtering is developed. Fuzzy logic system is used to estimate uncertain functions in nonlinear systems. A fuzzy state observer is designed to measure the unknown state. The developed finite-time command filtering feedback control method overcomes well the computational complexity problem due to the calculation of the derivatives of virtual control signals. A compensation mechanism is also introduced to compensate for the error caused by the filter. The proposed method ensures not only that all signals in the closed-loop system are finite-time bound, but also that the tracking error converges to a small neighborhood around the origin. The effectiveness of the proposed method is demonstrated in the simulation results.

This article concentrates on the design of a novel event-based adaptive neural network (NN) control algorithm for a class of multiple-input-multiple-output (MIMO) nonlinear discrete-time systems. A controller is designed through a novel recursive design procedure, under which the dependence on virtual controls is avoided and only system states are needed. The numbers of the event-triggered conditions and parameters updated online in each subsystem reduce to only one, which largely reduces the computation burden and simplifies the algorithm realization. In this case, radial basis function NNs (RBFNNs) are employed to approximate the control input. The semiglobal uniformly ultimate boundedness (SGUUB) of all the signals in the closed-loop system is guaranteed by the Lyapunov difference approach. The effectiveness of the proposed algorithm is validated by a simulation example.

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 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.

This paper investigates the tracking control problem of a class of high-order distributed systems subjected to limited communication bandwidth. An event-triggered control method is proposed, where the controller is triggered only when specific events happen. Moreover, the computational complexity is reduced by introducing command filters for virtual control signals. Specifically, the backstepping scheme is adopted as the main design framework, by which the n-th order nonlinear system is divided into n command-cascaded first order subsystems. And virtual control commands are sent through a second-order low-pass filter, by which the time derivatives of the virtual commands can be obtained directly. The theoretical analysis shows the stability of the proposed method. The tracking performance is illustrated by a simulation example.

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.

The article investigates an adaptive practical fixed-time tracking control of nonlinear systems with prescribed boundary constraints. The main control objective is that the system output variable tracks the desired signal at fixed time, and the tracking error can also converge to the prescribed boundary constraints. Primarily, a new coordinate transformation is introduced, which will be utilized in the proposed controller. Next, based on the backstepping scheme, the sufficient conditions for the existence of the adaptive practical fixed-time tracking controller are presented. Meanwhile, the fuzzy logic systems are employed to approximate to unknown parts in the controlled system. Theoretical analysis shows that the tracking error converges to the prescribed boundary constraints at fixed time. At the same time, all the signals in the closed-loop controlled system are bounded and the controlled system is practically fixed-time stable. At last, simulation results verify the effectiveness of the proposed scheme by comparing the cases with/wihtout prescribed boundary constraints.

In this paper, we investigate the adaptive fast finite-time tracking control problem for a class of uncertain nonlinear strict-feedback systems by using backstepping technique and fast finite-time stable theory. Dynamic surface control approach is introduced to reduce the computational complexity because of the repeated differentiation of virtual signals in the traditional backstepping algorithm. By employing the approximation of fuzzy logic systems, a fuzzy-based adaptive fast finite-time output tracking control approach is presented, which can guarantee the convergence of tracking error and the boundedness of all closed-loop signals in the fast finite-time. In the final, the validity of the developed control method is proved by the simulation results.

The problem of fuzzy-based adaptive event-triggered tracking control is investigated for a class of non-strict-feedback nonlinear systems within fixed-time interval in this paper. Fuzzy logic system (FLS) is employed to approximate the packaged unknown nonlinearities. Event-triggered mechanism is employed to schedule the data transmission dependent upon errors exceeding certain threshold. And combining backstepping design algorithm with Lyapunov stability theorem, a fuzzy-based adaptive event-triggered controller is developed. The presented control scheme eliminates the singularity problem that may occur in the design process and guarantees the boundedness of all the closed-loop signals. And the tracking error converges into a small neighborhood of zero in fixed-time. Meanwhile, the Zeno behavior is also avoided. At last, the effectiveness of the proposed approach is demonstrated by simulation results.

This article investigates an adaptive practical fixed-time control strategy for the output tracking control of a class of strict feedback nonlinear systems. By utilizing a backstepping algorithm, finite-time Lyapunov stable theory, and fuzzy logic control, a novel adaptive practical fixed-time controller is constructed. Fuzzy logic systems are introduced to approximate the unknown items of the system. Theoretical analysis proves that under the presented control strategy, the closed-loop system is practically fixed-time stable, and the tracking error converges to a small neighborhood of the origin within a fixed-time interval, in which the convergence time has no connection with the initial states of the system. In the meantime, all the signals of the closed-loop system are bounded. Finally, a numerical example is presented to indicate the feasibility and effectiveness of the proposed method.

This paper addresses the finite-time tracking control problem for a class of nonaffine nonlinear systems with unknown dead zones using an adaptive fuzzy control scheme. The unknown nonlinear functions of the system are approximated by the fuzzy logic systems and a finite-time stability theorem is used to construct the control signal. The novelty of the proposed control method is that the tracking system can reach the stable equilibrium within a finite period of time without the knowledge of the boundaries of the dead zone parameters. The simulation results show that the system is semi-global practical finite-time stable and the tracking deviation converges to a small neighborhood of zero in a finite period of time.

This article focuses on an annular domain finite-time connectively bounded (ADFTCB) problem for a large-scale system with expanding construction (LSWEC). The LSWEC is built via adding new subsystems into the original system which is operating. Inspired by the notion of finite-time annular domain stability (FTADS), a new concept, ADFTCB, is presented in this article, and it is extended to LSWEC for the first time. First of all, the mathematical models of LSWEC and LSWEC with observer are built, and then the corresponding decentralized state-feedback stabilizers and output-feedback stabilizers with observers are designed with the aid of finite-time Lyapunov theory and linear matrix inequality (LMI) method which can make the closed-loop system ADFTCB. A simulation study is provided to demonstrate the feasibility and effectiveness of the presented strategy.

This paper, for the first time, presents an adaptive finite-time fuzzy funnel controller for nonaffine nonlinear systems via backstepping. To ensure the tracking error with prescribed boundedness, a modified transformation for funnel error is developed and embedded in the procedure of control design. The unknown packaged nonlinear functions appeared in the controller design process are approximated by using fuzzy logic systems. It is proved that the proposed method guarantees that the output tracking error falls within a preset funnel and all signals in the closed-loop system are semi-globally practically finite-time bounded (SGPFB). Simulations are carried out to demonstrate the effectiveness of the controller design scheme.

This paper addresses the trajectory tracking control problem of a class of nonstrict-feedback nonlinear systems with the actuator faults. The functional relationship in the affine form between the nonlinear functions with whole state and error variables is established by using the structure consistency of intermediate control signals and the variable-partition technique. The fuzzy control and adaptive backstepping schemes are applied to construct an improved fault-tolerant controller without requiring the specific knowledge of control gains and actuator faults, including both stuck constant value and loss of effectiveness. The proposed fault-tolerant controller ensures that all signals in the closed-loop system are semiglobally practically finite-time stable and the tracking error remains in a small neighborhood of the origin after a finite period of time. The developed control method is verified through two numerical examples.

This paper aims to give a design strategy on the prescribed performance H∞tracking control problem for a class of strict-feedback stochastic nonlinear systems based on the backstepping technique. Generally, by using the backstepping design method, the stochastic nonlinear systems can only be made to be bounded in probability and it is difficult to achieve the H∞performance criterion due to the positive constant term appeared in the stability analysis. Thus, a novel concept with regard to the bounded-H∞ performance is proposed in this paper to overcome the design difficulty. By using the new concept and the adaptive neural network technique as well as Gronwall inequality, an adaptive neural network prescribed performance bounded-H∞tracking controller is designed. Therein, neural networks are used to approximate the unknown packaged nonlinear functions. The assumption that the approximation errors of neural networks are square-integrable in some literature is eliminated. The designed controller guarantees that all the signals in the closed-loop stochastic nonlinear systems are bounded in probability, the tracking error is constrained into an adjustable neighborhood of the origin with the prescribed performance bounds, and the controlled system has a given H∞disturbance attenuation performance for external disturbances. Finally, the simulation results are provided to illustrate the effectiveness and feasibility of the proposed approach.

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.

This paper addresses the problem of adaptive neural output-feedback decentralized control for a class of strongly interconnected nonlinear systems suffering stochastic disturbances. An state observer is designed to approximate the unmeasurable state signals. Using the approximation capability of radial basis function neural networks (NNs) and employing classic adaptive control strategy, an observer-based adaptive backstepping decentralized controller is developed. In the control design process, NNs are applied to model the uncertain nonlinear functions, and adaptive control and backstepping are combined to construct the controller. The developed control scheme can guarantee that all signals in the closed-loop systems are semiglobally uniformly ultimately bounded in fourth-moment. The simulation results demonstrate the effectiveness of the presented control scheme.

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.

The state-feedback decentralized stabilization problem is considered for interconnected nonlinear systems in the presence of unmodeled dynamics. The functional relationship in affine form between the strong interconnected functions and error signals is established, which makes backstepping-based fuzzy control successfully generalized to strong interconnected nonlinear systems. By combining adaptive control with both backstepping design and the approximation property of fuzzy systems, an adaptive decentralized control algorithm is developed. It is demonstrated by both theoretical analysis and simulation study that the proposed control strategy ensures semiglobally uniformly ultimately bounded of all signals within the closed-loop systems.

In this paper, we propose a novel recurrent neural network to resolve the redundancy of manipulators for efficient kinematic control in the presence of noises in a polynomial type. Leveraging the high-order derivative properties of polynomial noises, a deliberately devised neural network is proposed to eliminate the impact of noises and recover the accurate tracking of desired trajectories in workspace. Rigorous analysis shows that the proposed neural law stabilizes the system dynamics and the position tracking error converges to zero in the presence of noises. Extensive simulations verify the theoretical results. Numerical comparisons show that existing dual neural solutions lose stability when exposed to large constant noises or time-varying noises. In contrast, the proposed approach works well and has a low tracking error comparable to noise-free situations.

This paper presents the development of an adaptive neural controller for a class of nonlinear systems with unmodeled dynamics and immeasurable states. An observer is designed to estimate system states. The structure consistency of virtual control signals and the variable partition technique are combined to overcome the difficulties appearing in a nonlower triangular form. An adaptive neural output-feedback controller is developed based on the backstepping technique and the universal approximation property of the radial basis function (RBF) neural networks. By using the Lyapunov stability analysis, the semiglobally and uniformly ultimate boundedness of all signals within the closed-loop system is guaranteed. The simulation results show that the controlled system converges quickly, and all the signals are bounded. This paper is novel at least in the two aspects: 1) an output-feedback control strategy is developed for a class of nonlower triangular nonlinear systems with unmodeled dynamics and 2) the nonlinear disturbances and their bounds are the functions of all states, which is in a more general form than existing results.

This paper presents an adaptive neural control approach for nonstrict-feedback nonlinear systems in presence of unmodeled dynamics, unknown control directions and input dead-zone nonlinearity. To handle the difficulty due to uncertain control directions, Nussbaum gain functions are applied. Based on the structural characteristic of radial basis function neural networks, a backstepping-based adaptive neural control algorithm is developed. The main contributions of this paper lie in the fact that a backstepping-based neural control algorithm is developed for nonstrict-feedback nonlinear systems with unmodeled dynamics, unknown control directions and actuator dead-zone, and the total number of adaptive laws is not greater than the order of control system. As a beneficial result, the controller is much easier to be implemented in practice with less computational burden. A simulation example is given to reveal the viability of the presented approach. It is demonstrated by both theoretical analysis and simulation study that the presented control strategy ensures the semiglobally uniform ultimate boundedness of all closed-loop system signals.

This paper investigates the uncertainty of the day-ahead distribution system scheduling considering the random variations of both Photovoltaic-based distributed generator (PV-DG) output power and load. Instead of Monte-Carlo simulation (MCS), a two-point estimation method (2PEM) is applied to obtain accurate and computation-efficient analysis results. Based on the two-year real-world hourly weather and load data in the city of Ottawa, the estimation accuracy of the 2PEM has been verified in an equivalent 44 kV distribution feeder system. In terms of computational efficiency, the 2PEM can significantly reduce the computation burden with comparison to MCS. By using the 2PEM, the impact of PV-DG output power and load variations on the uncertainty of the distribution system scheduling under different seasons is thoroughly studied. The analytical results show that the range of standard deviation of optimally scheduled DG generation for this distribution feeder system is larger in summer than that in winter.

This paper considers the master and slave synchronization control for bilateral teleoperation systems with time delay and backlash-like hysteresis. Based on radial basis functions neural networks' approximation capabilities, two improved adaptive neural control approaches are developed. By Lyapunov stability analysis, the position and velocity tracking errors are guaranteed to converge to a small neighborhood of the origin. The contributions of this paper can be summarized as follows: 1) by using the matrix norm established using the weight vector of neural networks as the estimated parameters, two novel control schemes are developed and 2) the hysteresis inverse is not required in the proposed controllers. The simulations are performed, and the results show the effectiveness of the proposed method.

In this paper, backstepping for a class of block strict-feedback nonlinear systems is considered. Since the input function could be zero for each backstepping step, the backstepping technique cannot be applied directly. Based on the assumption that nonlinear systems are polynomials, for each backstepping step, Lypunov function can be constructed in a polynomial form by sum of square (SOS) technique. The virtual control can be obtained by the Sontag feedback formula, which is equivalent to an optimal control-the solution of a Hamilton-Jacobi-Bellman equation. Thus, approximate dynamic programming (ADP) could be used to estimate value functions (Lyapunov functions) instead of SOS. Through backstepping technique, the control Lyapunov function (CLF) of the full system is constructed finally making use of the strict-feedback structure and a stabilizable controller can be obtained through the constructed CLF. The contributions of the proposed method are twofold. On one hand, introducing ADP into backstepping can broaden the application of the backstepping technique. A class of block strict-feedback systems can be dealt by the proposed method and the requirement of nonzero input function for each backstepping step can be relaxed. On the other hand, backstepping with surface dynamic control actually reduces the computation complexity of ADP through constructing one part of the CLF by solving semidefinite programming using SOS. Simulation results verify contributions of the proposed method.

This paper is concerned with the observer-based fuzzy output-feedback control for stochastic nonlinear multiple time-delay systems. On the basis of the consistent form of virtual input signals and increasing characteristics of the system upper bound functions, a variable splitting technique is employed to surmount the difficulty occurred in the nonlower-triangular form. In the controller design procedure, a state observer is first designed, and then an adaptive fuzzy output-feedback control method is presented by combining backstepping design together with fuzzy systems' universal approximation capability. The proposed adaptive controller guarantees the semi-global boundedness of closed-loop system trajectories in terms of fourth-moment. Two simulation examples are displayed to demonstrate the feasibility of the suggested controller.

This paper considers the problem of adaptive neural control of nonlower triangular nonlinear systems with unmodeled dynamics and dynamic disturbances. The design difficulties appeared in the unmodeled dynamics and nonlower triangular form are handled with a dynamic signal and a variable partition technique for the nonlinear functions of all state variables, respectively. It is shown that the proposed controller is able to ensure the semi-global boundedness of all signals of the resulting closed-loop system. Furthermore, the system output is ensured to converge to a small domain of the given trajectories. The main advantage about this research is that a neural networks-based tracking control method is developed for uncertain nonlinear systems with unmodeled dynamics and nonlower triangular form. Simulation results demonstrate the feasibility of the newly presented design techniques.

An approximation-based adaptive neural controller is constructed for uncertain stochastic nonlinear systems in nonstrict-feedback form appearing dead-zone and output constraint. Neural networks (NNs) are directly utilized to approximate the unknown nonlinear functions existing in systems. A barrier Lyapunov function is introduced to ensure that the trajectory of output is limited within a predetermined range. By integrating NNs into the backstepping technique, an adaptive neural controller is designed to guarantee all variables existing in the considered closed-loop system are semi-globally uniformly ultimately bounded, and by appropriately tuning several design parameters online, the tracking error can be converged to a small neighborhood of the origin. Simulations on a numerical example are given to demonstrate the effectiveness of the method proposed in this paper.

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.

Adaptive neural intelligent control is investigated for a class of pure-feedback nonlinear time-delay systems with unmodeled dynamics in nonlower-triangular form, which views the lower-triangular structure as a special structure. A variable partition technique is applied to surmount the difficulty in the nonlinear functions of whole state variables. By utilizing the backstepping recursive design approach and the universal approximation capability of neural networks, an adaptive neural controller is systemically designed. Then, based on the utilization of Lyapunov-Krasovskii functionals, the semiglobally uniform boundedness of all closed-loop signals is guaranteed. Finally, the suggested control method is verified through a numerical example. The main advantage of this paper is that an intelligent control method is developed for pure-feedback nonlinear systems with state time delay, unmodeled dynamics and nonlower triangular form. Further developments will focus on how to deal with the problem of output feedback control of pure-feedback nonlinear time-delay systems with unmodeled dynamics and nonlower-triangular structure.

In this paper, an adaptive neural decentralized control approach is proposed for a class of multiple input and multiple output uncertain stochastic nonlinear strong interconnected systems. Radial basis function neural networks are used to approximate the packaged unknown nonlinearities, and backstepping technique is utilized to construct an adaptive neural decentralized controller. The proposed control scheme can guarantee that all signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded in the sense of fourth moment, and the tracking errors eventually converge to a small neighborhood around the origin. The main feature of this paper is that the proposed approach is capable of controlling the stochastic systems with strong interconnected nonlinearities both in the drift and diffusion terms that are the functions of all states of the overall system. Simulation results are used to illustrate the effectiveness of the suggested approach.

In this paper, we consider the problem of observer-based adaptive neural output-feedback control for a class of stochastic nonlinear systems with nonstrict-feedback structure. To overcome the design difficulty from the nonstrict-feedback structure, a variable separation approach is introduced by using the monotonically increasing property of system bounding functions. On the basis of the state observer, and by combining the adaptive backstepping technique with radial basis function neural networks' universal approximation capability, an adaptive neural output feedback control algorithm is presented. It is shown that the proposed controller can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded in the sense of mean quartic value. Simulation results are provided to show the effectiveness of the proposed control scheme.

This paper focuses on the problem of approximation-based adaptive fuzzy tracking control for a class of stochastic nonlinear time-delay systems with a nonstrict-feedback structure. A variable separation approach is introduced to overcome the design difficulty from the nonstrict-feedback structure. Mamdani-type fuzzy logic systems are utilized to model the unknown nonlinear functions in the process of controller design, and an adaptive fuzzy tracking controller is systematically designed by using a backstepping technique. It is shown that the proposed controller guarantees that all signals in the closed-loop system are fourth-moment semiglobally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value. Simulation results are provided to demonstrate the effectiveness of our results. Further developments will consider how to generalize the proposed strategy to nonstrict-feedback nonlinear systems with input nonlinearities.

This paper considers the problem of adaptive neural control of stochastic nonlinear systems in nonstrict-feedback form with unknown backlash-like hysteresis nonlinearities. To overcome the design difficulty of nonstrict-feedback structure, variable separation technique is used to decompose the unknown functions of all state variables into a sum of smooth functions of each error dynamic. By combining radial basis function neural networks' universal approximation capability with an adaptive backstepping technique, an adaptive neural control algorithm is proposed. It is shown that the proposed controller guarantees that all the signals in the closed-loop system are four-moment semiglobally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value. Simulation results further show the effectiveness of the presented control scheme.

This paper is concerned with the problem of adaptive fuzzy tracking control for a class of pure-feedback stochastic nonlinear systems with input saturation. To overcome the design difficulty from nondifferential saturation nonlinearity, a smooth nonlinear function of the control input signal is first introduced to approximate the saturation function; then, an adaptive fuzzy tracking controller based on the mean-value theorem is constructed by using backstepping technique. The proposed adaptive fuzzy controller guarantees that all signals in the closed-loop system are bounded in probability and the system output eventually converges to a small neighborhood of the desired reference signal in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the proposed control scheme.