A data-driven hierarchical control strategy is proposed to address the leader-following consensus problem for nonlinear networked multi-agent systems (MASs) with unknown dynamics under Byzantine attacks. The proposed hierarchical framework decouples the leader-following consensus control into leader state estimation and trajectory tracking, only using input/output data of systems. Specifically, a discrete-time distributed observer is first proposed to securely estimate the leader state utilizing the mean-subsequence-reduced-falgorithm, which effectively filters out malicious data from Byzantine agents in networked MASs. Then, a data-driven decentralized controller is developed to track the estimated leader state. In addition, we extend this strategy into a dynamic event-triggered data-driven hierarchical control algorithm, which not only securely achieves the leader-following consensus but also conserves network communication resources. Finally, simulation results demonstrate the effectiveness of the proposed methods.

In this paper, the practically predefined-time (PPT) consensus control problem is explored for nonlinear multiagent systems (MASs) affected by external disturbances and unknown control gains. First, a predefined-time disturbance observer is designed to eliminate the effects of lumped disturbance, ensuring that the rapid convergence of the lumped disturbance estimation error within predefined time. Second, a predefined-time dynamic surface filter is proposed to alleviate the issue of “explosion of complexity”. Then, the predefined-time controller is developed by combining smooth function to avoid singularity problem. By employing Lyapunov stability analysis, it is proven that the PPT stability of MASs can be ensured, which consensus tracking error can converge to a small region near zero within predefined time. The simulations further validate the efficacy and superiority of the proposed predefined-time control algorithm.

This paper addresses an event-triggered optimal connectivity-preserving formation control problem for a class of nonlinear multiagent systems (MASs) with limited communication ranges and input constraints. The connectivity-preserving, determined by the limited communication ranges, is achieved by introducing an error transformation. To achieve performance guarantee, a prescribed-time bound function is developed to predefine the settling time and steady-state accuracy for position-related consensus errors, while the settling time remains unaffected by initial conditions. Subsequently, an unconstrained optimal formation control problem is formulated through a non-quadratic cost function that incorporates transformed errors and non-quadratic utility function. On the other hand, a dynamic memory event-triggered mechanism (DMETM) is established to save communication resource, allowing dynamic variables with historical information to possess larger event-triggered intervals compared to traditional dynamic event-triggered mechanism. By using single critic neural network (NN) adaptive dynamic programming (ADP), a distributed event-triggered optimal formation controller is derived, where an improved weight updating law using past measurements ensures the learning ability of critic NN under finite excitation condition. The uniformly ultimately bounded stability of the closed-loop systems is proven using Lyapunov method while excluding Zeno behavior. Finally, the effectiveness of the proposed approach is demonstrated through a practical example involving mobile robots.

This paper investigates an adaptive iterative learning control (AILC) method for multiagent systems (MASs) performing multiple tasks. Different from traditional results for the single task, a multiple tasks case is considered in this work, which can complete various cooperative control. It should be pointed out that only one of the multiple tasks is performed in each iteration. For multiple tasks, a neural network (NN) is employed to create a mapping relationship between the input and output of nonlinearity, which is integrated into AILC to improve the control input. Additionally, an auxiliary signal is developed to compensate for the residual error caused by NN approximation and differentiator estimation. Then, a termination condition including mean square error and desired performance is established for the AILC method. By utilizing Lyapunov stability theory, it is proven that the tracking error converges to zero without termination condition and satisfies the desired accuracy with termination condition. In the simulation, multiple single-link manipulators are used to perform three different cooperative control tasks to validate the effectiveness of the proposed approach. Note to Practitioners—Most of the existing AILC methods are investigated to perform a single task for MASs. However, practical applications of MASs, such as manipulators, unmanned vehicles, and aerospace, often require the ability to perform multiple tasks. One motivation is to effectively learn control experience from different tasks. To achieve this, an NN is designed to learn experiences, which are further incorporated into AILC method to perform multiple tasks. In addition, due to limitations in computing resources, controllers cannot be learned indefinitely in practical applications. To address this challenge, a termination condition is established to stop learning when the desired performance is met. Based on the above considerations, the proposed AILC method with termination condition can reduce computational resources and flexibly perform multiple tasks in practical applications.

This paper investigates the challenge of achieving event-triggered optimal consensus control for multiagent systems (MASs) with multiple constraints, encompassing saturation constraint at the input and performance constraint at the output. To achieve performance constraint while satisfying input saturation, a flexible prescribed performance method (FPPM) is designed. Utilizing non-negative signals generated by the improved auxiliary system to design the performance functions, the FPPM can adaptively adjust the performance constraint boundaries to ensure safe operation of the MASs with multiple constraints. Meanwhile, the proposed FPPM can achieve different performance behaviors by changing core parameters without the need to alter the control structure. Subsequently, a simplified reinforcement learning algorithm with actor-critic structure is integrated into the FPPM. By designing actor-critic neural networks and dynamic event-triggered mechanism, optimal consensus control for MASs under multiple constraint conditions is achieved cleverly while avoiding unnecessary communication transmissions. Finally, a simulation example verifies the effectiveness of the proposed method. Note to Practitioners—Considering the limitations of physical devices and the practical requirements for control performance, the input saturation constraint and performance constraint often coexist during the operation of practical systems, such as robotic systems, manipulator systems and aerospace systems. Therefore, this paper aims to design an event-triggered reinforcement learning algorithm for MASs with multiple constraints. To resolve the conflict problem caused by input saturation and performance constraint, a FPPM with adjustable performance functions is proposed. By flexibly adjusting the performance constraint boundaries, the coexistence problem of multiple constraints can be solved effectively. Meanwhile, the constructed FPPM framework can achieve various performance behaviors by adjusting parameters according to the practical application scenario without changing the controller structure. Additionally, the proposed event-triggered reinforcement learning algorithm can optimize the designed cost function and promote the utilization of communication resources.

In this article, we concentrate on the adaptive fuzzy containment control approach for a class of nonlinear multiagent systems with deferred constraint and actuator failure. First, considering that not all agents can directly receive the leader signals, this article constructs a distributed prescribed-time estimator to provide each agent with a corresponding reference signal, thereby the containment problem is constructed as a tracking problem. Subsequently, with the help of the prescribed-time scaling function and the barrier function, the problem of deferred output constraint is reformulated as a boundedness problem of the new variable. By introducing several useful lemmas, the designed controller can ensure that the closed-loop signals are bounded in the presence of actuator fault in the system. In addition, through the designed fuzzy control algorithm, it can strictly guarantee that the system output converges within the ideal range after the settling time. The superiority and effectiveness of this method are verified through robots experiments.

This article addresses the problem of distributed fuzzy adaptive pinning control for multiagent systems with output saturation via adopting the dynamic event-triggered mechanism. With the framework of the backstepping technique, a new adaptive pinning control protocol is developed, where an effective fuzzy strategy and a class of tuning functions are integrated into the control protocol to reduce the required design adaptive parameters. Then, the output saturation of nonlinear multiagent systems is first addressed via the signal compensation method. Moreover, a dynamic event-triggered mechanism about control information is proposed, where two dynamic laws are designed to further increase the adjustment margin of the controller. Finally, simulation results are utilized to demonstrate the suitability and feasibility of theoretical algorithm.

In this article, we focus on the distributed group asynchronous consensus problem for cyber-physical systems (CPSs) with unknown dynamics and switching topologies. This article considers a class of networked distributed CPSs composed of cloud computing systems, and it is subjected to delay detection models and topology switching. First, an asynchronous switching observer is tailored for each group of agents to guarantee the precise acquisition of the leader's information. Further, we introduce a model-free adaptive control method to devise controllers for each group of agents, which can continue to learn adaptively only from the agent's input and output data without knowing the agent dynamics. Finally, the stability of both the observer and controller are proved, respectively. The observers' and controllers' effectiveness is further confirmed by the simulation results.

This article focuses on the optimal consensus control problem for multiagent systems (MASs) with discontinuous constraints. The case of discontinuous constraints is a particular instance of state constraints, which has been studied less but occurs in many practical situations. Due to the discontinuous constraint boundaries, the traditional barrier function-based backstepping methods cannot be used directly. In response to this thorny problem, a novel constraint boundary reconstruction technique is proposed by designing a class of switch-like functions. The technique can convert discontinuous constraint boundaries into continuous ones, and it strictly proves that when the states satisfy the transformed constraint boundaries, the original constraints are also absolutely fulfilled. Meanwhile, with the aid of the barrier function and distributed event-triggered estimator, an improved coordinate transformation is constructed, which can remove the "feasibility condition" and simplify the controller design. In addition, by introducing prediction error and revised term into the learning process of neural networks (NNs), the optimal consensus problem is resolved by constructing a modified reinforcement learning strategy. Finally, the stability of the MASs is testified through the Lyapunov stability theory, and a simulation example verifies the effectiveness of the proposed method.

In this paper, the tracking control problem is studied in the model-free adaptive control (MFAC) framework for a class of discrete-time single-input single-output nonlinear systems affected by dynamic sparse attacks and measurement disturbances. The system outputs are measured by multiple sensors, but an attacker can manipulate nearly half of the sensors simultaneously in a time-varying manner. First, considering the communication burden caused by multiple sensors, a voting-based event-triggered mechanism is introduced to minimize data transmission under attacks. The triggering condition is designed according to tracking performance so that the system is updated only at the triggering instants while maintaining satisfactory control performance. Then, to minimize the effects of measurement disturbances and dynamic sparse attacks on the control performance of the MFAC algorithm, two data fusion algorithms are developed to estimate the system output from the transmitted data. Moreover, an event-triggered extended state observer is designed to mitigate the negative impact of nonlinear residual terms caused by estimation errors on the MFAC algorithm, and based on this, a controller that updates only at the triggering instants is designed. Finally, simulation examples confirm the effectiveness of the proposed MFAC algorithm.

This article proposes a distributed optimal attitude synchronization control strategy for multiple quadrotor unmanned aerial vehicles (QUAVs) through the adaptive dynamic programming (ADP) algorithm. The attitude systems of QUAVs are modeled as affine nominal systems subject to parameter uncertainties and external disturbances. Considering attitude constraints in complex flying environments, a one-to-one mapping technique is utilized to transform the constrained systems into equivalent unconstrained systems. An improved nonquadratic cost function is constructed for each QUAV, which reflects the requirements of robustness and the constraints of control input simultaneously. To overcome the issue that the persistence of excitation (PE) condition is difficult to meet, a novel tuning rule of critic neural network (NN) weights is developed via the concurrent learning (CL) technique. In terms of the Lyapunov stability theorem, the stability of the closed-loop system and the convergence of critic NN weights are proved. Finally, simulation results on multiple QUAVs show the effectiveness of the proposed control strategy.

In this article, an adaptive optimal consensus control problem is studied for multiagent systems (MASs) with external disturbances, unmeasurable states, and prescribed constraints. First, by using neural networks (NNs), a composite observer is constructed to estimate the unmeasurable states and disturbances simultaneously. Then, the consensus error is guaranteed within a prescribed boundary by presenting an improved prescribed performance control (PPC) technique, and the initial conditions for the error are eliminated. In addition, the updating laws of actor-critic NNs are established by using a simplified reinforcement learning (RL) algorithm based on the uniqueness of optimal solution, and the asymmetric input saturation is resolved by designing auxiliary system instead of using nonquadratic cost functions in other optimal control methods. Finally, the boundedness of all signals in the closed-loop system is proved by using Lyapunov stability theory. The effectiveness of the proposed control method is verified by a simulation example.

This article concentrates on the adaptive neural control approach of n -link flexible-joint electrically driven robots. The presented control method only needs to know the position and armature current information of the flexible-joint manipulator. An adaptive observer is designed to estimate the velocities of links and motors, and radial basis function neural networks are applied to approximate the unknown nonlinearities. Based on the backstepping technique and the Lyapunov stability theory, the observer-based neural control issue is addressed by relying on uplink-event-triggered states only. It is demonstrated that all signals are semi-globally ultimately uniformly bounded and the tracking errors can converge to a small neighborhood of zero. Finally, simulation results are shown to validate the designed event-triggered control strategy.

This article studies the fixed-time formation-containment control problem for a group of Euler-Lagrange (EL) systems with unknown disturbances. A layered control-oriented framework, composed of leader formation layer and follower containment layer, is constructed to realize the formation-containment (FC) performance. Firstly, two novel distributed fixed-time estimators with/without time-varying formation variables are developed to obtain the ideal position and velocity for each agent in the two layers, respectively. Then, an improved adaptive integral sliding mode disturbance observer (AISMDO) with reconstructed errors is established to obtain the estimation of external disturbances, which shows less conservatism and provides better estimation performance. Furthermore, considering the potential collisions among agents and obstacles, two artificial functions are incorporated into the backstepping technique to develop the adaptive fuzzy controller. Theoretical analysis shows that all signals in the closed-loop system are bounded in fixed time. Finally, an illustrative simulation is presented to validate the effectiveness of the proposed theoretical algorithm.

In the fault-tolerant control (FTC) tasks of nonstrict-feedback nonlinear systems, unmeasurable states, disturbance, and actuator faults are recognized as the main factors that obstacle the effective controller design and, thus, the tracking performance improvement. To tackle these obstructions, a fuzzy observer is introduced to address the difficulties of the unmeasurable states involving nonstrict-feedback nonlinear systems by benefiting from the approximation property of fuzzy logic systems. Owing to the newly employed damping term in the intermediate control law being utilized to compensate for the possibly unlimited number of faults, the proposed FTC strategy is able to deal with actuator faults properly without imposing tighter requirements on the fault mechanism. To reach fast transient performance, stability of finite time is reached by exploiting the backstepping method. The investigated strategy ensures that all the responses of the systems are semiglobal practical finite-time stable. Meanwhile, the tracking error converges to a small neighborhood of the origin within finite time. In addition, to demonstrate its effectiveness, the provided approach is applied to the position tracking of a robotic system, which shows anticipated control performances in spite of various uncertainties.

This paper considers the distributed containment control problem for human-in-the-loop (HiTL) multiagent systems (MASs) subject to unknown time-varying parameters and input saturation. A smooth function containing positive integrable time-varying function is embedded in the controller to compensate for the negative effects of unknown time-varying parameters and uncertain disturbances. Meanwhile, an auxiliary system with the same order as the considered system is skillfully introduced into the backstepping control method to overcome the problem of input saturation. By constructing an adaptive command filter with error compensation mechanism, the problems of the computation burden and filtering errors are solved simultaneously. Moreover, the output signals of followers can converge into the convex hull spanned by multiple dynamic leaders which are controlled by a human operator. Based on the Lyapunov stability theory, it is shown that the containment errors can asymptotically converge into the prescribed bounds. Finally, two simulation examples evaluate the effectiveness of the presented control scheme.

An adaptive fuzzy control strategy is proposed for a single-link flexible-joint robotic manipulator (SFRM) with prescribed performance, in which the unknown nonlinearity is identified by adopting the fuzzy-logic system. By designing a performance function, the transient performance of the control system is guaranteed. To stabilize the SFRM, a dynamic signal is applied to handle the unmodeled dynamics. To cut down the communication load of the channel, the event-triggered control law is developed based on the switching threshold strategy. The Lyapunov stability theory and backstepping technique are applied coordinately to design the control strategy. The semiglobally ultimately uniformly boundedness can be ensured for all signals in the closed-loop system. The designed control method can also guarantee that the tracking error can converge to a small neighborhood of zero within the prescribed performance boundaries. At the end of the article, two illustrative examples are shown to validate the designed event-triggered controller.

This article studies the fixed-time fuzzy adaptive bipartite containment quantized control problem for nonlinear multiagent systems subject to unknown external disturbances and unknown Bouc–Wen hysteresis. The output and input control signals of the systems are quantized by sector-bounded quantizer. A disturbance observer and a fuzzy state observer are simultaneously designed to estimate unknown external disturbances and unmeasured states, respectively. Then, to solve the difficulty caused by Bouc–Wen hysteresis, a distributed control strategy is presented by using the disturbance observer. In addition, the bipartite containment control performance of multiagent systems can be realized, and the stability of the closed-loop multiagent systems can be proved to be the semi-global practical fixed-time stability by Lyapunov theory and fixed-time theory. Finally, a practical simulation example is shown to demonstrate the effectiveness of the proposed scheme.

This article studies the command-filter-based fixed-time bipartite containment control problem for a class of nonlinear stochastic multiagent systems (MASs). The considered stochastic MASs in nonstrict feedback form is subject to unknown nonlinear functions and stochastic disturbances, which can be solved by exploiting the universal approximation property of radial basis function neural networks. In addition, the event-triggered mechanism is used to improve the utilization of communication resources while avoiding Zeno behavior. The control protocol based on the command-filtered backstepping technique is proposed to ensure that the followers can converge to the convex hull formed by the leaders. Moreover, the closed-loop stability of stochastic MASs is proved to be semiglobal practical fixed-time stability. Finally, a numerical example simulation and an actual system simulation about a group of five single-link manipulator systems are presented to verify the effectiveness of the proposed method.

This article considers the Nussbaum gain adaptive control issue for a type of nonlinear systems, in which some sophisticated and challenging problems, such as periodic disturbances, dead zone output, and unknown control direction are addressed. The Fourier series expansion and radial basis function neural network are incorporated into a function approximator to model time-varying-disturbed function with a known period in nonlinear systems. To deal with the problems of the dead zone output and unknown control direction, the Nussbaum-type function is recommended in the design of the control algorithm. Applying the Lyapunov stability theory and backstepping technique, the proposed control strategy ensures that the tracking error is pulled back to a small neighborhood of origin and all closed-loop signals are bounded. Finally, simulation results are presented to show the availability and validity of the analysis approach.

This article investigates the event-triggered containment control problem for stochastic nonlinear multiagent systems with unknown Bouc–Wen hysteresis input. Based on the backstepping technique, an adaptive fuzzy event-triggered containment control scheme is proposed, which is conditionally updated only at the sampled instants. Fuzzy logic systems are used to approximate the unknown nonlinear functions. In addition, a Nussbaum function is utilized to eliminate the effect of unknown hysteresis. Moreover, an event-triggered mechanism is introduced to reduce the communication burden. By using stochastic Lyapunov stability theory and graph theory, it is proved that all signals in the closed-loop system are semiglobally uniformly ultimately bounded. Meanwhile, all the followers’ outputs converge to the dynamic convex hull spanned by the dynamic leaders. Finally, the effectiveness of the proposed control scheme is illustrated by some simulation results.

The finite-time consensus fault-tolerant control (FTC) tracking problem is studied for the nonlinear multi-agent systems (MASs) in the nonstrict feedback form. The MASs are subject to unknown symmetric output dead zones, actuator bias and gain faults, and unknown control coefficients. According to the properties of the neural network (NN), the unstructured uncertainties problem is solved. The Nussbaum function is used to address the output dead zones and unknown control directions problems. By introducing an arbitrarily small positive number, the "singularity" problem caused by combining the finite-time control and backstepping design is solved. According to the backstepping design and Lyapunov stability theory, a finite-time adaptive NN FTC controller is obtained, which guarantees that the tracking error converges to a small neighborhood of zero in a finite time, and all signals in the closed-loop system are bounded. Finally, the effectiveness of the proposed method is illustrated via a physical example.

This paper studies the quantized cooperative control problem for multiagent systems with unknown gains in the prescribed performance. Different from the finite-time control, a speed function is designed to realize that the tracking errors converge to a prescribed compact set in a given finite time for multiagent systems. Meanwhile, we consider the problem of unknown gains and input quantization, which can be addressed by using a lemma and Nussbaum function in cooperative control. Moreover, the fuzzy logic systems are proposed to approximate the nonlinear function defined on a compact set. A distributed controller and adaptive laws are constructed based on the Lyapunov stability theory and backstepping method. Finally, the effectiveness of the proposed approach is illustrated by some numerical simulation results.

In this paper, an adaptive fuzzy output feedback control problem is investigated for a class of stochastic nonlinear systems in which the fuzzy logic systems are adopted to approximate the unknown nonlinear functions. A reduced-order observer and a general fault model are designed to observe the unavailable state variables and describe the actuator faults, respectively. An event-triggered control law is developed to reduce the communication burden from the controller to the actuator. Meanwhile, the barrier Lyapunov functions are constructed to guarantee that all the states of the stochastic nonlinear system are not to violate their constraints. Furthermore, an observer-based adaptive fuzzy event-triggered control strategy is proposed for the full-state-constrained nonlinear system with actuator faults based on backstepping technique, which can guarantee that all the signals in the closed-loop system are bounded and the tracking error converges to a small neighborhood of the origin in a finite time. Finally, simulation results are given to illustrate the effectiveness of the proposed control scheme.

This paper addresses the containment control problem of nonidentical networks with external disturbance via adaptive distributed observer method. We first present a formulation for containment error, which ensures all the followers' outputs converge to the convex hull spanned by the leaders' reference outputs. Then by using an adaptive distributed observer, the leaders' system matrices and the states of convex hull are both estimated. Furthermore, a novel global regulate equation is designed to restrain the external disturbance, and the problem of containment control for multiagent systems is solved by a dynamic output feedback approach. Finally, some simulation results are given to illustrate the validity of the theoretical results.

This paper investigates the adaptive tracking control problem for a class of uncertain single-input and single-output strict-feedback nonlinear systems with unknown control direction and disturbances. Dynamic surface control is utilized to handle the problem of “explosion of complexity” occurred in the conventional backstepping design. In order to escape analytic calculation, a first-order filter is used to generate the command signals and their derivatives. Moreover, Nussbaum function is employed to handle the problem of the unknown control coefficient. New controllers and adaptive laws are designed by combining the compensation tracking error and the prediction error that exist between the system state and the serial-parallel estimation model. It is proved that all the variables in the closedloop system are bounded and the tracking error is driven to the origin with a small neighborhood. Finally, the simulation results are presented to verify the effectiveness of the proposed approach.

This paper is focused on the observer-based adaptive fuzzy control problem for nonlinear stochastic systems with the nonstrict-feedback form, in which some complicated and challenging issues including unmeasurable states, input quantization and actuator faults are addressed. The fuzzy logic systems are introduced to approximate the nonlinear functions existing in the control system. A fuzzy observer is designed to observe the unavailable state variables. In order to handle the negative effects resulting from input quantization and actuator faults, a damping term with the estimation of unknown bounds as well as a positive time-varying integral function are constructed, respectively. Furthermore, an observer-based adaptive fuzzy control scheme is proposed for the considered systems to compensate for the effects of input quantization and actuator fault based on adaptive back-stepping approach. The proposed control strategy can guarantee that all the signals in the closed-loop system are bounded. Finally, simulation results are provided to illustrate the effectiveness of the proposed adaptive control scheme.

Adaptive fuzzy fault-tolerant control problem for a class of uncertain switched stochastic nonlinear systems with time-varying asymmetric output constraints is addressed in this study. Under the action of well-designed asymmetric nonlinear mapping, fuzzy control technology, and backstepping recursive design scheme; the actuator faults of both loss of effectiveness and lock-in-place are considered to develop the adaptive fuzzy controller. The boundedness of all signals as well as the convergence of the output tracking error of the closed-loop plant to an arbitrary small neighborhood about zero are guaranteed by the developed fuzzy adaptive control strategy, and the time-varying output constraints are not violated. A simulation example is worked out to demonstrate the validity of the proposed control scheme.