This paper investigates the preset trajectory tracking control problem of vehicular platoon systems (VPS) with state constraints and preassigned performance requirements using reinforcement learning (RL). Specifically, both velocity and acceleration constraints are simultaneously considered along with performance requirements, thus providing a more comprehensive guarantee of system safety and stability. Existing approaches based on barrier Lyapunov functions (BLF) can tackle these issues but are prone to nonlinear growth and singularity problems, which complicates controller design. To overcome these limitations, a novel two-step state transformation strategy is proposed. First, a nonlinear mapping function (NMF) is employed to reconstruct the states, embedding velocity and acceleration constraints directly into the transformed state space. Second, a preset-trajectory-based preassigned performance control (PPC) strategy is adopted to convert the performance requirements into a tracking task. This strategy effectively mitigates nonlinear growth and singularity issues, simplifying controller design and stability analysis. On this basis, a simplified RL algorithm based on neural networks (NNs) within the actor–critic framework is integrated with the backstepping method, to enhance the overall control performance. The proposed method guarantees internal stability and string stability of the platoon. Simulation results validate the effectiveness and advantages of the proposed method.

This paper investigates constrained multi-autonomous underwater vehicle (AUV) systems with hysteresis output. First, two novel shift functions are proposed to construct new state variables, addressing the issue of initial position and velocity variables of AUVs exceeding predefined boundaries. Based on these new state variables and combined with a coordinate transformation method, asymmetric time-varying full-state constraints independent of the initial conditions are achieved. Moreover, an innovative predefined-time convergence criterion is introduced. Based on this criterion, the proposed strategy ensures robust consensus within a predefined time under asymmetric full-state constraints, while effectively handling external disturbances, hysteresis, and saturation issues. A novel scaling inequality related to the hyperbolic tangent function is also proposed. Based on this scaling inequality, the sign function is replaced with the hyperbolic tangent function in the controller, and the proposed control scheme completely avoids issues of singularity and chattering. By leveraging neural networks (NN) and adaptive parameters to manage uncertainties and complex terms, the proposed control scheme successfully avoids the explosion of complexity. Notably, through adaptive parameter estimation, the negative impacts on system stability caused by deviations of the neural network weight matrix from its optimal value and approximation errors introduced by the neural network are mitigated. The closed-loop system is proven to be predefined-time stable. In addition, the sensitivity of the system to measurement noise is analyzed, and a NN-based observer is proposed to significantly mitigate the adverse effects caused by noise. Finally, the effectiveness of the proposed control scheme is validated through numerical simulation.

This paper is concerned with the fixed-time optimal bipartite containment control issue for stochastic nonlinear multiagent systems in the presence of unknown Bouc-Wen hysteresis. Initially, under the optimized backstepping framework, the approximation solution of the Hamilton-Jacobi-Bellman equation is obtained via the reinforcement learning algorithm. Then, the neural networks are utilized to shape an identifier-critic-actor structure to approximate unknown dynamics, evaluate system performance, and implement control behavior, respectively. Moreover, an intermediate variable is devised to cope with the unknown control coefficient resulting from Bouc-Wen hysteresis. Theoretical analysis shows that all states of the closed-loop system are semi-global practical fixed-time stable, and its convergence time is capable of adjusting by choosing appropriate design parameters. Finally, a numerical example is performed to solidify the effectiveness of the proposed strategy. Note to Practitioners—It is well known that fixed-time convergence is one of the significance performance metrics in many industrial systems including manipulator systems, robotic systems as well as unmanned aerial systems. Motivated by this fact, this article devotes the first attempt to investigate the fixed-time optimal bipartite containment control issue for stochastic nonlinear multiagent systems in the presence of unknown Bouc-Wen hysteresis according to the reinforcement learning control strategy. Theoretical analysis and simulation examples both show that all state signals of the closed-loop system are semi-global practical fixed-time stable, and its convergence time is capable of adjusting by choosing appropriate design parameters.

This paper explores event-triggered impulsive bipartite consensus for multi-agent systems (MASs) with random actuation delay and quantization communication. In these control systems, event-triggered delayed impulse control (ETDIC) has been developed through a combination of continuous monitoring and periodic data acquisition. This approach ensures that both continuous measurement and periodic sampling methods are incorporated into its design and implementation. By using Lyapunov method, the systems achieve mean-square exponential bipartite consensus. For the continuous event-triggered mechanism (ETM), Zeno behavior is excluded. For periodic ETM, furthermore provided is an upper constraint on the sampling period. Lastly, the theoretical conclusions are validated using numerical examples.

This article investigates the problem of bipartite synchronization with a non-autonomous leader in fractional-order multi-layer signed network. To address the chattering phenomenon induced by the use of sign functions in existing studies for mitigating the influence of bounded unknown leader inputs, a continuous controller and a dynamic event-triggered controller are proposed, respectively. The continuous controller is introduced a decay function to ensure the continuity of the control input, thereby effectively avoids chattering. The dynamic event-triggered controller leverages the characteristics of event-triggered control, the input remains constant within triggered intervals, which confines discontinuities to discrete triggering instants. This approach not only eliminates chattering but also reduces the frequency of control updates. Besides, the measurement error is designed by synchronization error and introduce a new trigger mechanism, avoiding the issue of the existence of the fractional-order right-Dini derivative at zero caused by measurement error designed through the controller with the sign function. Notably, the controllers proposed in this paper are not only applicable to non-autonomous systems but also to those subject to external disturbances as well as traditional autonomous leader systems. The stability of the error system is demonstrated by Lyapunov method. In the end, the proposed corollaries and theorems are verified by three simulations.

This article aims at the leader-following secure consensus problem of nonlinear multiagent systems (MASs) with switching topologies, where the agents are not only suffered from the aperiodic malicious denial-of-service (DoS) attacks but also affected by instantaneous disturbance from the external environment. Due to the existing challenge of instantaneous disturbance about occurrence time being unknown, the impulsive-based switching network structure is put forward to tackle the impact of external instantaneous disturbance on MASs. Then, a novel hybrid event-triggered and impulsive control protocol is developed to guarantee that nonlinear MASs can resist DoS attacks and achieve the consensus control objective. Contrasted with the methods of continuous control, the developed hybrid event-triggered and impulsive control protocol using the discontinuous sampled state has certain merits saving control resources. Based on the Lyapunov theory, the stability of the closed-loop system is proven, and the Zeno behavior can be excluded successfully. An example is supplied to elicit the availability of the presented methodology.

Phase-change memory (PCM) is a novel type of nonvolatile memory and is suitable for artificial neural synapses. This article investigates the Lagrange global exponential stability (LGES) of a class of PCNNs with mixed time delays. First, based on the conductivity characteristics of PCM, a piecewise equation is established to describe the electrical conductivity of PCM. By using the proposed piecewise equation to simulate the neural synapses, a novel PCNN with discrete and distributed time delays is proposed. Then, using comparative theory and fundamental inequalities, the LGES conditions based on the M-matrix are proposed in the sense of Filippov, and the exponential attractive set (EAS) is obtained based on M-matrix and external input. Moreover, the Lyapunov global exponential stability (GES) conditions of PCNNs without external input are obtained by using the inequality technique and eigenvalue theory, which is a form of M-matrix. Finally, two simulation examples are given to verify the validity of the obtained results.

Ever since the reinforcement learning (RL) method was proposed, the optimal control problem for multiagent systems (MASs) has been intensively explored in light of the limitation of the control resource. However, most of the consequences have overlooked the denial-of-service (DoS) attacks which are often encountered in engineering scenarios. Thus, the current investigation makes the first attempt to explore the optimized containment control issue with a dynamic event-triggered mechanism for heterogeneous stochastic MASs subject to DoS attacks. For the purpose of achieving optimal control, the optimized backstepping technique is developed by resorting to a simplified RL algorithm based on the identifier–critic–actor structure. Then, a novel dynamic event-triggered mechanism is put forward to update the control input signals only at triggering instants so as to reduce the communication burden. Furthermore, by means of stochastic Lyapunov stability theory, it is verified that all signals in the closed-loop system are cooperatively semi-globally uniformly ultimately bounded in probability, in the simultaneous presence of disturbances and DoS attacks. Finally, the validation of the presented strategy is demonstrated via a simulation example.

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

In this article, a neuroadaptive event-triggered containment control strategy combined with the dynamic surface control (DSC) approach is proposed for nonlinear multiagent systems (MASs) with input saturation. Based on the event-triggered communication mechanisms, the updates of neural network weight and controllers are implemented solely under triggering conditions of violation, which markedly reduces unnecessary communication resources and minimizes inefficient control costs compared with the traditional control method. Radial basis function neural networks (RBF NNs) are employed to handle the nonlinear uncertainties of MASs. Simultaneously, an adaptive compensatory mechanism is incorporated within the backstepping process to address the nonlinear effect posed by input saturation. Additionally, we demonstrate the system stability by extending the Lyapunov theorem to jump and continuous scenarios while excluding Zeno behavior, realizing that all followers can enter the convex hull constructed by leaders. Finally, the effectiveness of the proposed methodology is verified through application simulations.

This article studies the optimized adaptive finite-time consensus control issue for stochastic nonlinear multiagent systems subject to non-affine nonlinear faults. Under the architecture of the adaptive optimized backstepping method, this article develops the neural-network-based simplified reinforcement learning algorithm with an identifier-critic-actor structure, where the identifier, critic and actor are put forward to estimate unknown dynamics, evaluate system performance and implement control behavior, respectively. Then, the Butterworth low-pass filter is introduced to compensate for the adverse effects brought by non-affine nonlinear faults. Furthermore, it is verified by Itô differential equation and the finite-time theory that the closed-loop system is semi-global finite-time stable in probability. Finally, the effectiveness of the control algorithm is illustrated by simulation examples.Note to Practitioners—This paper was motivated by the problem of finite-time convergence is one of significance performance index in many practical application. For systems with high transient performance standards, such as robotic systems, manipulator systems and unmanned aerial systems, finite time convergence is of practical importance. Accordingly, distinguished from the previous investigation results, this article develops the neural-network (NN)-based simplified reinforcement learning (RL) algorithm with an identifier-critic-actor structure, where the identifier, critic and actor are put forward to estimate unknown dynamics, evaluate system performance and implement control behavior, respectively. We believe that the novel research method will bring a research spring for the constrained systems. Preliminary simulation experiments suggest that this approach is feasible. In future research, we will address the fixed time control protocol designs for nonlinear multi-agent systems.

This paper investigates a neuro-adaptive fixed-time tracking control issue for switched nonlinear systems subject to asymmetric time-varying constraints and unknown control gains. Unlike the current study on constraint problems, the system’s initial condition is unavailable in this article, which causes specific difficulties in constructing the Barrier Lyapunov Function. A novel shifting function is presented to unify the initial values of all system states. In addition, the system convergence time becomes known and adjustable by utilizing the Nussbaum gain technique and fixed-time stability criterion. An adaptive neural tracking control scheme is proposed based on the learning ability of neural networks and fixed-time theory. To alleviate the computational burden, we present the single learning parameter method such that the number of adaptive laws is reduced significantly. Furthermore, a novel switching threshold mechanism that considers the system errors is developed to balance the communication burden and control performance. Finally, the simulation example illustrates the feasibility of the proposed control strategy.

This article investigates a leader-following bipartite consensus issue for uncertain nonlinear heterogeneous multiagent systems (MASs). Initially, within the framework of optimal control theory, we employ the reinforcement learning (RL) algorithm to derive an approximate solution to the Hamilton-Jacobi-Bellman equation (HJBE). Specifically, the neural networks (NNs) are utilized to construct the Actor-Critic structure with the aim of implementing control behavior and evaluating system performance, respectively. An additional network is employed to address nonlinear uncertainties existing in the system. Furthermore, we design a static threshold event-triggered mechanism (ETM) to achieve the event-triggered state feedback-based control strategy. By utilizing this event-triggered state information, we reconstruct the approximate optimal controller and update laws of neural network weights, effectively reducing the communication burden while ensuring that all signals of the MASs remain bounded. Finally, two simulation examples are carried out to demonstrate the feasibility of the proposed method.

The current investigation explores the leader-following consensus problem for nonlinear multiagent systems under the output feedback control mechanism and the event-triggered communication mechanism. Owing to the physical instrument constraints, a significant portion of the state variables is not readily available. Therefore, this article put forward a distributed event-based leader-following consensus protocol only using agents' relative output measurements and underlying neighbors. Furthermore, this article develops two event-triggered mechanisms simultaneously, one is the event-triggered communication mechanism in the sensor-to-controller channel, and another is the event-triggered controller update in the controller-to-actuator track. Besides that, it is proven that the developed event-triggered control protocol can settle the leader-following consensus problem of the nonlinear multiagent systems, and the Zeno behavior is excluded in both the channels. Finally, we perform two simulation examples to illustrate the efficacy of the obtained results.

This article investigates the event-triggered adaptive containment control problem for a class of stochastic nonlinear multiagent systems with unmeasurable states. A stochastic system with unknown heterogeneous dynamics is established to describe the agents in a random vibration environment. Besides, the uncertain nonlinear dynamics are approximated by radial basis function neural networks (NNs), and the unmeasured states are estimated by constructing the NN-based observer. In addition, the switching-threshold-based event-triggered control method is adopted with the hope of reducing communication consumption and balancing system performance and network constraints. Moreover, we develop the novel distributed containment controller by utilizing the adaptive backstepping control strategy and the dynamic surface control (DSC) approach such that the output of each follower converges to the convex hull spanned by multiple leaders, and all signals of the closed-loop system are cooperatively semi-globally uniformly ultimately bounded in mean square. Finally, we verify the efficiency of the proposed controller by the simulation examples.

The neural-approximation-based adaptive nonlinear containment control issue for multiagent systems with full-state constraints is studied by invoking the backstepping approach. First, the barrier Lyapunov functions are established to deal with the state constraining issue in the multiple leaders/followers control scenarios. Then, by introducing the first-order filter, the system communication burden is substantially reduced. Moreover, the event-triggered controller is constructed by utilizing the switching-based mechanism so that the system security, control accuracy, resource consumption, and imposed state constraints are neatly balanced. We prove the output of each follower can converge to the desired hull formulated by leaders under the premise that the imposed state constraints are never violated. Besides, the considered closed-loop signals are uniformly bounded. We finally present a simulation example to show the validity of the developed approach.

This article focuses on the neural-network (NN)-based adaptive tracking control issue for a class of high-order nonlinear multiagent systems both subjected to the immeasurable state variables and unknown external disturbance. Combining with the radial basis function NNs (RBF NNs), the composite disturbance observer and state observer for each follower are established, respectively. The purpose of this work is to develop NN-based adaptive tracking control schemes such that the output of each follower ultimately tracks that of the leader and all the signals of the closed-loop systems are semiglobally uniformly ultimately bounded by utilizing the backstepping technique. Furthermore, so as to cope with the sparsity of the control resources, the proposed method is extended to the event-triggered case and the adaptive event-triggered tracking control protocol is formulated for nonlinear multiagent systems. Finally, the numerical example is performed to verify the efficacy of the proposed approach.

Based on radial basis function neural networks (RBF NNs) and backstepping techniques, this brief considers the consensus tracking problem for nonlinear semi-strict-feedback multiagent systems with unknown states and disturbances. The adaptive event-triggered control scheme is introduced to decrease the update times of the controller so as to save the limited communication resources. To detect the unknown state, external disturbance, and reduce calculation workload, the state observer and disturbance observer as well as the first-order filter are first jointly constructed. It is shown that all the output signals of followers can uniformly track the reference signal of the leader and all the error signals are uniformly bounded. A simulation example is carried out to further prove the effectiveness of the proposed control scheme.

This article focuses on the adaptive control issue for uncertain nonlinear systems with time-varying full-state constraints. First, a novel integral barrier Lyapunov functions (IBLFs)-based neural backstepping control approach is designed, which circumvents the trouble of conversion in the traditional used BLFs. And then, the sliding-mode disturbance observers (SMDOs) are established to deal with the immeasurable disturbances in each order of the state-constrained uncertain nonlinear systems. Besides, the dynamic threshold-based event-sampling mechanism is constructed to deal with the sparsity of resources and system controlling burden. Finally, according to the given design approach, an event-triggered adaptive controller is developed and ensures disturbance observation errors uniformly converge to the origin in finite time, and all the signals in the closed-loop system are semiglobally uniformly ultimately bounded. A developed numerical simulation case verifies the validity of the proposed approach.

In this article, an event-triggered adaptive control strategy is proposed to achieve the leaderless-following consensus for a class of cyber–physical systems under the direct topology. Because the deception attacks, state time delay, and unknown external disturbance appear simultaneously, the existing method is hard to apply directly. The difficulty of this issue lies in that the actual system states are unavailable and control efficiencies are unknown, which caused by the deception attack. So as to tackle these knotty problems, the Nussbaum gain functions are employed to replace the control gains, and the available compromised system variables are applied in the controllers. In addition, the proposed disturbance observer based on the compromised state further improves the robustness of the system. To eliminate the influence of state time delays, the appropriate Lyapunov–Krasovskii functionals are used in the backstepping design process. Moreover, the computation and communication burden is dramatically decreased than by adopting the event-triggered mechanism and less adaptive laws. The boundedness of all signals in the closed-loop system is guaranteed via the Lyapunov stability theorem. Finally, the simulation results are provided to demonstrate the availability of the proposed control strategy.

This paper investigates the leader-following consensus control problem for a class of nonlinear multiagent systems subject to sensor and actuator faults under a fixed directed graph. First, a fault compensation mechanism is proposed because of multiple faults wherein the adaptive parameters substitute the fault coefficients. Then, the command filtering method is employed to avoid the burst of complexity rendered by the duplicative differentiation of the virtual control signal. Furthermore, the neural networks-based state observers are designed to reconstruct the unmeasurable states of the nonlinear multiagent systems. According to the given design approach, a switching threshold-based event-triggered adaptive fault-tolerant control strategy is developed and ensures all the signals in the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB). Finally, the simulation result is provided to demonstrate the validity of the presented method.

This article, for the first time, extends the zeroing neural network (ZNN) method to address the problem of dynamic quaternion-valued matrix inversion. Due to the noncommutative property of quaternion multiplication, the complex representation method is first adopted to transform quaternion-valued matrices into the corresponding complex-valued matrices. Then, based on two kinds of ways to deal with nonlinear activation functions in the complex-valued domain, this article proposes two quaternion-valued ZNN (QVZNN) models for dynamic quaternion-valued matrix inversion. In addition, a novel nonlinear activation function is given to accelerate the convergence rate of the models to reach the predefined-time convergence. The detailed theoretical analysis, together with four theorems, are given to show the excellent properties of the QVZNN models. Furthermore, the upper bound of the convergence time is derived analytically with the residual error being zero theoretically. Finally, two numerical examples are provided to verify the theoretical results and the effectiveness of the QVZNN models for the dynamic quaternion-valued matrix inversion, and an application to mobile manipulator control is provided to indicate the practical application value of the QVZNN models.

This paper is concerned with the consensus issue for a class of multiagent systems with Markovian switching topology under aperiodic sampled data measurements. By constructing a novel piecewise stochastic Lyapunov-Krasovskii functional, some novel conditions with less conservative are established such that the consensus is achieved in the mean square sense. In contrast to some previous publications, the sample period is no longer fixed and the transition probability matrix of Markovian switching topology is uncertain. This issue which is of practical and theoretical significance is further investigated when the sampled data controller of each agent is suffered from distinct time-varying input delay. Quite different with the related studies, a maximally allowable input delay upper bound is replaced by the permissible input delay interval. Furthermore, the corresponding consensus is elegantly obtained in terms of linear matrix inequalities. Finally, the effectiveness and practicability of our consensus criteria are well illustrated by the numerical examples.

This paper focuses on the problem of the exponential synchronizationlike criteria for state-dependent impulsive dynamical networks (SIDNs). Two types of sufficient conditions, which are applied to ensure every solution intersecting each impulsive surface exactly once, are derived. For each type of collision conditions, combining with comparison principle and inequality techniques, some sufficient conditions are obtained to ensure local exponential synchronizationlike for SIDN. Moreover, a quiet different impulsive strategy concerning the trigger rules of impulsive instants is proposed. Finally, an example is given to demonstrate the effectiveness of our results.

This paper formulates and studies a more general model of coupled switched neural networks with impulsive time window. The main feature of impulsive time window is that impulses can exist the stochastic instants of the whole switching interval not the switching instants and a pre-specified instants. Moreover, the impulsive numbers of every subsystems is not the same. Using switching Lyapunov functions and a generalized Halany inequality, some general criteria which characterize the impulses and switching effects in aggregated form, for asymptotically synchronization and exponential synchronization of this general model are established.