As the foundation of next-generation wireless networks, distributed learning (DL) is expected to be integrated into 6 G communication networks, profoundly advancing the transformation of intelligent connectivity. However, network-induced delays critically degrade the performance of DL algorithms in practical deployments. Beyond the communication limitation, many emerging applications involve antagonistic interactions among agents, introducing additional complexity. To overcome these challenges, we propose a decentralized distributed cooperation–competition learning (DCCL) algorithm based on neuro-fuzzy networks, designed for latency communication networks. The algorithm innovatively employs the signed graph to naturally encode the coupling coopetition relationships among agents, and incorporates the delay model into its design. It demonstrates superior adaptability for DL problems with bimodal coalitional adversarial interactions in latency-prone mission-critical services. Moreover, we extend the neuro-fuzzy network into a distributed version, and the resulting distributed neuro-fuzzy model inherently preserves the interpretability characteristic and superior learning capability. Based on structural balance theory and discrete Lyapunov stability theory, we rigorously prove the convergence of the DCCL algorithm and derive an explicit sufficient condition in the form of a maximum allowable latency tolerance. The proposed algorithm benefits privacy protection by transmitting only model parameters. Experiments are conducted to validate the performance of the DCCL algorithm on several datasets for regression and classification. Furthermore, we discuss the limitations of the DCCL algorithm, providing a balanced perspective for future research.

A coordinated control challenge is addressed in 6-degree-of-freedom (6-DOF) fixed-wing multiple autonomous aerial vehicle (multi-AAV) systems under communication and state constraints. The primary obstacle in achieving this goal arises from managing frequent information interactions and the assurance that UAV states converge within prescribed bounds. On the one hand, a novel dynamic self-triggering mechanism is effectively proposed. Unlike current state-of-the-art approaches, the proposed dynamic self-triggering communication mechanism features a larger triggering threshold and eliminates the need for continuous monitoring of system state information. This reduces the demand on system communication and sensor resources. On the other hand, a new time-varying constraint bounded function is introduced to effectively relax restrictions on the initial system state. Then, the coordinated translational/rotational controllers are designed to ensure minimal consensus tracking error. Semi-physical simulations highlight the effectiveness of the proposed control algorithm. Note to Practitioners—In actual environment, the multi-UAVs flight always requires inter-communication to ensure the stable performance of the entire formation. However, period-based communication leads to a waste of communication resources. The event-triggering communication mechanism lowers the communication frequency of UAVs, thereby reducing energy consumption. Nevertheless, most existing control results on event-triggered communication overlook the fact that continuous monitoring of state information still causes unnecessary energy consumption. To further investigate the problem, a dynamic self-triggering mechanism is proposed in this study, which can determine the subsequent triggered moment based on the state information of the current triggered moment. In addition, the state of UAVs due to safety and physical constraints ought to be constrained. Therefore, a prescribed-time constrained control strategy is proposed, which not only improves the transient performance (e.g. small overshoot and fast adjustment time), but also ensures that the UAV state converges within a given constraint bound.

An adaptive fuzzy dynamic event-triggered control approach is proposed for a fleet of fixed-wing unmanned aerial vehicles (UAVs) operating under jointly connected switching topologies. The primary challenge lies in addressing asynchronous switching topologies caused by topology identification delays. To tackle this, asynchronous distributed observers are constructed, and topological switching rules are designed, ensuring that all follower UAVs can estimate the leader UAV's state by leveraging asynchronous distributed state errors. Additionally, a novel dynamic event-triggering mechanism is introduced. Compared to state-of-the-art methods, the proposed triggering function directly couples the external state variable with the last triggered value, dynamically regulates the triggered interval based on the control performance, and minimizes the number of occurrences while maintaining the system performance. An adaptive fuzzy translational and rotational controller is further developed to enable the follower UAVs to accurately track the state of the leader UAV while ensuring that all closed-loop states remain globally uniformly ultimately bounded (GUUB). The proposed strategies are validated for effectiveness and superiority through a semi-physical simulation platform

An adaptive fuzzy prescribed-time connectivity-preserving consensus protocol is designed for a class of stochastic nonstrict-feedback multiagent systems, in which periodic disturbances, switched nonlinearities, input saturation, and limited communication ranges are taken into consideration simultaneously. The connectivity, determined by the limited communication ranges and initial positions of agents, is preserved by incorporating an error transformation. Further, a common Lyapunov function is considered to deal with the switching modes. By combining a reduced fuzzy logic system with Fourier series expansion, a novel approximator is constructed to deal with periodically disturbed nonlinearities and to surmount the difficulty brought by the nonstrict-feedback structure. More importantly, distinctly from the existing finite/fixed-time control strategies where the settling time is heavily dependent on the accurate value of the initial states and control parameters, the settling time of the proposed prescribed-time consensus is completely independent of the initialization and control parameters and can be given a priori only according to actual demands. Based on the Lyapunov stability theory, the designed controller ensures that the connectivity-preserving consensus is achieved in prescribed time and all the signals remain bounded in probability. To the end, the feasibility of the proposed consensus protocol is demonstrated by simulation.

This article addresses the adaptive neural tracking control problem for a class of uncertain stochastic nonlinear systems with nonstrict-feedback form and prespecified tracking accuracy. Some radial basis function neural networks (RBF NNs) are used to approximate the unknown continuous functions online, and the desired controller is designed via the adaptive dynamic surface control (DSC) method and the gain suppressing inequality technique. Different from the reported works on uncertain stochastic systems, by combining some non-negative switching functions and dynamic surface method with the nonlinear filter, the design difficulty is overcome, and the control performance is analyzed by employing stochastic Barbalat's lemma. Under the constructed controller, the tracking error converges to the accuracy defined a priori in probability. The simulation results are shown to verify the availability of the presented control scheme.

In this paper, a neural network (NN)-based distributed cooperative identification strategy with event-triggered communication is studied for a group of coupled identical nonlinear systems. We develop a distributed cooperative learning law in the context of event-triggered communication, where an agent will transmit its NN weights to its neighbors only when its weight trigger error norm exceeds an exponentially decreasing threshold. It is proven that the estimated weights of all radial basis function NNs converge to a small neighborhood of their optimal values. Therefore, the unknown nonlinear function is approximated along the union of all the system trajectories. It is further proven that there exists a positive minimum interevent interval and Zeno behavior can be avoided. Finally, we give a simulation example to demonstrate these features.

In this paper, an event-based distributed cooperative learning (DCL) law is proposed for a group of adaptive neural control systems. The plants to be controlled have identical structures, but reference signals for each plant are different. During control process, each agent intermittently broadcasts its neural network (NN) weight estimation to its neighboring agents under an event-triggered condition that is only based on its own estimated NN weights. If communication topology is connected and undirected, the NN weights of all neural control systems can converge to a small neighborhood of their optimal values. The generalization ability of NNs is guaranteed in the event-triggered context, that is, the approximation domain of each NN is the union of all system trajectories. Furthermore, a strictly positive lower bound on the interevent intervals is also guaranteed to avoid the Zeno behavior. Finally, a numerical example is given to illustrate the effectiveness of the proposed learning law.

This paper investigates the fuzzy adaptive practical tracking problem for a class of nonlinear pure-feedback systems with quantized input signal. In the control scheme design process, the considered system is transformed into a plant with a strict-feedback form by borrowing the mean value theorem of differential, then fuzzy logic systems are used to compensate for some uncertain nonlinearities in the considered plant and the classical adaptive technique is employed to handle some unknown parameters. In the backstepping design, some nonnegative switching functions are introduced to develop the desired fuzzy controller, and Barbalat's lemma is used to analyze the stability and the control performance of the closed-loop system. It can be shown that under the novel adaptive fuzzy controller, all the closed-loop signals are semiglobally uniformly ultimately bounded, and especially the tracking error satisfies the accuracy assigned a priori. A simulation example is presented to verify the effectiveness of the proposed control method.

In this paper, the problem of the global finite-time adaptive stabilization for nonlinearly parametrized systems with multiple unknown control directions is addressed. Different from the previous results, the control directions of the considered systems are completely unknown. Adopting the adding a power integrator design technique, we develop an adaptive switching controller with a tuning parameter. Due to control directions unknown, a novel logic switching regulation is established based on Lyapunov function method to overcome this main obstacle. According to this switching rule, the design parameter is tuned online in a switching way. With the help of the obtained adaptive switching controller, the global finite-time stability of the closed-loop systems is shown. To verify the effectiveness of the control algorithm, a simulation example is presented.

In this paper, we investigate optimized adaptive control and trajectory generation for a class of wheeled inverted pendulum (WIP) models of vehicle systems. Aiming at shaping the controlled vehicle dynamics to be of minimized motion tracking errors as well as angular accelerations, we employ the linear quadratic regulation optimization technique to obtain an optimal reference model. Adaptive control has then been developed using variable structure method to ensure the reference model to be exactly matched in a finite-time horizon, even in the presence of various internal and external uncertainties. The minimized yaw and tilt angular accelerations help to enhance the vehicle rider's comfort. In addition, due to the underactuated mechanism of WIP, the vehicle forward velocity dynamics cannot be controlled separately from the pendulum tilt angle dynamics. Inspired by the control strategy of human drivers, who usually manipulate the tilt angle to control the forward velocity, we design a neural-network-based adaptive generator of implicit control trajectory (AGICT) of the tilt angle which indirectly "controls" the forward velocity such that it tracks the desired velocity asymptotically. The stability and optimal tracking performance have been rigorously established by theoretic analysis. In addition, simulation studies have been carried out to demonstrate the efficiency of the developed AGICT and optimized adaptive controller.

A novel-function approximator is constructed by combining a fuzzy-logic system with a Fourier series expansion in order to model unknown periodically disturbed system functions. Then, an adaptive backstepping tracking-control scheme is developed, where the dynamic-surface-control approach is used to solve the problem of “explosion of complexity” in the backstepping design procedure, and the time-varying parameter-dependent integral Lyapunov function is used to analyze the stability of the closed-loop system. The semiglobal uniform ultimate boundedness of all closed-loop signals is guaranteed, and the tracking error is proved to converge to a small residual set around the origin. Two simulation examples are provided to illustrate the effectiveness of the control scheme designed in this paper.

For the first time, this paper addresses the problem of adaptive output-feedback control for a class of uncertain stochastic nonlinear strict-feedback systems with time-varying delays using neural networks (NNs). The circle criterion is applied to designing a nonlinear observer, and no linear growth condition is imposed on nonlinear functions depending on system states. Under the assumption that time-varying delays exist in the system output, only an NN is employed to compensate for all unknown nonlinear terms depending on the delayed output, and thus, the proposed control algorithm is more simple even than the existing NN backstepping control schemes for uncertain systems described by ordinary differential equations. Three examples are given to demonstrate the effectiveness of the control scheme proposed in this paper.