This paper presents a novel dual event-driven hierarchical control architecture to achieve fully distributed practical prescribed-time consensus (Pd-TC) tracking for uncertain multi-agent systems (MASs). Firstly, a distributed estimate layer is established to reconstruct the leader’s states, guaranteeing practical prescribed-time convergence of estimation errors independent of global information. The proposed communication-triggered event-triggered mechanism (ETM) eliminates continuous communication among neighboring followers, effectively reducing communication resource consumption. Then, utilizing the estimated information, a local control layer is designed to realize practical Pd-TC tracking for uncertain MASs, where the control-update ETM reduces unnecessary control updates to conserve limited control resources, and adaptive gains eliminate the dependence on the bounds of disturbances and uncertain inherent parameters. Furthermore, a rigorous analysis confirms the exclusion of Zeno behavior in both communication-triggered and control-update ETMs. Finally, the proposed control architecture is applied to multiple ground vehicles, validating the theoretical findings.

In this article, the problem of practical prescribed-time (PT) cooperative path following (CPF) is investigated for underactuated autonomous surface vehicles (ASVs), which are not equipped with velocity sensors and subject to unmodeled dynamics and actuator saturation. First, a practical PT velocity observer (PTVO) is designed to estimate unmeasurable velocity information, which is then employed in the design of the guidance law and controller. At the kinematic level, a cooperative guidance law based on aperiodic intermittent communication is developed for synchronized path following, effectively saving communication resources. At the dynamic level, an aperiodic intermittent controller incorporating neural networks (NNs) is designed to approximate unmodeled dynamics and effectively avoid continuous operation of actuators with input saturation. Meanwhile, the intermittent adaptive law is constructed to estimate the optimal weights of the NNs, thereby reducing their complexity. The closed-loop system is verified to converge to a residual set within a PT interval. Finally, we conduct numerical simulations to demonstrate the effectiveness of the proposed algorithms.

This article develops a self-triggered prescribed-time (PT) smooth bipartite formation tracking control (BFTC) strategy for uncertain nonlinear multiagent systems (NMASs) operating over directed graphs. An adaptive backstepping framework is employed for formation control design. To enhance the applicability of distributed protocols, we investigate practical BFTC for multiagent systems (MASs) with followers that are subject to unknown nonlinear dynamics, external disturbances, and actuator faults within cooperative-competitive interaction topologies. Radial basis function neural networks (RBFNNs) are employed to approximate these uncertainties, leveraging their universal approximation capability and localized response characteristics. Importantly, in contrast to previous studies, this work achieves user-defined tracking performance suitable for practical NMAS implementations. The proposed bipartite formation tracking controller guarantees compliance with the user-specified settling time without reliance on initial conditions. Furthermore, considering the constraints imposed by limited communication bandwidth, a distributed dynamic self-triggered control (DSTC) mechanism is developed to enhance transmission efficiency. Unlike traditional strategies, the proposed DSTC dynamically adjusts triggering intervals based on bipartite formation tracking errors (BFTEs). This adaptability facilitates a real-time balance between communication load and system performance. Simulation results validate the efficacy of the proposed control strategy.

This paper investigates the practical prescribed-time consensus (Pd-TC) for nonlinear multi-agent systems (MASs) in the presence of uncertain disturbance, employing intermittent adaptive dynamic event-triggered and self-triggered controllers, respectively. A novel lemma for achieving the practical prescribed-time stability (Pd-TS) is proposed within the framework of intermittent control (IC), where a single parameter exclusively bounds the settling time. To further reduce the triggered instants, a dynamic variable is introduced to construct the dynamic event-triggered mechanism (D-ETM). Utilizing the proposed lemma, an intermittent adaptive dynamic event-triggered controller is developed by incorporating D-ETM with an intermittent adaptive control scheme, which achieves the practical Pd-TC for uncertain nonlinear MASs. Notably, the developed controller is devoid of global information, such as algebraic connectivity and system scale. Following this, an intermittent adaptive self-triggered controller is designed to eliminate the necessity for continuous monitoring. The results presented above are finally applied to Chua’s system, accompanied by a numerical example to demonstrate the efficacy of the designed controllers.

This article adopts the event-triggered control strategy (E-TCS) to achieve the practical predefined-time synchronization (PPTS) for dynamic complex networks (DCNs) with Markov switching topologies under stochastic denial-of-service (SDoS) attacks. We consider the Markov switching topologies, and the coupling weight of the complex networks between nodes is dynamic. For the proposed E-TCS, the minimum inter-event interval can be directly obtained, thereby eliminating the Zeno phenomenon. By employing the time-varying function, all states of the DCNs can achieve PPTS within the predefined time. Concretely, in contrast to finite/fixed-time synchronization, utilizing PPTS enables the arbitrary setting of convergence time, independent of initial values and controller parameters. Notably, the SDoS attacks occur with a certain probability within the attack intervals. Moreover, the intermittent attacks and the average non-attack rate are considered, and this approach leads to less conservative results. Additionally, we prove that a higher average non-attack rate makes it easier for all states of the DCNs to achieve PPTS. Finally, the validity of the proposed E-TCS is verified by the examples of Chua’s circuit and the Kuramoto oscillator network.

This article develops a new observer-based practical predefined-time distributed Nash equilibrium seeking (DNES) algorithm for a network of players in noncooperative games under aperiodically intermittent control (AIC). The proposed intermittent controller is designed in an aperiodic manner, offering a broader applicability compared with the existing periodically intermittent controllers. Considering the players with uncertain disturbances, a disturbance observer is established, which facilitates the development of the practical predefined-time DNES algorithm. The proposed predefined-time control algorithm can ensure the convergence of the players’ actions within an adjustable neighborhood around the Nash equilibrium in a prespecified time, regardless of the initial states and control parameters. Moreover, the dynamic event-triggered communication scheme is employed, allowing players to exchange information only when the triggering condition is satisfied, thereby reducing the communication burden. In addition, the Zeno behavior is excluded. Finally, a simulation example of connected automated ground vehicles is provided to demonstrate the theoretical results.

In this study, the fixed-time synchronization (FTSn) problem is investigated for coupled reaction-diffusion systems (RDSs) with time-varying delay based on an aperiodically intermittent control (AIC) strategy. For the fixed-time control, the convergence time can be estimated in advance, irrespective of initial states. Additionally, unlike the previous studies with the semi-intermittent control strategy, the FTSn is achieved for the coupled RDSs via completely AIC by adopting the average control rate, then the mechanism is more general. Meanwhile, the utilization of average control rate indicates that the results obtained are less conservative. Furthermore, a new auxiliary function is designed to demonstrate that the fixed-time convergence of the coupled RDSs can be guaranteed with or without the presence of time-varying delay. Finally, numerical examples are provided to verify the effectiveness of the theoretical results.

In this paper, an aperiodically intermittent event-based control strategy is developed to investigate the practical fixed-time consensus (FTC) tracking problem of nonlinear multi-agent systems (MASs). Different from the traditional event-based scheme, we incorporate the event-based scheme into the intermittent control mechanism, and the aperiodically intermittent event-based mechanism is developed, which can significantly save resources, particularly in terms of reducing the energy consumption of communication. Additionally, our proposed mechanism enables practical intermittent event-based FTC tracking for a directed graph, while eliminating the dependence on initial states for convergence time estimation. Moreover, the measurement error and intermittent event-based controller are constructed based on the hyperbolic tangent function, then the non-differentiable problem and Zeno behavior can be avoided. Furthermore, an improved triggering mechanism of the event-based scheme is designed to avoid continuous monitoring in control intervals. Hence, resource consumption can be further reduced. Finally, the multiple ground vehicles and Chua’s circuit are considered in simulation examples to verify the effectiveness of theoretical results.Note to Practitioners—This paper addresses the FTC tracking problem of MASs via intermittent event-based control for a directed graph, which can be applied to multiple ground vehicles and Chua’s circuit system. Unlike the asymptotic and finite-time stability results, the upper bound of the convergence time can be estimated, which is unrelated to the initial states and can better satisfy the application requirements. Considering the limitation of communication bandwidth and saving resources, we take the event-based scheme into the intermittent control mechanism, and a new aperiodic intermittent event-based controller is designed under the fixed-time convergence. Contrary to the traditional fixed-time control strategies via intermittent control or event-based control, the proposed algorithms in this study can effectively reduce the update frequency of the controller and significantly save energy under intermittent monitoring, which is more friendly for control engineers. The feasibility of the obtained results is demonstrated by examples of multiple ground vehicles and Chua’s circuit. Potential applications of the proposed control algorithms include smart grid, cooperative search and exploration.

This paper investigates the T-S fuzzy-based bipartite quasi-synchronization of fractional-order heterogeneous coupled reaction-diffusion neural networks. In the considered neural networks, interactions between adjacent neurons are time-varying, cooperative, and competitive, and heterogeneity and T-S fuzzy system rule are simultaneously introduced to characterize the parameter uncertainty arising from complexity and ambiguity in the real world. A new time-varying graph-theoretic Lyapunov function is given for time-varying coupled reaction-diffusion neural networks. Meanwhile, a more general fractional-order derivative law is provided to estimate the derivative of this function, which includes the existing fractional-order derivative laws. Based on a fuzzy-based aperiodically intermittent control, some sufficient conditions are offered for the bipartite quasi-synchronization under a time-varying graph-theoretic Lyapunov function, and the allowable error bound is given. Finally, we carry out some simulations numerically to show the validity of the theory.

Numerous previous findings on the synchronization of fractional-order networks have been conducted through event-triggered control (ETC) or intermittent control (IC), separately. Motivated by the benefits of IC and ETC, this article designs an effective event-triggered intermittent control (ETIC) to investigate the bipartite synchronization of fractional-order fuzzy signed networks. The system dynamics are constructed to describe the nonlinear signed networks via the fuzzy logic and the short-memory performance. Notably, this article represents the first attempt to design the ETIC for fractional-order networks in the sense of exponential convergence. This approach avoids the constantly updating states of IC and the uninterrupted input of ETC. By employing the Lyapunov method, some sufficient conditions for the synchronization of the considered networks are obtained. In addition, the Zeno phenomenon is eliminated so that the infimum of interval length is positive, which ensures the feasibility of the designed controller. Finally, two numerical experiment examples of the fractional-order Chua's circuits model and the fractional-order power system without load disturbance are carried on to illustrate the effectiveness and practicability of our theoretical analysis.

In this article, the practical fixed-time synchronization (PFIXTS) problem of multilayer complex networks (CNs) is investigated based on an intermittent event-triggered control (IE-TC) strategy. Under a new framework of intermittent control (IC), a practical fixed-time stability lemma is proposed. In addition, the conservatism of the results is reduced resulting from the use of average control rate (ACR) for IC. Based on the practical fixed-time stability lemma, a new theorem is developed to achieve the PFIXTS for multilayer CNs, which can further reduce the energy consumption of communication and save resources. Moreover, the emergence of Zeno behavior in the IE-TC strategy is excluded. Finally, the effectiveness of the results is verified by numerical simulations.

In this article, finite-time synchronization is investigated for fractional-order fuzzy time-varying coupled neural networks subject to reaction–diffusion by establishing a new framework under fuzzy-based feedback control and fuzzy-based adaptive control. For the considered networks, we put forward an innovative graph-theory-based time-varying Lyapunov function. To overcome the difficulty of estimating the fractional derivative of this function, this article proposes a novel fractional derivative rule. Through graph theory and the Lyapunov method, several finite-time synchronous criteria are obtained for the considered networks, and the estimation of the settling time is derived. Finally, the numerical results are shown to demonstrate the practicability of the given results.

This article focuses on the bounded stabilization issue for stochastic Takagi–Sugeno (T–S) fuzzy systems with external disturbances under fuzzy intermittent event-triggered control. Different from the common intermittent control scheme, the intermittent control proposed is based on an event-triggered mechanism instead of a traditional time-triggered mechanism during the work intervals. As a result, it reduces unnecessary sampling times and resource waste to a great extent. Meanwhile, the minimum interexecution time is obtained for T–S fuzzy systems under the stochastic case. In addition, this article presents a novel Lyapunov function, which simplifies the proof compared to the traditional Lyapunov function for intermittent control. Based on the average control rate adopted and the Lyapunov method, a bounded stability criterion is established, which is less conservative. Then, a corollary is given under the fuzzy event-triggered control. Finally, an example is shown to illustrate the effectiveness of the results obtained.

This study proposes a novel dynamic event-triggered impulsive control (ETIC) scheme to study the exponential stabilization of general stochastic nonlinear systems, where the impulsive sequence is determined by a dynamic event-triggered mechanism. The dynamic ETIC can effectively reduce controller updates and significantly save energy under the same decay rate compared to traditional static event-triggered impulsive generators. Additionally, there is a guaranteed positive minimum inter-event time for each sample path solution of systems. Furthermore, the proposed dynamic ETIC scheme is employed to stabilize stochastic complex networks based on the graph theory and the Lyapunov method. Finally, we provide two illustrative examples to verify the effectiveness and correctness of the proposed dynamic ETIC scheme.

This article deals with the almost surely exponential synchronization issue for complex dynamical networks (CDNs) under noise control. Different from most of the existing literature, aperiodically intermittent discrete observations noise control is proposed. It is worth noting that the state in noise work time is discretely observed rather than continuously. Meanwhile, some sufficient conditions are presented based on stochastic analytical techniques and the Lyapunov method. Besides, the upper bounds of noise rest rate and the time lag between two consecutive observations are estimated. Moreover, it is clear that CDNs are easier to achieve the almost surely exponential synchronization when noise control gain becomes larger. To demonstrate the effectiveness and feasibility of analytical results, two applications about single-link robot arm systems as well as second-order oscillator systems are given. At the same time, some numerical simulations are exhibited.

This article focuses on quasi-synchronization of fuzzy heterogeneous complex networks. An aperiodically intermittent control strategy based on discrete-time state observations (aperiodically intermittent discrete-time state observations control for short) is designed. Different from intermittent control strategies referred in existing literatures, the control duration of the control strategy used in this article is based on discrete-time state observations, which makes the control used in this article somewhat less demanding and more effective. Under the aperiodically intermittent discrete-time state observations control strategy, a valid approach combining Lyapunov method with graph theory is proposed in this article. Throughout this article, a theorem and a corollary to the quasi-synchronization criterion of fuzzy heterogeneous complex networks are established. The results show that when the control gain is larger, the convergence domain is smaller. Finally, an illustrative example is presented and the simulation of this example shows the feasibility and validness of the obtained results.

This article discusses the exponential stability in mean square of Takagi–Sugeno fuzzy systems (T-SFSs) under the stochastic case. Moreover, stochastic factors are taken into account to make the model more general. Different from traditional time-triggered control, we introduce event-triggered control strategy into intermittent control and then intermittent dynamic event-triggered control (IDE-TC) is developed, which can reduce updates of the controller and save resources. Besides, we eliminate Zeno phenomena, which is independent of mathematical expectation. Furthermore, the minimum interexecution time by the IDE-TC can be obtained directly for T-SFSs under the stochastic case. In addition, in order to illustrate the theoretical results, an application about double-link robot arm model is given. Meanwhile, we exhibit some numerical simulations.

A new consensus protocol with aperiodically intermittent discrete-time state observation noise (AIDSON) is introduced. With the help of the proposed AIDSON, the almost sure exponential consensus (ASEC) of multiagent systems is investigated. Through the Lyapunov method and stochastic comparison principle, some sufficient conditions can be obtained. Moreover, the upper bounds of the rest rate of intermittent communication noise and the duration between two consecutive observations are estimated. Additionally, the larger the noise intensity is, the faster multiagent systems reach the ASEC. Furthermore, the established results are applied to the consensus analysis of single-link robot arms and oscillators and some simulations are presented.

A novel intermittent dynamic event-triggered control is proposed to investigate the exponential synchronization in mean square (ESMS) of stochastic complex networks (SCNs). In contrast to existing literature, the proposed intermittent control is based on dynamic event-triggering instead of static time-triggering during the control interval. Meanwhile, the number of event triggers can be reduced by introducing an exponential function. Moreover, for each sample path solution of SCNs, the existence of a minimum positive inter-event time is guaranteed in all the event-generators proposed in this paper. In addition, based on the Lyapunov method and the graph theory, synchronization criteria for the ESMS of SCNs under the intermittent dynamic event-triggered control are established. Finally, theoretical results are applied to islanded microgrid systems and simulations are given to verify the effectiveness of the results.

This paper investigates the exponential synchronization (ES) problem for complex networks (CNs) under an intermittent adaptive event-triggered control (IAE-TC) strategy which is based on dynamic IAE-TC during the control activation intervals. In this control mechanism, the intermittent controller has adaptability to the evolution results of the controlled networks and is activated only when the event-triggered condition is violated. Then, by employing this kind of control strategy and the Lyapunov method, some sufficient conditions are proposed to achieve the ES of CNs and it is proven that the Zeno behavior can be eliminated. Besides, an application about the islanded microgrid system and some numerical simulations are provided to verify the effectiveness of the derived theoretical results. Moreover, in the numerical simulations, it is shown that the dynamic IAE-TC strategy can decrease the number of event-triggered instants more availably than the static one.

The pth moment exponential synchronization (PMES) problem for time-varying complex dynamical networks (CDNs) with multiple time-varying delays (TCDNMTDs) by aperiodically intermittent control is studied in this paper. Compared with related work, the coupling structure of CDNs is time varying. Also, internal time-varying delays and coupling time-varying delays are taken into consideration and they are different from each other. It is worth emphasizing that the intermittent control scheme proposed here is nonperiodical. Some criteria are derived to make TCDNMTDs achieve PMES by using the Lyapunov method and graph theory. Additionally, we also consider the synchronization of second-order Kuramoto oscillators and coupled Chua's circuits and some numerical simulations are presented to verify the validity of our results.

In this paper, to investigate the exponential synchronization of stochastic neural networks, a new periodically intermittent discrete observation control (PIDOC) is first proposed. Different from the existing periodically intermittent control, our control in control time is feedback control based on discrete-time state observations (FCDSOs) instead of a continuous-time one. By employing the Lyapunov method, graph theory, and theory of differential inclusions, the exponential synchronization of stochastic neural networks with a discontinuous right-hand side is realized by PIDOC and some sufficient conditions are presented. Especially, when control width tends to control period, PIDOC will be reduced to a general FCDSO and we give some detailed discussions. Then, we provide some corollaries about synchronization in mean square, asymptotical synchronization in mean square, and exponential synchronization of stochastic neural networks under FCDSO. Finally, some numerical simulations are provided to demonstrate our analytical results.