This paper investigates the achievement of leader-following consensus for high-order linear multiagent systems with constrained control input under intermittent event-triggered and self-triggered control. Therein, the novel intermittent event-triggered and self-triggered control, which can automatically exclude Zeno behaviour, are proposed for the first time in the consensus problem of multiagent systems with constrained control input. Notably, the aforementioned controls are both designed in a fully distributed manner throughout all undirected communication graphs. Then, this paper employs Lyapunov method to provide sufficient conditions for leader-following consensus of multiagent systems. Subsequently, the theoretical results are utilised in multi-robot formation. Finally, a numerical simulation is provided to demonstrate the effectiveness of the theoretical results.

In this paper, we aim to study the mean exponential stability of stochastic highly nonlinear delay system with regime-switching diffusion, multi-links and distributed delay under aperiodic intermittent control. To address the stability challenges posed by high nonlinearity, multiple time delays, stochastic disturbances, complex network topology, and abrupt mode switching, we propose an effective solution as follows: Novel Lyapunov functionals containing both quadratic term and q-power term () of state variables are constructed, and the auxiliary timers are designed to avoid the discontinuity of control. By combining graph theory, Dupire's functional derivatives and Dupire's functional It & ocirc; formula, we successfully prove that the infinitesimal generator is strictly negative defined on the working period and resting period of control, respectively, and then derive the sufficient conditions ensuring mean exponential stability. The key constraints include strongly connected graph structure, strict inequalities of Lyapunov function coefficients, strict inequalities of growth restrictions on coupling functions and distributed delay, and average working time ratio, respectively. The stochastic delayed FitzHugh-Nagumo system with state-switching is applied, and the aperiodic intermittent control is designed, where the numerical simulation results indicate the effectiveness of our results.

This paper investigates the mean-square exponential synchronization problem of stochastic delayed hybrid networked systems with control dependent noise (SDHNSCN) on semi-Markov switching multi-links networks under output feedback control with transmission-count-based weighted try-once-discard protocol (TC-WTODP). As a novel weighted try-once-discard protocol (WTODP), TC-WTODP is capable of automatically increasing the weights of sensors disconnected from the communication network at a certain transmission instant. Meanwhile, it is designed to address the problem that the existing WTODP cannot capture information from certain sensors that remain unscheduled for a long period when their measured outputs change slightly. Moreover, the application of TC-WTODP marks the first time the scheduling protocol is integrated into multi-links networks. Based on this proposed protocol, using the Lyapunov method and the emulation approach, we derive synchronization criteria for SDHNSCN for the first time. Notably, the maximum allowable transmission interval (MATI) of the designed protocol can be dynamically adjusted according to the upper bound of time-varying delays. Subsequently, we apply the main results to stochastic hybrid multi-links networked oscillator systems. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.

In this paper, the stability of stochastic complex networks with impulsive effects vulnerable to asynchronous DoS attacks is studied. The volatile event-triggered control (ETC) is advanced, featuring a control gain characterized by a sign-indefinite function that follows specific volatile patterns. Furthermore, the concept of average volatile gain under DoS attacks is proposed to quantify the volatile control gain. To address the challenges posed by volatile control gain and DoS attacks, a generalized differential inequality is proposed, resulting in a broader application of the main results. Using stochastic analysis techniques, graph-theoretic methodology, and the Lyapunov method, improved stability criteria are established. In particular, the joint potential unstable factors of impulsive effects and DoS attacks on stability are theoretically revealed. Stochastic hybrid networks that apply ETC can achieve stability under certain conditions if the magnitude of the impulsive effects and the frequency and duration of DoS attacks are sufficiently limited. Additionally, by incorporating the dwell time into ETC, the Zeno phenomenon can be avoided. Finally, a numerical example is provided to illustrate the validity of the obtained results.

This paper is the first to investigate the leader-following consensus of high-order nonlinear multiagent systems under a novel prescribed performance adaptive control. To address the limitations of existing prescribed performance control, which require continuous exponential prescribed performance functions with fixed decay rates that cannot be determined theoretically, this paper proposes a class of arbitrary non-increasing, piecewise differentiable prescribed performance functions with freely adjustable decay rates that can be decided theoretically. Leveraging the proposed prescribed performance functions and a class of natural logarithm barrier Lyapunov functions, we construct novel prescribed performance barrier Lyapunov functions, which consider the influence of adaptive parameters. Under the developed control, sufficient conditions are provided for the systems to satisfy time-varying prescribed performance and achieve consensus via above Lyapunov functions. Finally, numerical simulations verify the effectiveness of theoretical results.

This article develops an asynchronous event-triggered impulsive decentralized control scheme for a class of complex-valued multilayer large-scale systems with time-varying coupling strengths and delays, under deception attacks where adversaries achieve their objectives by tampering with historical data. Unlike existing studies on event-triggered impulsive control where all node controllers are activated synchronously, each node in the proposed framework independently determines its triggering instants based on its own state. Initially, the interconnection effects are neglected, and node-specific Lyapunov functions are constructed and analyzed. Subsequently, graph-theoretic techniques, combined with the Razumikhin method, are employed to handle the cross-coupling terms and to derive several sufficient conditions. These conditions guarantee the p-th moment exponential stability of the closed-loop system while explicitly accounting for communication delays and attack probabilities. Finally, the theoretical results are applied to inertial neural networks, and numerical simulations demonstrate the effectiveness of the proposed control strategy.

This paper focuses on the exponential stability of time-varying hybrid stochastic large-scale networks, in which a novel discrete-time observation control strategy with volatile control gain is imposed. The control gain exhibits sign-indefinite characteristics that follow certain volatile patterns. Then, the strategy can preferably respond to extrinsic perturbances and defend actuators and facilities by comparison with the position in constant gain. To quantify the volatile control gain, a concept of average volatile discrete-time observation control gain is proposed. In light of stochastic analysis theory and Lyapunov method, we establish improved stability criteria. In contrast to earlier results, the piecewise continuous, time-varying, and indefinite functions replace the constant coefficient of the upper bound estimation for the operator of the Lyapunov function, i.e., it can be positive or negative along time evolution, which shows wider applications of our results. Furthermore, considering the phenomenon of controller failure and packet losses, obtained results are applicable for analyzing the stabilization via intermittent discrete-time observation control and nonuniform discrete-time observation control, respectively. Finally, two applications to oscillator systems and single-link robot arms are presented and numerical simulations are exploited to illustrate the feasibility. Note to Practitioners-This paper is motivated by existing results on discrete-time observation control for the dynamics of hybrid stochastic large-scale networks. The existing results mainly require continuous updates to the control signals while maintaining a constant control gain. This is challenging to achieve on digital computers and often does not effectively respond to external disturbances. This paper designs a new hybrid control called volatile discrete-time observation control, and a concept of the control gain is proposed to quantify the volatile control gain. Specifically, the obtained results also apply to scenarios involving control failures and packet loss. The results are applied to oscillator systems and single-link robot arms, demonstrating their effectiveness and it is expected that the proposed approach can be extended to more practical physical engineering systems.

This paper examines the stability of stochastic Takagi-Sugeno (T-S) fuzzy complex networks under cyber attacks by introducing a dynamic event-triggered delayed impulsive control strategy, which determines impulsive moments based on the system state rather than fixed time intervals. A dynamic event-triggered condition is designed by incorporating a dynamic variable, network topology, and node Lyapunov functions, with impulsive jumps tied to the system's historical state. To avoid Zeno behavior, a timer sequence ensures a positive minimum inter-event time. Cyber attacks are modeled using two independent Bernoulli-distributed random variables to reflect their stochastic nature. Stability criteria are rigorously established using graph theory and the proposed control strategy, with numerical simulations demonstrating the framework's effectiveness.

In this article, the synchronization problem of delayed multilinked large-scale networks is investigated via intermittent delayed event-triggered control (ETC). Time delays are considered in intermittent delayed ETC, which integrates delayed aperiodically intermittent control and event-triggered mechanisms (ETMs). Furthermore, both continuous ETM and periodic ETM are studied based on continuous measurements and periodic sampling, respectively. By introducing the exponential term into continuous ETM, the number of event triggers can be decreased. By means of periodic ETM, continuous monitoring can be avoided and an estimate for the upper bound of the sampling period is obtained. To address the challenges posed by intermittent delayed ETC and time delays, a generalized Halanay inequality is put forward, resulting in a wider application of the main results. In virtue of Lyapunov method, novel differential inequality technique, and graph theory, synchronization criteria for drive-response systems under intermittent delayed ETC are developed. Finally, an application to single-link robot arm systems is discussed, and corresponding numerical simulations are performed to demonstrate the validity of the theoretical results.

In this paper, the almost sure synchronization of stochastic multi-layer networks with noise coupling is studied by means of pinning intermittent volatile event-triggered control. During the control interval, the determination of control updates follows an event-triggered mechanism with waiting time, which avoids continuous monitoring and also eliminates Zeno behavior. In contrast to the existing literature that focuses on moment synchronization, we study almost sure synchronization on stochastic multi-layer networks, where noise coupling with time-varying and nonlinear features plays an active role. In addition, the control gain displays sign-indefinite characteristics that follow some volatility patterns, including synchronizing control and desynchronizing inputs. A concept of average volatile control gain is presented to quantify the control gain. To cope with the challenges posed by volatile gain and intermittent control input, a generalization of Halanay-type inequality is proposed, its coefficients are time-varying and piecewise continuous, which shows that the results have a wider range of applications. Based on the stochastic analysis technique, graph theory, and Lyapunov method, the synchronization criteria are established. Finally, the feasibility is illustrated by simulation examples. Note to Practitioners-This paper was motivated by existing results on pinning intermittent control and event-triggered control about almost sure synchronization. The existing results mainly require that the control signals were updated in a consecutive manner during control activation intervals, which may hardly be implemented on digital computers. This paper designs a novel hybrid control method named pinning intermittent volatile event-triggered control, and therefore, the proposed approach is more friendly for control engineers. In addition, the volatile control gain is considered. The results obtained are applied to a spring-mass-damper system, demonstrating their effectiveness and it is expected that the proposed approach can be extended to more practical physical engineering systems.

This paper investigates the problem of stochastic event-triggered impulsive control for stochastic complex networks with time delays under cyber attacks. To account for the influence of cyber attacks, the variations in event-triggered parameters induced by these attacks are incorporated into the design as stochastic event-triggered conditions. A stochastic event-triggered impulsive control strategy is then proposed for complex networks with time delays. Unlike existing impulsive control methods, which typically assume that control input instants are independent of the system state, the proposed method is state-dependent and explicitly considers the impact of cyber attacks on the impulsive control gain-an aspect often overlooked in most control approaches addressing cyber attacks. By constructing auxiliary functions and integrating graph theory with the Razumikhin method, several criteria are derived to ensure the exponential synchronization of stochastic complex networks with time delays under cyber attacks. Finally, simulation results are provided to validate the effectiveness and advantages of the proposed method.

This paper investigates the exponential synchronization of time-delayed stochastic complex networks under deception attacks. Unlike traditional methods that rely on fixed or preset impulsive sequences, a state-dependent dynamic event-triggered impulsive control strategy is proposed, integrating the advantages of both event-triggered mechanisms and impulsive control. This strategy dynamically adjusts the impulsive moments by monitoring the system’s dynamic state. Adaptive parameters are incorporated into the event-triggered conditions, resulting in a Lyapunov-based adaptive event-triggered mechanism driven by subsystem state information. This mechanism allows each subsystem to independently determine its trigger moments using only its state information, rather than the whole system information. Additionally, stochastic variables following the Bernoulli distribution are introduced to model deception attacks, making the control strategy more applicable to real-world scenarios. Based on the Lyapunov functions of subsystems and graph theory, sufficient conditions for ensuring exponential synchronization are provided, excluding Zeno behavior. Finally, numerical simulations confirm the effectiveness and practicality of the theoretical results.

This article investigates the stability of functional differential systems on networks adopting event-triggered multi-delayed impulsive control. We construct a new event-triggered mechanism (ETM) type using the Lyapunov function and the network topology. Combined with the ETM and multi-delayed impulsive control, in which the impulsive jumps are related to the current and past states, we propose a multi-delayed event-triggered impulsive control strategy. This controller will execute the control tasks only when the systems violate the preset ETM. In the view of the Razumikhin method and the graph theory, some criteria are given to avoiding Zeno behavior under this ETM and achieving exponential stability, which is related to the event-triggered parameters, network topology, and impulsive intensity. As an application of our theoretical results, a class of coupled oscillation systems is considered and numerical simulations are presented to verify the practicability and effectiveness.

This article studies exponential synchronization of complex networks under deception attacks via event-triggered impulsive control. A new event-triggered mechanism is proposed to avoid Zeno behavior based on the topology of the networks and the Lyapunov function of the subsystem. Using a combination of the Lyapunov method and graph theory, several criteria for synchronization of complex networks under attacks are given, which are related to the event-triggered parameters, the topology of the network, and the attack signal sent by enemies. Given the prevalence of delays, we also extend the obtained results to delayed deception attacks, where malicious attackers modify state data from past moments. Finally, the theory applies to circuit systems under deception attacks and delayed deception attacks, respectively, and numerical simulations are given to verify the effectiveness and practicality of our results.

This article studied the synchronization of multi-link stochastic complex networks via impulsive control in the sense of infinite dimension. Considering that the existence and uniqueness of solutions are the premises for studying the synchronization of infinite-dimensional stochastic systems, we have proven the existence and uniqueness of mild solutions by the combination of the mild Itô's formula, graph theory, and the contraction mapping principle. The restriction on the domain of mild solution is removed, which also makes the contraction coefficient less conservative since the use of the mild Itô's formula. Secondly, the criteria for achieving exponential synchronization of infinite-dimensional stochastic systems are obtained with the assistance of graph theory and the Lyapunov method. These criteria are related to network topology and average impulsive interval. Finally, the theoretical results are applied to a class of multi-link BAM neural networks with reaction-diffusion, and several numerical simulations are given.

This paper is mainly concerned with the quasi-synchronization of stochastic heterogeneous networks (SHNs). Furthermore, the control strategy adopted here combines the advantages of aperiodically intermittent pinning control (AIPC) and sampled-data control, namely intermittent pinning sampled-data control. Different from intermittent control referred to in existing results, the restriction of the lower bound of control rate for AIPC, which is called the quasi-periodicity condition, is removed. As the main results, through an auxiliary timer, Lyapunov method, and inequality techniques, several sufficient conditions for quasi-synchronization of SHNs are derived. Especially, two different estimations of sampling error are given and the obtained results indicate that the maximum allowable bound of the sampling interval can be calculated easily. Then, some easily verified quasi-synchronization criteria are provided. Finally, to show the feasibility of our theoretical results, two numerical examples are provided.

In this article, we investigate the input-to-state stability (ISS) of stochastic systems via intermittent event-triggered control. The control update sequence during the control intervals is determined through an event-triggered mechanism (ETM), where the periodic ETM and continuous ETM are considered separately. For the continuous ETM, a positive minimum inter-execution time is ensured by adding waiting time, which avoids Zeno behavior. For the periodic ETM, with the help of Halanay-like inequality, the maximum allowable bound of the sampling period is given. The number of control updates is further reduced by adding a dynamic term. In addition, sufficient conditions for ISS in stochastic systems are proposed by designing an auxiliary timer and applying the Lyapunov method. Finally, two numerical examples are presented to verify the validity of the results.

Input delays and deception attacks may cause instability of impulsive control systems. However, they have rarely studied in impulsive stochastic complex networks. This work establishes a criterion for the exponential stability of delayed impulsive stochastic complex networks under deception attacks in the mean square sense through the graph theory and a novel method. The proposed theory provides an impulsive control design method for stochastic complex networks with input delays under deception attacks with randomness. The designed impulsive control scheme ensures the exponential stability of the controlled systems. Finally, the practicality of the theoretical results was verified through numerical simulation.

In this article, a novel dynamic periodic event-triggered control (DPE-TC) is proposed to investigate input-to-state stability (ISS) in multilayer coupled systems (MCSs). Different from the existing literature, a dynamic term is introduced to event-triggered control (E-TC), which can reduce the number of event triggers as the interexecution times are prolonged on the whole. Moreover, a periodic sampling is adopted, from where the Zeno phenomenon is naturally avoided. Based on the Lyapunov method and graph theory, ISS for coupled systems under the DPE-TC is established. Meanwhile, a dynamic event-triggered control with dwell-time is proposed, and a corollary to ensure the ISS of MCSs is also provided. Eventually, results are applied to second-order oscillators and a numerical example is given to prove the validity of the theoretical results.

This article studies quasi-synchronization of stochastic complex networks under hybrid impulses. With parameter mismatches, different from the previous quasi-synchronization results in the sense of mean square on stochastic complex networks, almost sure quasi-synchronization is investigated, in which noises have a positive effect on the synchronization. By utilizing the Lyapunov method, stochastic analysis theory, average impulsive interval, and average impulsive gain, we formulate the almost sure quasi-synchronization criteria when the average impulsive interval z(0) satisfies z(0)<+infinity and z(0)=+infinity, respectively, where the synchronizing impulses and the desynchronizing impulses are simultaneously considered. It is worth noticing that in our criteria of quasi-synchronization, the mutual restraints among the average impulsive interval, average impulsive gain, and noise intensity are given. Moreover, for the criteria in this article, the piecewise continuous scalar functions cannot only replace the constant coefficient of the upper bound estimation for the diffusion operator of a Lyapunov function in available literature but also even be unbounded, which has wider applications than some existing works. Our corollaries regarding complete synchronization and analyses of the synchronization for stochastic complex networks with aperiodic intermittent noises provide sufficient conditions in closed form. Finally, the theoretical results are applied to a coupled chaotic Lorentz system, and several numerical examples are presented to demonstrate the advantages of the theoretical results.