This paper investigates the synchronization control problem for a class of state-dependent switching neural networks with time-varying delay and semi-Markov jump parameters. A new intermittent discrete adaptive event-triggered control scheme is proposed to reduce control cost and communication burden. Specifically, a time-window mechanism is introduced to characterize the intermittent operation, where the activation width is determined by the synchronization error state at the beginning of each intermittent period. Furthermore, the triggering threshold is updated in a discrete adaptive manner according to the variation between the current sampled state and the most recently transmitted state. A switched Lyapunov-Krasovskii functional is constructed by incorporating the characteristics of semi-Markov jumps, time-varying delay, sampling period, and intermittent operation. Based on this framework, sufficient conditions are derived to guarantee exponential synchronization of the considered master-slave system. Finally, two numerical examples and two image encryption-decryption applications are provided to demonstrate the effectiveness of the proposed results.

This paper addresses robust boundary control for uncertain time-delay reaction-diffusion systems subject to semiMarkovian switching, where the coexistence of spatial diffusion, time-varying delays, norm-bounded parameter uncertainties, and time-varying transition rates brings substantial difficulties to stability analysis and controller synthesis. To overcome these challenges, a mode-dependent integral sliding-mode surface is constructed and a robust boundary sliding-mode controller is developed to guarantee finite-time reachability of the sliding manifold in the mean-square sense. On the manifold, a modedependent Lyapunov-Krasovskii functional is established, and sufficient stability conditions are derived in the form of linear matrix inequalities by explicitly incorporating the bounded time-varying transition rates. As a result, the closed-loop sliding dynamics are ensured to be robustly mean-square exponentially stable, and the controller gains can be obtained by solving the proposed LMIs. A numerical example further demonstrates the effectiveness of the proposed method.

This article investigates the mean-squared leader-following consensus problem of nonlinear multi-agent systems under semi-Markov switching topologies. By integrating the merits of three advanced control approaches, a novel aperiodic intermittent dynamic event-triggered mechanism is developed to further save network resources. Moreover, the developed mechanism is only executed during the working interval of each intermittent period, and the communication instants are determined by a predefined discrete triggering condition, while the internal dynamic variable can be adjusted adaptively with random sampling signals. By fully taking the information of semi-Markov switching parameters, virtual delay, and internal dynamic variables into account, a general Lyapunov functional is constructed to depict the dynamical evaluation of systems. Then, two less-conservative consensus criteria are derived by virtue of the developed control mechanism, the general Lyapunov functional, and other analysis methods. In the end, two numerical examples are provided to demonstrate the effectiveness of our approach in reducing the waste of network resources.

This research focuses on the asymptotic stability of quaternion-valued neural networks (QVNNs) under diversified random network attacks and introduces a novel adaptive event-triggered (AET) communication protocol. First, this study explicitly accounts for the potential for network attacks. A dynamic threshold update mechanism is proposed, which incorporates a weighted factor to modulate the update strength of the threshold, and designs an AET control strategy based on non-periodic sampling. This approach enhances the system’s responsiveness to state changes and optimizes bandwidth utilization. Next, a new loop function is constructed, and less conservative asymptotic stability criteria are formulated depending on AET conditions. Finally, numerical simulations and application examples in pseudo random number generators (PRNGs) validate the reliability of the proposed approach, demonstrating its potential value in the fields of cryptography and secure communications.

This paper investigates the security quasi-synchronization issue for a class of semi-Markov Delayed Memristive Neural Networks (semi-MDMNNs) subject to deception attacks based on intermittent control mechanism. Different from the existing results, a new type of network attacks mode, named Random Occurring Delayed Deception Attacks (RODDAs), is proposed by considering the occurrence characteristics and lagged effect of realistic network attacks. Besides, a new Event-driven Intermittent Control Mechanism (EDICM) is designed by selecting an auxiliary function that does not depend on the initial state of the system and considering the evolution law of the system state. Then, new effective quasi-synchronization criteria are presented for the master–slave semi-MDMNNs under RODDAs by utilizing the EDICM, iterative analysis, interval matrix method, inequalities scaling technique, and so on. Numerical simulation results show that the RODDAs can significantly degrade the systems performance, the new EDICM can further save the control cost and ensure security quasi-synchronization of semi-MDMNNs simultaneously. The modeling, analysis and control methods provided in this paper will further enrich the theoretical framework and application scenarios of complex nonlinear systems.

The leader-following consensus problem for a class of multi-agent systems with nonlinear disturbances and time-varying delays under semi-Markovian switching topologies is investigated in this paper. A novel aperiodically intermittent time-triggered communication protocol is proposed and constructs a minimum working interval ratio related to the performance degradation rates of the system in different intervals. This protocol triggers control updates only when the communication error states between followers and their neighboring agents satisfy the predefined triggering conditions, thereby significantly reducing energy consumption. In addition, in order to fully consider the influence of time delay and nonlinear coupling in practical applications, by constructing a more general Lyapunov functional, some sufficient stability conditions expressed in linear matrix inequalities (LMIs) to ensure the leader-following consensus of multi-agent systems are strictly derived. Finally, the effectiveness of the proposed method is verified by numerical simulation.

The subject of this passage is the stability and stabilization issues of semi-Markov jump systems (SMJSs) with parameter uncertainty. To introduce new concepts, a novel Lyapunov-Krasovskii functional (LKF) is formulated to fully leverage the properties of actual sampling patterns, which incorporate information regarding states within the sampled-data intervals. Subsequently, several relaxed matrices are presented in the LKF, which are not required to be positive definite. On the basis of certain integral techniques, necessary criteria are established to ensure the stochastic stability of SMJSs while mitigating the effects of parameter uncertainty. Furthermore, the developed quantized sampled-data controller enhances control performance. Ultimately, an example is given to showcase the advantages and superior performance of the proposed method.

This paper studies the problem of mean square exponential stability for Reaction Diffusion Memristive Neural Networks (RDMNNs) with Time-varying Delayed (TD) and semi-Markovian Parameters(SMPs). First, a RDMNNs model considering both TD and SMPs is established. Second, to achieve a balance between convergence speed and control cost, a novel two-sided intermittent boundary control (TSIBC) strategy is designed, which incorporates more information regarding the two-sided boundaries and SMPs. Then, leveraging the Lyapunov stability theory and inequality analysis technology, a new stability criterion for the semi-Markov delayed RDMNNs is derived. Finally, a numerical example is given to verify the effectiveness of the proposed control strategy.

This paper investigates the robust H-infinity stabilization problem for Takagi-Sugeno (T-S) fuzzy network probabilistic time-delay systems with network-induced time-varying delays. To this end, a novel event-triggered strategy based on relative error is designed. Compared to traditional event-triggered strategies, this approach incorporates a buffer to effectively utilize known transmitted historical sampled data, which not only improves the system's dynamic process but also significantly reduces communication overhead. Subsequently, by comprehensively considering network-induced delays and the event-triggered scheme, a Piecewise Lyapunov functional is constructed. Through a series of Linear Matrix Inequalities (LMIs), the controller gains and event-triggered parameters are derived. Finally, the effectiveness of the proposed method is validated through simulation case studies.

This paper investigates the anti-synchronization control problem for a class of Memristor-based Neural Networks with time-delay and semi-Markov jump parameters. Firstly, to further effectively utilize the network resources, a novel Intermittent Discrete Dynamic Event-triggered (IDDET) scheme is introduced, where the dynamical update law of the IDDET scheme is designed to be related to the current sampling state. Secondly, by fully considering the information of jump parameters, time-delay, sampling period, and interaction of the current and past states, a general common Lyapunov functional is constructed. Then, with the virtue of inequalities analysis technique and quadratic polynomial negative definite lemma, a new less conservative criterion guaranteeing anti-synchronization for the underlying master-slave systems is derived in the form of Linear Matrix Inequalities (LMIs). In the end, the validity of our results is illustrated through a numerical example.

The aim of this paper is to investigate a novel fractional order integral inequality (FOII) for reducing the conservatism of the stability and the non-fragile sampled-data control (NFSDC) criterion for the uncertain fractional-order systems (FOSs) with time-varying delay (TVD). Firstly, in order to estimate the quadratic derivative of fractional-order integral more accurately, a new FOII with free weighting matrix is proposed, which has a tighter upper bound than the existing FOII. Second, in order to more accurately reflect the delay variation and reduce the data transmission frequency, the influence of uncertainty and time-varying delay are considered, the NFSDC scheme followed by the discussed stability criterion is given based on our novel piecewise Lyapunov functional and introduced FOII. Finally, three numerical examples demonstrate the feasibility and superiority of the proposed method.

In this paper, a new stochastic self-adaptive subgradient extragradient approximation algorithm incorporated inertial technique is proposed to solve the stochastic pseudomonotone variational inequality problem. The convergence, convergence rate and oracle complexity of the algorithm are investigated. A numerical example illustrates the effectiveness of the new algorithm. The numerical results show that our algorithm is competitive with other related algorithms in the literature [Yang et al. Variance-based modified backward-forward algorithm with line search for stochastic variational inequality problems and its applications. Asia-Pac J Oper Res. 2020;37(3):2050011] and [Wang et al. A self-adaptive stochastic subgradient extragradient algorithm for the stochastic pseudomonotone variational inequality problem with application. Z Angew Math Phys. 2022;73(4):164]. Finally, the main results obtained are applied to solve image restoration problem.

This paper investigates the exponential synchronization problem of Interval Type-2 Fuzzy Neural Networks with time-varying delay. To save control cost and limited bandwidth, an Intermittent Event-Triggered Control strategy that combines the advantages of an intermittent control scheme and event-triggered control scheme is proposed. Unlike traditional periodic intermittent event-triggered control, we consider a general periodic intermittent event-triggered control scheme with variable width in this paper. In addition, a low conservative exponential synchronization criterion was established by combining the Lyapunov stability theory, reciprocally convex inequality, and integral inequality. Finally, a numerical example is provided to demonstrate the effectiveness and feasibility of the proposed scheme.

This paper focuses on the fixed-time synchronization problem of semi-Markov reaction-diffusion neural networks (RDNNs) under asynchronous boundary control. Firstly, asynchronous boundary control and semi-Markov jumps are introduced into RDNNs, overcoming the limitation that traditional synchronous control systems and controllers can only follow the same switching rule. Secondly, by designing an asynchronous controller and utilizing the Lyapunov function method as well as matrix inequality analysis techniques, a sufficient condition for fixed-time synchronization based on linear matrix inequalities is derived. Finally, the effectiveness of the proposed design method is verified through a numerical example.

This paper aims to address the exponential stability and stabilization problems for a class of delayed nonlinear Markov jump systems under randomly occurring Denial-of-Service (DoS) attacks and packet loss. Firstly, the stochastic characteristics of DoS attacks and packet loss are depicted by the attack success rate and packet loss rate. Secondly, a Period Observation Window (POW) method and a hybrid-input strategy are proposed to compensate for the impact of DoS attack and packet loss on the system. Thirdly, A Dynamic Event-triggered Mechanism (DETM) is introduced to save more network resources and ensure the security and reliability of the systems. Then, by constructing a general common Lyapunov functional and combining it with the DETM and other inequality analysis techniques, the less conservative stability and stabilization criteria for the underlying systems are derived. In the end, the effectiveness of our result is verified through two examples.

This article focuses on fuzzy structural adaptive optimal control issue of discrete-time nonlinear complex networks (CNs) via adopting the reinforcement learning (RL) and Takagi-Sugeno fuzzy modeling approaches, where the control gains are subjected to structured constraints. In accordance with the Bellman optimality theory, the modified fuzzy coupled algebraic Riccati equations (CAREs) are constructed for discrete-time fuzzy CNs, while the modified fuzzy CAREs are difficult to solve directly through mathematical approaches. Then, a model-based offline learning iteration algorithm is developed to solve the modified fuzzy CAREs, where the network dynamics information is needed. Moreover, a novel data-driven off-policy RL algorithm is given to compute the modified fuzzy CAREs, and the structural optimal solutions can be obtained directly by using the collected state and input data in the absence of the network dynamics information. Furthermore, the convergence proofs of the presented learning algorithms are provided. In the end, the validity and practicability of the theoretical results are explicated via two numerical simulations.

This paper is concerned with the security stabilization problem for a class of Complex-valued Neural Networks (CVNNs) with Markov Jump Parameters (MJPs) and Additive Time-varying Delays (ATVDs) under Random Deception Attacks (RDAs). Different from the existing literature, the instant and strength of RDAs considered in this paper is both random, which is more in line with the real situation. Secondly, a general Lyapunov-Krasovskii Functional (LKF) contains more information about MJPs and ATVDs is constructed, and a new Complex-valued Reciprocally Convex Inequality (CVRCI) containing more free matrices and ATVDs parameters is proposed, which play a key role in reducing the conservativeness of security stabilization criteria. Thirdly, a Discrete Event-triggered Mechanism (DETM) is introduced to mitigate the transmission burden of communication networks, in which the triggering condition of DETM mainly relies on the current sampled state and the last triggered state. Then, by combining with the LKF, CVRCI, DETM, and other analysis techniques, some less conservative security stabilization criteria for the underlying systems are provided in terms of Linear Matrix Inequalities (LMIs). Finally, the effectiveness of our results are verified by two numerical examples and a practical example.

This study examines the stability and stabilization issues of a type of state-quantized, time-varying delayed (TVD) Takagi–Sugeno (T–S) fuzzy semi-Markov jump systems. First of all, in order to obtain more information of T–S fuzzy systems, an augmented fuzzy Lyapunov–Krasovskii Functional (LKF) is formatted including a quadratic fuzzy Lyapunov matrix (QFLM). In addition, a novel quadratic polynomial inequality (QPI) is applied to narrow the estimation gap for TVD and a quantized controller is used to reduce control accuracy. Then, the sufficient conditions for system stability and stabilization via quantized controller are attained on the basis of Lyapunov stability theory and linear matrix inequalities method. Finally, three examples show how the constructed controller can successfully regulate the examined system and the proposed technique is less conservative than those of the former ones.

This article is centered on the synchronization issue of fuzzy reaction-diffusion dynamic networks (RDDNs) with multiple cyberattacks. A novel attack-resilient dynamic event-triggered policy and the relevant fuzzy attack-resilient controller are designed via considering the deception and irregular (aperiodic) denial-of-service (DoS) attacks simultaneously. Based on a novel piecewise Lyapunov-Krasovskii functional with the realistic sampling information and some inequality techniques, some criteria are derived to ensure that the synchronization of fuzzy RDDNs can be realized in the presence of the deception and irregular DoS attacks. Lastly, simulation examples containing the colour image encryption/decryption are supplied to exhibit the advantages and practicality of the developmental theories.