This paper investigates the secure optimal load frequency control (LFC) problem for Markovian multi-area power systems under false data injection (FDI) attacks. First, by employing the Markov jump process to describe the power system’s state changes induced by FDI attacks, a Markovian multi-area power system model is constructed. Subsequently, considering the secure optimal LFC design of the Markovian multi-area power system, coupled Riccati equations (CREs) are derived. Then, to solve these CREs, an adaptive weight-dependent iteration algorithm is proposed. By progressively increasing the weight of the latest step information, the algorithm can accelerate convergence. Finally, the effectiveness of the secure LFC is validated through a simulation example of a Markovian three-area power system. Compared with the fixed weight iteration algorithm, the proposed adaptive weight-dependent iteration algorithm exhibits faster convergence and lower residuals.

This paper investigates a class of McKean-Vlasov stochastic neural networks (MV-SNNs) subject to Lévy noise, mixed time-varying delays, and coefficients that depend on both the state and its probability distribution. Existing methods struggle to concurrently address the solution’s existence and uniqueness, long-term dynamics analysis, and the construction of stability criteria. To tackle this, we develop a systematic analytical framework via an innovative methodology that combines fixed point theory with the resolvent operator (RO) technique. First, novel criteria for the existence and uniqueness of mild solutions are established. Second, by integrating the RO with Hölder’s inequality and Itô’s isometry, sufficient conditions for the global attracting set (GAS) and quasi-invariant set (QIS) are derived, enabling quantitative analysis of long-term dynamics. Furthermore, using the RO together with Gronwall’s inequality, Chebyshev’s inequality, and the Borel-Cantelli lemma, we establish criteria for mean square and almost sure exponential stability. These moment stability criteria inherently guarantee solution existence and uniqueness without requiring additional constraints. Finally, two examples demonstrate the applicability and effectiveness of the theoretical results.

This paper investigates the exponential stabilization of stochastic complex network switched systems (SCNSSs) with a novel event-triggered switching control, which comprises a primary control and a secondary control. In this control, “switching” has two implications. One is consistent with the switching signal of the system and the other refers to the switching between the primary control and the secondary control. Moreover, unlike traditional systems that utilize a single event-triggering mechanism (ETM), this paper introduces multiple ETMs to improve the control strategy by determining the updating instants of the primary control and the switching instants between the primary and secondary controls. Under the proposed novel event-triggered switching control, the asynchronous problem of time series is solved and the mean-square exponential stabilization for SCNSSs is obtained. Finally, the effectiveness of theoretical results is demonstrated through the simulation conducted on a stochastic oscillator system with multiple nodes.

This study proposes a novel and cohesive framework to address stochastic finite-time consensus (FTC) problems, with the following main contributions: (i) We first introduce the original stochastic delay systems and, based on this, analyze the effects of Lévy noise, actuator faults, and Markov switching. Both leaderless and leader-follower topologies are considered, and a new control algorithm is proposed to investigate the fault-tolerant control problem under the influence of communication delays and Markov switching dynamics. (ii) To ensure that the states converge to a bounded compact set, the convergence analysis uses strong mathematical techniques, such as stopping time theory and the evolution of finite-time stochastic theory, to achieve mean-square and almost certain consensus. (iii) An important aspect of this study is the consideration of Markov-switching actuator faults, where fault occurrence and recovery evolve randomly according to a Markov process, introducing additional stochastic uncertainties into the system dynamics. Additionally, two numerical examples are provided to validate the correctness of the theoretical results.

This work reports design problem of the memory sampled-data (SD) controller for interval type-2 fuzzy singular systems (SSs) with external disturbances. First, an improved free-weighting matrix inequality is introduced for concerning fuzzy SSs to reduce conservatism of the integral terms. Then, a novel looped-functional-based Lyapunov-Krasovskii functional (LKF) is constructed that incorporates the data from sampling interval $\mathbf {z}(t)$ to $\mathbf {z}(t_{k})$ . With the help of improved integral inequality and novel LKF, a new set of admissibility conditions is developed in the form of linear matrix inequalities (LMIs). The developed criteria based on the memory SD controller ensure that the proposed systems is admissible with an $H_{\infty }$ attenuation level. Finally, numerical simulations are given to illustrate the usefulness and benefit of the proposed methods.

In this article, we investigate the exponential stabilization of stochastic systems with sampled-data output. Two kinds of piecewise continuous functions (with/without noise) called intersample predictors are constructed to approximate discrete output signals. Corresponding predictor-based observers are then designed to obtain a good convergence of the estimation error. Based on the proposed predictors and observers, novel event-triggered strategies are developed to achieve exponential stabilization and address the asynchronism issue in input-output measurements. Finally, an illustrative example is provided to verify the effectiveness of the theoretical results.

Adaptive fixed/predefined-time control to synchronize discontinuous multiple delay neural networks (DMDNNs) under unknown parameters identification is studied in this paper. To overcome the influence under uncertain factors in the DMDNNs, adaptive control technology is introduced into the design of controllers. In order to identify unknown parameters for state dependent switching in the DMDNNs within a fixed/predefined settling time, a fixed/predefined time identification method is derived. Under the premise that fixed time synchronization (FTS) is implemented in DMDNNs, adaptive fixed time identifier and controller are redesigned to achieve synchronization and identify unknown parameters in the DMDNNs within a predefined settling time. By the Lyapunov stability method, the corresponding synchronization criteria under FTS and predefined-time synchronization (PTS) are derived. FTS/PTS and identification of parameters under DMDNNs have potential applications in secure communication, pattern recognition, and other fields.

In this paper, fixed-time and practical fixed-time control of switched Filippov systems on networks with nondifferential delays are studied. Firstly, by using the comparison principle and intermittent control interval method, intermittent fixed-time stability lemmas with unified exponential conditions are proposed. The estimation of the settling-time shows that the elasticity number in the control interval plays a vital role. In order to solve the unavailability of global information, without using the auxiliary timer function, intermittent practical fixed-time lemmas with unified exponential conditions are established, which can improve the related ones greatly. It is necessary to point out that the residual set is relevant to the constant parameters of the system. The constant parameters of the system can be used to get a needed attraction region. Based on newly established stability lemmas, the fixed-time control and practical fixed-time control of the addressed switched Filippov systems are achieved based on the designed intermittent-type quantized control strategies, which enables the quantized control to be performed in intermittent intervals. Some previous control strategies are improved. Finally, numerical examples and simulations are provided to verify the validity of the obtained results. Note to Practitioners—Intermittent control has become popular recently since it saves more costs and is more practical in engineering. As for the complex networks, it is not enough to use intermittent control only, but also to consider the bandwidth of signal transmission. So, how to enable the quantized control to be performed in intermittent intervals is an interesting question. In addition, the global information of many models is unidentifiable, practical fixed-time control will be more realistic. Is the residual set in practical fixed-time control relevant to the intermittent control interval? These questions puzzled the authors and prompted this study.

This paper investigates the adaptive fuzzy event-triggered optimized consensus tracking control problem for uncertain stochastic nonlinear multi-agent systems (MASs) with unknown dynamic and time-delay. Typically, optimal control is derived by the solution of the Hamilton-Jacobi–Bellman (HJB) equation, but it is usually challenging to solve this equation since inherent nonlinearity and unknown dynamics. Specifically, the complexity of the MASs in controller design is further exacerbated by the issue of state interdependence. To achieve optimized consensus control, the adaptive dynamic programming strategy is derived using the negative gradient of a simple positive function. As a result, the designed optimized consensus tracking control is relatively simple and can eliminate the persistence excitation (PE) assumption. The fuzzy logic systems (FLSs) are utilized to approximate the current and delayed states of unknown nonlinear functions; the identifier is proposed to estimate the stochastic multi-agent dynamic; the critic and actor FLSs are designed to evaluate control performance and execute control behavior, respectively. Furthermore, the event-triggered control (ETC) method is developed to save transmission load and communication resources. Moreover, we demonstrate that all signals for the MASs are semi-globally uniformly ultimately bounded (SGUUB) in mean square, and that the states of the follower agents can reach consensus with the leader’s state. Finally, a numerical example is illustrated to demonstrate the effectiveness of the proposed method. Note to Practitioners—With environmental protection and energy conservation becoming dominant trends, improving efficiency is regarded as a fundamental principle in control design. In addition, MASs are widely affected by factors such as stochastic disturbance, model unknown, time-delay, and uncertain factors, which further increase the difficulty of controller design. In this work, the optimized control approach is developed to design the control strategy for MASs to achieve the control task with the minimum utilization rate of control resources. In practical application scenarios such as spacecraft control or aircraft operation, the designed optimized control scheme can not only minimize fuel consumption to complete the predetermined tasks but also eliminate the PE assumption and strong assumptions on the time-delay nonlinear functions. Furthermore, the proposed ETC strategy effectively reduces the communication resource and network transmission in practice. Therefore, the control strategy designed in this work is more easily applicable to practical engineering.

The optimal consensus fault-tolerant control (FTC) problem for unknown time-delays nonlinear stochastic multi-agent systems (MASs) with hybrid actuator faults is investigated via adaptive dynamic programming (ADP) under the dynamic event-triggered control (ETC) mechanism in this paper. In control design, FLSs with delayed states are utilized to design an adaptive state identifier for estimating the unknown delayed dynamics in stochastic MASs. The fault estimator is constructed to detect actuator bias fault in real-time. By utilizing the ADP algorithm with identifier-actor-critic structure, a simplified fuzzy adaptive optimal consensus FTC strategy is developed, which does not require persistent excitation (PE) assumption. Furthermore, a dynamic ETC strategy is designed to further optimize the data transmission efficiency, effectively enhancing the system flexibility and resource utilization. Theoretical analysis indicates that the proposed control scheme can ensure that all signals of the nonlinear stochastic MASs are semi-globally uniformly ultimately bounded (SGUUB) in mean square, while achieving consensus between the follower’s states and the state of the leader. Finally, a numerical simulation validates the efficacy and feasibility of the proposed control strategy. Note to Practitioners—With the intensification of the global energy crisis, energy consumption optimization has become a crucial performance indicator of modern control design. In this paper, the optimal consensus FTC strategy is developed for unknown nonlinear stochastic MASs with time delays and actuator failures, which can achieve control requirements while minimizing control costs. The proposed control strategy can be applied to practical scenarios such as aerospace, formation control, and power systems. Compared with the existing control algorithms, the proposed control strategy avoids complex dynamic modeling and strong assumptions of nonlinear functions, and does not require PE assumption. In addition, a novel dynamic ETC strategy has been developed, which effectively improves resource utilization and data transmission efficiency compared with traditional continuous-time control and general ETC strategies. Consequently, the control strategy designed in this paper exhibits broader applicability and stronger practical value.

In this article, the adaptive neural network prescribed performance control issue is followed with interest for a class of non-triangular structural stochastic highly nonlinear interconnected systems under hybrid attacks, that is, injection attack and deception attack. Unlike the previous achievements, the original states of the system are unknown under the influence of hybrid attacks, and it is particularly difficult to handle highly nonlinear interconnection functions of non-triangular structure in the system. Hence, an effective variable separation method based on adaptive compensation technology is constructed, such that the complex nonlinear functions can be separated and further simplified, and then approximated by neural network. By utilizing a prescribed performance function, the tracking error of the system can converge in a fixed time based on the Lyapunov stochastic stability theory and the framework of the backstepping technology. Ultimately, the reliability and effectiveness of the proposed control strategy can be verified by a practical example. Note to Practitioners—With the rapid increase of the complexity of the practical engineering systems, such as manipulator system, automated highway systems and so on, it is difficult to be described by the common nonlinear system model. Moreover, these networked practical systems are often plagued by external attacks, which seriously affects the performance of the system and makes it difficult to design the control scheme. Therefore, this paper investigates a class of stochastic highly nonlinear interconnected system model which is more in line with the practical demand. On this basis, in order to improve the control efficiency of the practical engineering systems and solve the influence of external attacks, a fixed-time prescribed performance adaptive control strategy is constructed to satisfies the control requirement of the complex stochastic system. The proposed control scheme is more convenient for physical implementation, and is also applied to the single-link manipulators system to prove its feasibility.

This paper investigates the non-overshooting tracking conditions forn-th order nonlinear systems with unmeasurable states. By designing state observers, the problem of unmeasurable states is addressed. The key to non-overshooting control (OC) is how to design appropriate controller to ensure the system is not only stable but also effectively solves the non-OC problem. Based on backstepping, a square root gain control algorithm is proposed in this paper, which ensures global asymptotic stability of the closed-loop system. Meanwhile, two main conclusions are drawn in non-OC: 1) If the initial values of the system states are equal to the initial values of the observer states, the conditions obtained by the proposed algorithm can achieve non-OC, i.e., the system overshoot is zero. Non-OC conditions for$n=1$,$n=2$,$n=3$, and$n\geq 4$order systems are obtained, respectively. And the conditions are relatively rich. Therefore, compared with existing algorithms, this algorithm not only ensures zero system overshoot, but also reduces conservatism; 2) If the initial values of the system states are not equal to the initial values of the observer states, the conditions obtained by this algorithm can achieve mean-non-OC, i.e., the system overshoot can be adjusted to any small value. In terms of simulation, the stability performance algorithm, non-OC algorithm, and mean-non-OC algorithm were verified using the mathematical models of the DC servo motor systems and Chua’s circuit system. Simulation results show that these control algorithms are effective. It also compares existing related results, highlighting the superiority of the algorithm presented in this paper.

In the rapidly evolving landscape of 5G and beyond 5G (B5G) mobile cellular communications, efficient data compression and reconstruction strategies become paramount, especially in massive multiple-input multiple-output (MIMO) systems. A critical challenge in these systems is the capacity-limited fronthaul, particularly in the context of the Ethernet-based Common Public Radio Interface (eCPRI) connecting baseband units (BBUs) and remote radio units (RRUs). This capacity limitation hinders the effective handling of increased traffic and data flows. We propose a novel two-stage compression approach to address this bottleneck. The first stage employs sparse Tucker decomposition, targeting the precoder tensor’s low-rank components for compression. The second stage further compresses these components using complex Givens decomposition and run-length encoding, substantially improving the compression ratio. Our approach specifically targets the Zero-Forcing (ZF) beamforming precoder in BBUs. By reconstructing this precoder in RRUs, we significantly alleviate the burden on eCPRI traffic, enabling more concurrent streams in the radio access network (RAN). Through comprehensive evaluations, we demonstrate the superior effectiveness of our method in Channel State Information (CSI) compression, paving the way for more efficient 5G/B5G fronthaul links.

This study focuses on the state tracking problems of chaotic Lur'e systems with nondifferentiable delay and partial channel restriction via intermittent observer. Different from the results obtained by existing chaotic Lur'e systems, the time delay involved in the chaotic Lur'e system explored in this study does not require that the time delay must be differentiable and there is no limit that the time delay must be bounded, which is more in accordance with the operating situation in practical engineering. Subsequently, aiming at the inevitable cyber-attack in the communication network environment, an intermittent observer based on the loss of partial measurement information induced by cyber-attack is constructed. Especially, in the operation process of the designed intermittent estimator, it breaks through the strict requirement that the observation width must be greater than the upper limit of the delay in the existing work, which intuitively reflects the wider application range and has more exploratory significance. Moreover, a meaningful lemma is designed, which effectively overcomes the invalidity of existing Lyapunov function or Lyapunov-Krasovskii functional methods for nondifferentiable systems, and develops novel criteria for partial information loss and nondifferentiable systems, presenting an important theoretical guidance for related topics. Numerical simulations are provided to verify the effectiveness of the proposed intermittent observer mechanism and the stabilization criteria of the error system. Finally, an application of the proposed intermittent observation result for two identical chaotic systems to a secure communication approach is provided.

This article addresses the fixed-time leaderless cluster synchronization of spatiotemporal community networks (SCNs) characterized by nonidentical node dynamics and reaction-diffusion feature. First, a signed SCN with reaction-diffusion effect is formulated, where the sign-based coupling is introduced to capture the dynamics of coopetition interactions among different communities. Second, to ensure the invariance of the synchronous manifold, an improved interdegree balance condition is proposed as a prerequisite for achieving cluster synchronization of the community network. Third, based on the local state information from adjacent nodes within each community, a time-limited controller is designed to enhance intracommunity coordination while avoiding the adverse effects of intercommunity competition on synchronization. Subsequently, with the help of the matrix decomposition technique and a Lyapunov-like method, several flexible leaderless cluster synchronization criteria are derived by establishing a nontrivial integral inequality and key properties of the intracommunity Laplacian matrix. Finally, the theoretical results are substantiated through a numerical example.

This article studies the distributed coordination control problem of the nonlinear stochastic multiagent system, which involves multiple inequality constraints, as well as random disturbances. The communication network is modeled as an undirected and connected graph, where each node has a cost function that is considered to be strongly convex. First, an algorithm is developed that utilizes state feedback and projection operations, along with auxiliary variables, to precisely estimate the optimal state and its derivatives in a distributed manner. Furthermore, the decision variable is subject to several inequality constraints, and there are no restrictions on the initial value. Taking into account the impact of nonlinearity resulting from drift coefficients, diffusion coefficients, and external disturbances on the system’s stability, the existing works cannot be directly applied to this study. Through the utilization of the${\rm It}\hat{\rm o}$formula and convex analysis, a novel analytical approach has been demonstrated to establish the asymptotic convergence of decision variable to the optimal value in mean square. This method distinguishes itself from the conventional convergence analysis techniques. Finally, the algorithm is utilized for the allocation of energy resources, resulting in the attainment of the optimal regulating method for power resource allocation.

This article primarily investigates thepth moment exponential stability of a class of highly nonlinear stochastic delayed systems subject to impulses and Markovian switching. Significantly, we establish sufficient conditions for thepth moment exponential stability of the considered system and derive an upper bound for the moment Lyapunov exponent. By using the comparison principle, impulsive effect is explored. Finally, the practicality and feasibility of the theoretical results have been demonstrated through a numerical simulation.

In this article, the conditions of ensuring nonovershooting tracking control (NOTC) for nonlinear pure-feedback systems (PFSs) are proposed. Presently, there are almost no results of guaranteed NOTC conditions for nonlinear PFSs. And the results in strict-feedback form are also very narrow. Based on these problems, this article obtains a more extensive conditions of NOTC for nonlinear PFSs. First, a controller is designed to make the closed-loop system (CLS) globally asymptotically stable, and a suitable CLS can be obtained through the designed controller. Then, by analyzing the CLS, the NOTC conditions of the first-order, second-order, and multiorder systems can be obtained, respectively. Finally, through the simulation results of two examples and comparing the simulation results of the existing algorithms, it is concluded that the algorithm in this article is effective and superior. In this article, for more general nonlinear PFSs, a wider range of NOTC conditions are obtained, and the obtained NOTC conditions are also suitable for strict-feedback form. Therefore, this algorithm reduces the conservatism.

This article investigates nonovershooting tracking control for a class of multiple-input–multiple-output (MIMO) nonlinear systems. Nonovershooting tracking control is desired in various practical situations, yet remains a challenging task with limited existing research. While the MIMO nonlinear system better represents real-world scenarios, the specific algorithm for nonovershooting tracking control has not been previously reported. In this study, a controller is designed to ensure system stability initially, while also achieving a closed-loop system for easy tracking error analysis. By deriving the expression of tracking error, a broad range of nonovershooting tracking conditions is identified through analytical analysis. The proposed nonovershooting control is shown to offer more extensive nonovershooting conditions compared to existing approaches, thereby reducing conservatism. Furthermore, this algorithm eliminates overshoot in MIMO nonlinear systems. Its effectiveness is validated through application to a two-degree-of-freedom robot manipulator.

In this article, the predefined-time (PdT) control of the switched neutral Filippov system (SNFS) is studied. Semi-intermittent-type and completely intermittent-type PdT stability lemmas are initially established. The indefinite function, united exponent parameter and intermittent time condition are adopted. The new completely intermittent-type PdT stability lemma shows that intermittent interval is related to the PdT parameter, and semi-intermittent-type one is not. Such results are new and some previous PdT stability lemmas are improved greatly. As an application, the SNFS is proposed, which is more generalized. Under the semi/completely intermittent time conditions framework, by designing discontinuous control strategy and bounded control strategy, the zero solution of the considered SNFS is PdT stable. For the PdT control, the control input constraint is considered for the first time. Finally, a numerical example and simulations are provided to illustrate the correctness of the main results.

This work reports design problem of the observer-based integral sliding mode control for switched time-delay systems via asynchronous switching and dissipative condition. The main purpose of observer is to estimate the system’s entire state information based on measurement outputs, and further the observer states are used to create the controller. First, an improved free-weighting matrix inequality is introduced for concerning switched systems (SSs) to reduce conservatism of the integral terms. Then, a novel asymmetric Lyapunov–Krasovskii functional (LKF) is constructed for analysing the exponential stability of SSs with time-delay. With the help of improved integral inequality and novel LKF, a new set of sufficient conditions is developed in the form of linear matrix inequalities (LMIs). The developed criteria based on the sliding mode controller with observer scheme ensure that the proposed systems is exponentially stable with dissipative performance. Finally, numerical simulations are given to illustrate the usefulness and benefit of the proposed methods.

This article is committed to investigate thepth moment input-to-state stability for stochastic nonlinear delayed systems involving multiple impulses. Via a series of auxiliary equations, Razumikhin method and stochastic analysis approach, we derive some new stability results under the combination of impulsive control and impulsive disturbance. For all we know, this article is the first attempt to study such a stability issue for the suggested systems. Additionally, the concepts of stabilizing impulse average dwell time (SIADT) and destabilizing impulse average dwell time (DIADT) are proposed, respectively, owing to the presence of multiple impulses. It should also be pointed out that the obtained criteria can loose some restrictions of the existing results and have wider applications. Particularly, we allow the cumulative strength of multiple impulses over a period to be greater than 1, which is more applicable to some extent compared with most of the existing literatures. Finally, the effectiveness and validity of the theory are supported by two examples.

This article investigates the issue of asynchronous event-triggered secure control for Markov jump systems (MJSs) under aperiodic denial-of-service (DoS) attacks. A memory-based mode-dependent resilient event-triggering scheme (MMRETS) based on aperiodically sampled data is designed to avoid Zeno behavior and continuous monitor, which has the advantages in mitigating the transmission times and tolerating the DoS attacks. Meanwhile, the asynchronous circumstance between the system and corresponding event-triggered controller in the absence of DoS attacks is characterized via a hidden Markov model (HMM). Subsequently, by using a novel Lyapunov functional and an iterative approach, sufficient conditions are obtained to guarantee the${\mathcal {H}}_{\infty }$performance of the resultant Markov closed-loop system. Finally, a practical truck-trailer model example is provided to illustrate the efficacy and benefits of the proposed methods.

The global polynomial synchronization (GPS) is investigated for memristive competitive neural networks (MCNNs) with proportional delays and uncertain parameters. First, via drawing support from differential inclusion theory and adopting the time-variant state feedback controllers, their error systems are synthesized into a vector form MCNNs. Then, a new proportional delay differential inequality (PDDI) is established through norm definition and Lipschitz condition for the vector form MCNNs mentioned-above. Several algebraic forms of synchronization criteria for the system proposed are achieved by applying the new PDDI. Each of these criteria is represented by only one inequality, rather than in the form of components, which facilitates validation. Compared to the commonly used method for constructing Lyapunov functionals in studying MCNNs, it is more concise. Ultimately, numerical examples are used to inspect the results acquired, and the GPS of one example is applied in image encryption and decryption. The empirical outcomes demonstrat the efficacy of the employed synchronization control approach, exhibiting robust resilience and heighten security in secure communication applications.

This paper focuses on the fuzzy model-based quantitative control for prefixed-time synchronization of reaction-diffusion (RD) complex networks under stochastic noise, cyber-attacks and saturation. Different from the existing finite/ fixed time synchronization, a concept of prefixed-time synchronization is proposed to cope with cyber-attacks and stochastic noise in the target system, rather than the common finite/fixed-time synchronization. Then, two different prefixed-time synchronization criteria are presented by designing two appropriate quantization controllers and adopting the well-known probability-density inequality and the generalized sector condition techniques. Note that the proposed quantization controller can effectively overcome the constraints of communication channel and bandwidth limitation caused by cyber-attacks. Especially, the given quantization controller does not adopt the common sign function so as to avoid the controller’s quivering behavior, which effectively reduces the conservatism. Finally, two simulation results are provided to verify the rationality and superiority of the developed control design scheme in this paper.Note to Practitioners—It is an indisputable fact that dynamic behaviors based on complex networks sometimes depend not only on their temporal information but also on spatial locations to a large extent, such as chemical and biological processes. Therefore, the research in this study is the complex networks with RD terms rather than the common complex networks of ordinary differential form. In addition, cyber-attacks, stochastic disturbance, actuator saturation, etc. exist widely in network systems, which are completely unavoidable. Therefore, when complex networks with reaction-diffusion terms are also affected by these factors, can they achieve synchronization? In particular, is existing fixed/finite time synchronization strategy still feasible when complex networks are suffer from stochastic disturbances rather than ordinary unknown/known bounded disturbances? These questions puzzled the authors and prompted this study.

This article is concerned about fixed-time (FT) synchronization of spatiotemporal networks (STNs) with the Robin boundary condition. Above all, a switching-type FT stability theorem and an integral inequality are established, which provide a novel theoretical tool for the rigorous analysis of FT control in STNs. Subsequently, three kinds of nontrivial power-law controllers are developed which are separately acted on the interior, the boundary, and the whole of the spatial domain. Based on these control schemes and Lyapunov-like method, several flexible criteria are obtained to achieve FT synchronization of STNs, and the upper bound of the synchronization time is explicitly estimated. Note that, the derived results here are also perfectly applicable to STNs with Neumann or Dirichlet boundary condition. Several illustrate examples are presented at final to confirm the developed controllers and criteria.

In this article, finite/fixed-time stabilization and energy consumption estimation of a class of discontinuous fuzzy inertial Cohen-Grossberg neural networks (CGNNs) are considered. The saturation function is utilized to design the control laws, which is different from the previous ones with the sign function since the saturation function is continuous and can reduce the chattering phenomenon. By using the Lyapunov method, comparison principle, and differential inequality theory, the finite/fixed-time stabilization is analyzed by analyzing the state variables inside and outside the unit spherical area, which is different from the direct calculation method using finite/fixed-time stability lemmas. Detailed analyses show the differences in the estimations of the settling time between the initial values inside and outside of the unit spherical area. The energy consumption is also estimated when the finite/fixed-time stabilization is achieved under the designed controller, which is discussed for the first time in the inertial networks. Finally, the validity of the theoretical results is demonstrated by a typical numerical example.

This article focuses on the fixed-time (FxT) synchronization of discontinuous fuzzy competitive neural networks (DFCNNs) with leakage-delays and state-dependent switching. Discontinuous activations, fuzzy terms, leakage delays, and state-dependent switching are considered into the competitive neural networks to increase the generality in practical applications. Before studying the synchronization, as an important theoretical basis, a new FxT stability lemma is established based on the method of nonscaling integral denominator, which is low conservative. Five different settling-time estimates are explicitly given by discussing the range of the exponents. Previous results are included and greatly improved. In order to achieve the FxT synchronization of the addressed DFCNNs, a continuously bounded control scheme is proposed by introducing a saturation function rather than a sign function, which cannot only solve the chattering phenomenon, but also ensure the boundedness of the control input. Some new leakage-delay-dependent synchronization criteria are derived for the DFCNNs. Finally, the validity of the main results is verified by numerical simulations.

The problem of adaptive fuzzy control based on the switching event-triggered mechanism for stochastic highly nonlinear system with time-varying delays, actuator faults, and nontriangular structure interconnections is investigated in this article. By constructing the corresponding Lyapunov–Krasovskii functional and variable separation method, the complex nonlinear functions with time-varying delays and highly nonlinearity can be handled. With the help of the fuzzy logic systems and adaptive compensation technique, the processing difficulty of the unknown nonlinear terms and the parameters of actuator faults is reduced. Simultaneously, the proposed control scheme can greatly decrease the waste of communication resources by a switching event-triggered mechanism. Then, all signals in the system are ensured to be bounded under Lyapunov stability theorem. Ultimately, the simulation example demonstrates the availability of the developed control scheme.

The future extensive usage of continuous measurable communication network for output feedback control in unmanned surface vehicle (USV) will inevitably increase the control cost, waste energy, and even reduce the system performance under stochastic cyber attacks. However, the existing study largely ignores the guaranteed cost control of USV under stochastic cyber attacks. To fill the knowledge gap, this paper attempts to focus on the guarantee cost control of USV systems by taking into account the finite measurable output sampling information and stochastic cyber attacks. Initially, a point output sampling control strategy based on finite measurable output sampling information is proposed, which has a strong application background and important theoretical research value in the field of power grid security. On this basis, a new stochastic composite system containing both system state and output sampling information is developed. Subsequently, a sampling-time-dependent Lyapunov function (LYFU) is exploited to ensure the workable criteria of the cost sampling controller, which can not only stabilize the stochastic composite system by means of the mean square exponential stability, but also reveal the upper bound (UPBO) of the quadratic cost function (COFU). Specially, in the strict sensu of minimizing the UPBO of the COFU, a meaningful design method for a suboptimal guaranteed cost output sampling controller is designed, which is a modulus-related LMI optimization algorithm. Finally, numerical simulation results of USV and additional vehicle lateral motion model are developed to demonstrate the validity and rationality of the proposed design method.

This article focuses on the problem of prefixed-time synchronization for stochastic multicoupled delay dynamic networks with reaction-diffusion terms and discontinuous activation by means of local intermittent sampling control. Notably, unlike the existing common fixed-time synchronization, this article puts forward a new synchronization concept, prefixed-time synchronization, based on the fact that stochastic noise and discontinuous activation can be seen everywhere in practical engineering, which can effectively perfect and improve the existing works. Specifically, a local intermittent in the time domain and point sampling control strategy in the spatial domain is proposed instead of a simple single intermittent control approach, which greatly reduces the control cost. In addition, by some effective means, including the famous Young's inequality, Jensen's inequality, and Hölder's inequality, we obtain two different synchronization criteria of the networks without delay and with multicoupling delays and deeply reveal the quantitative relationship among control period, point sampling length, and network scale. Finally, a numerical example is given to verify the effectiveness of the developed method and the practicability by Chua's circuit model.

In this article, a novel distributed gradient neural network (DGNN) with predefined-time convergence (PTC) is proposed to solve consensus problems widely existing in multiagent systems (MASs). Compared with previous gradient neural networks (GNNs) for optimization and computation, the proposed DGNN model works in a nonfully connected way, in which each neuron only needs the information of neighbor neurons to converge to the equilibrium point. The convergence and asymptotic stability of the DGNN model are proved according to the Lyapunov theory. In addition, based on a relatively loose condition, three novel nonlinear activation functions are designed to speedup the DGNN model to PTC, which is proved by rigorous theory. Computer numerical results further verify the effectiveness, especially the PTC, of the proposed nonlinearly activated DGNN model to solve various consensus problems of MASs. Finally, a practical case of the directional consensus is presented to show the feasibility of the DGNN model and a corresponding connectivity-testing example is given to verify the influence on the convergence speed.

This article is dedicated to studying the discrete time output sampling stabilization problem of T–S fuzzy (TSF) time-varying delay systems with stochastic disturbance and actuator saturation. Different from the existing sampling control that is converted to input time-delay type, the fuzzy sampling in this article is output sampling feedback control at discrete time points. More importantly, the proposed method eliminates the limitation of previous results on the relation between the magnitude of the time delay and the upper/lower bound of the sampling interval. Especially, based on the provided two different analysis methods of the multipiecewise time-dependent Lyapunov–Krasovskii functional and the multisegment time-dependent Lyapunov–Razumikhin function, which can effectively capture more dynamic characteristics of the target system and greatly reduce the conservatism of the relevant results. Finally, two practical models are provided to demonstrate the rationality and superiority of the developed approach.

This article aims to study the fixed-time (FxT) synchronization of different dimensional Filippov systems. New FxT stability lemmas containing the classical inequality$\dot {V}\leq {-c}_{1}V^{a}-c_{2}V^{b}$proposed by Polyakov are established. Different from the previous FxT stability lemmas in the literature, the proposed one shows the new conclusion that the settling times can be larger or smaller as long as$c_{1}$and$c_{2}$satisfy the certain relationships, which synchronously reveals that the relationships between the control gains can lead to different settling times. Besides, a generalized economical inequality condition$\dot {V} \leq -c_{1}V-c_{2}V^{\upsilon +{\mathrm{ sign}}(V-r)}$is proposed and a novel FxT stability lemma is also established. The complete theoretical proof is given to reveal that$r=1$leads to desired settling time, some previous related results are improved. Based on the new FxT stability lemmas and differential inclusion theory, algebraic inequality conditions are provided to guarantee the FxT synchronization, which reports the first result on the FxT synchronization of different dimensional Filippov systems. Finally, numerical examples are provided to verify the correctness of the main theoretical results.

In this article, a general Filippov system with nondifferentiable and unbounded delays is studied, which is different from the previous delayed Filippov systems. First, based on the differential inclusion theory and Kakutani’s fixed point theorem, the periodicity of solutions is proved and sufficient criteria are derived. Second, fixed-time (FxT) stabilization is studied by designing a new control law with a unified steepness exponent, which is more simpler than the previous ones with two steepness exponents. Since the delays are nondifferentiable and unbounded, rather than constructing the Lyapunov–Krasovskii functions, by constructing a suitable Lyapunov function, the FxT stabilization is analyzed and estimation of the settling-time (ST) is given through analyzing the state variables inside and outside the unit spherical area. The energy consumption is also estimated when the FxT stabilization is achieved under the designed controller. Third, given that smaller ST and lower energy consumption are usually preferred, the optimization problem is further considered. The optimal control parameters are selected based on the normalization approach and maximum principle. Finally, the validity of the theoretical results is demonstrated by a numerical example, where the delay function is composed of the Takagi function and the absolute value function.

In this article, the finite-time (FnT) control of a class of discontinuous memristor-based fuzzy inertial neural networks with proportional delays is discussed. The proposed model is more generalized. Different from the use of the finite/fixed-time stability lemmas in the previous works, by constructing the unit ball and discussing the subordinate relationship between the states and the unit ball, the finite/fixed-time stability are analyzed in detail. This method can avoid the rough thinking that the state variables of the system start from greater than 1. Also, the control constraint is taken into account and a quantized controller is designed, which can not only help achieve the finite/fixed-time stability, but also can prevent the singularity when using the norm forms and chattering when using the sign function in the controllers. In addition, the energy consumptions generated by the quantized controller are estimated in FnT and fixed-time stability processes. The criteria show that the energy consumptions are relevant to the proportional delays, when the proportional coefficient is 1, the energy loss reaches the minimum value. Finally, numerical example and simulation are provided to verify the validity of the obtained results.

This paper aims to study the fixed-time stabilization of a class of delayed discontinuous reaction-diffusion Cohen-Grossberg neural networks. Firstly, by providing some relaxed conditions containing indefinite functions and based on inequality techniques, a new fixed-time stability lemma is given, which can improve the traditional ones. Secondly, based on state-dependent switching laws, the periodic wave solution of the formulated networks is transformed into the periodic solution of ordinary differential system. By utilizing differential inclusions theory and coincidence theorem, the existence of periodic solutions is obtained. Thirdly, based on the new fixed-time stability lemma, the periodic solutions are stabilized at zero in a fixed-time, which is a new topic on reaction-diffusion networks. Moreover, the established criteria are all delay-dependent, which are less conservative than the previous delay-independent ones for ensuring the stabilization of delayed reaction-diffusion networks. Finally, two examples give numerical explanations of the proposed results and highlight the influence of delays.

This paper is concerned with the finite time$H_{\infty} $composite anti-disturbance control problem for Markov switched descriptor systems with multiple disturbances and packet loss via a disturbance observer. Significantly, the switching topology of descriptor systems is controlled by nonhomogeneous Markov switching processes, whose time-varying transition probability is limited by a convex hull. Subsequently, a Bernoulli random variable is exploited to characterize the intermittent measurement mode behavior of controller-actuator packet loss. Furthermore, the stochastic$H_{\infty} $finite time boundiness of the composite system and simultaneously suppression and rejection of external disturbances are established by resorting to disturbance observer-based robust control (DOBC) strategy and a new stochastic Lyapunov function technique. More importantly, a relaxed variable method is provided to eliminate the coupling between Lyapunov variables and the system matrix in the process of stability analysis, instead of eliminating the coupling by means of commonly-used traditional inequalities, which effectively increases the flexibility of the obtained stable results and greatly reduces the computational complexity of controller/observer in the existing works. Finally, the effectiveness and practicability of the developed results are verified by two practical engineering models.

This study investigates an outlier-resistant state estimation problem for singularly perturbed complex networks (SPCNs) with sojourn probabilities and randomly occurring coupling strengths. Aiming at better describing the dynamic behavior of the network topology for SPCNs, a novel switching law associated with the time-varying sojourn probabilities is developed, and the variation of sojourn probabilities is arranged by a high-level deterministic switching signal. Meanwhile, a sequence of mode-dependent variables is employed to describe the randomly occurring coupling strength. Subsequently, to alleviate the side effects from possible measurement outliers, a dynamic saturation function-based state estimator is designed, whose saturation level is adaptively varying based on previous estimation errors. In virtue of Lyapunov theory and mode-dependent average dwell-time strategy, it can be verified that the resulting dynamics is stochastic$\mathcal {H}_{\infty }$finite-time bounded. To this end, a simulation example is presented to show the validity of the proposed estimator design method.

This article mainly focuses on putting forward new fixed-time (FIXT) stability lemmas of delayed Filippov discontinuous systems (FDSs). By providing the new inequality conditions imposed on the Lyapunov-Krasovskii functions (LKF), novel FIXT stability lemmas are investigated with the help of inequality techniques. The new settling time is also given and its accuracy is improved in comparison with pioneer ones. For the purpose of illustrating the applicability, a class of discontinuous fuzzy neutral-type neural networks (DFNTNNs) is considered, which includes the previous NTNNs. New criteria are derived and detailed FIXT synchronization results have been obtained. Finally, typical examples are carried out to demonstrate the validity of the main results.

In this article, we construct an adaptive fuzzy decentralized fault-tolerant control strategy for stochastic nonlinear interconnected system with nontriangular structural uncertainties, unmodeled dynamics, and actuator faults. During the controller design process, the difficultly of system controller design caused by nontriangular structural uncertainties that mixed unmodeled dynamics are handled by utilizing the variable separation technique and fuzzy logic system. Then, based on the adaptive compensation technique, a fault-tolerant controller is designed to solve the influence of actuator faults for system stability. Finally, the stability of the stochastic nonlinear interconnected system can be ensured by stochastic Lyapunov stability theory. In addition, numerical and practical simulations also illustrate the effectiveness of the proposed control strategy.

When studying the stability of time-delayed discontinuous systems, Lyapunov-Krasovskii functional (LKF) is an essential tool. More relaxed conditions imposed on the LKF are preferred and can take more advantages in real applications. In this article, novel conditions imposed on the LKF are first given which are different from the previous ones. New fixed-time (FXT) stability lemmas are established using some inequality techniques which can greatly extend the pioneers. The new estimations of the settling times (STs) are also obtained. For the purpose of examining the applicability of the new FXT stability lemmas, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is formulated which is more generalized than the existing ones. Using differential inclusions theory, set-valued map, and the newly obtained FXT stability lemma, some algebraic FXT stabilization criteria are derived. Finally, examples are given to show the correctness of the established results.

In recent years, the adaptive exponential synchronization (AES) problem of delayed complex networks has been extensively studied. Existing results rely heavily on assuming the differentiability of the time-varying delay, which is not easy to verify in reality. Dealing with nondifferentiable delay in the field of AES is still a challenging problem. In this brief, the AES problem of complex networks with general time-varying delay is addressed, especially when the delay is nondifferentiable. A delay differential inequality is proposed to deal with the exponential stability of delayed nonlinear systems, which is more general than the widely used Halanay inequality. Next, the boundedness of the adaptive control gain is theoretically proved, which is neglected in much of the literature. Then, the AES criteria for networks with general delay are established for the first time by using the proposed inequality and the boundedness of the control gain. Finally, an example is given to demonstrate the effectiveness of the theoretical results.

This article proposes fixed-time stability lemmas for the Filippov system via some new inequality approaches. The adopted method no longer needs to integrate the Lyapunov function$V$on the two integral intervals, which is quite different from the existing ones. Some new estimations of the settling times are provided. Also, the steepness exponents of the Lyapunov function$V$in the previous fixed-time stability lemmas are improved. In order to further study the nondifferentiable delayed neural networks modeled by the Filippov system, a class of discontinuous uncertain Cohen–Grossberg neural networks (CGNNs) with mixed delays is formulated and the distributed delays are nondifferentiable, which is more general. Due to the existence of nondifferentiable distributed delays, the existence of the periodic solutions is proved by Kakutani’s fixed-point theorem before considering the stability. By virtue of the obtained fixed-time stability lemmas and the constructed delay-product-type Lyapunov–Krasovskii functional, the fixed-time stabilization is obtained via a no-chattering controller. Clearly, the designed controller does not contain integral terms and delay terms for dealing with the time delays in the closed-loop system, which is more simplified and practical. Finally, two examples help examine the correctness of the main results.

This article discusses the problem of event-triggered controls (ETCs) for stochastic functional differential systems (SFDSs). For the stabilization of SFDSs, we design a proper degenerate Lyapunov functional and propose a novel ETC. The degenerate Lyapunov functional is more general than the traditional positive definitive Lyapunov functionals and ETC has a prominent advantage of reducing communication resources compared with periodic sampled-data feedback controls because time updating is based on a certain event. Also, a fixed positive lower bound on the stochastic interexecution times is guaranteed by this novel event-triggering mechanism. Together with ETC and the degenerate Lyapunov functional, the boundedness, mean square exponential stabilization, and globally asymptotical stabilization of SFDSs can be established for different choices of parameters. Finally, the obtained results are validated through numerical simulations.

In this article, we study the synchronization of multiplex networks with random topologies and any number of layers. We propose a general framework for analyzing the synchronization of multiplex networks with or without layer similarity. Using random matrix theory, we obtain sufficient conditions of synchronization for multiplex networks under strong and weak interlayer coupling, respectively. We show, both analytically and numerically, that for weak interlayer coupling, increasing layer similarity can first promote synchronization and then hinder synchronization, while for strong interlayer coupling, synchronization can be suppressed. However, increasing the number of layers can always facilitate synchronization only if the interlayer coupling is strong. Finally, the theoretical results are verified by numerical simulations.

In this article, the global polynomial synchronization (GPS) using proportional delay inertial neural networks (PDINNs) as a drive-response system is studied. A feedback controller is designed, which is easy to implement in hardware. The order reduction method is used to reduce the error system of the studied systems to the first-order differential equations. The novel proportional delay differential inequalities (DDIs) in norm form are established by applying Lagrange’s mean value theorem, derivative definition, constructing auxiliary function method, and properties of matrix and vector norm. By applying the novel constructed DDIs, two GPS criteria of the studied systems are acquired, which are embodied in the form of matrix norm and are easy to verify. Ultimately, the theoretical results are supported by numerical examples.

As is known to all that the Lyapunov-Krasovskii functional (LKF) has played a vital role in studying the fixed-time (FXT) stability of the time-delayed Filippov discontinuous systems. When investigating the FXT stability of the time-delayed discontinuous systems, the interesting topic is to provide the more relaxed conditions imposed on the LKF and obtain the more accurate settling-time (ST). This paper aims to investigate the new FXT stability lemma with more relaxed conditions for the time-delayed Filippov discontinuous systems. By using some novel inequality techniques and analytical methods, the new FXT stability lemma is established and more accurate ST is estimated. The traditional discussion about$0 < V < 1$and$V \geq 1$is not required. For the purpose of validation, FXT stabilization of discontinuous inertial networks with mixed time delays is considered. By using differential inclusions theory and the new FXT stability lemma, the delay-dependent FXT stabilization criteria are derived. It is the first time to derive the delay-dependent FXT stabilization criteria for the discontinuous inertial networks. Finally, examples are given to show the effectiveness of the established results.

This article is concerned with the intermittent estimator-based mixed passive and [Formula: see text] control for the high-speed train (HST) with multiple noises, actuator stochastic fault, and sensor packet loss. First, an intermittent estimator is designed to track the undetectable status of HSTs in response to only partial information available due to sensor failures. Then, two different stability criteria are developed by adopting two different Lyapunov function strategies. Simultaneously, in order to reduce the control cost and accelerate the convergence time, two different algorithms are designed. It is worth emphasizing that different from the existing results of HST subject to actuator fault, this article adopts a more flexible fault representation mode, namely, semi-Markov switching mode, which is more in line with the practical background and has a higher valuable application. Especially, the Lyapunov function designed in this article can drive the system state to decrease monotonically in both the "working interval" and the "rest interval," so as to avoid the phenomenon of state impulsive jump. Finally, through the test of HST experimental value of Japan's Shinkansen, the simulation results show the effectiveness and rationality of the proposed control method and also make a comparative analysis with related works, to prove the advantages of the control technology proposed in this article.

This article identifies a new upper bound norm for the intervalized interconnection matrices pertaining to delayed dynamical neural networks under the parameter uncertainties. By formulating the appropriate Lyapunov functional and slope-bounded activation functions, the derived new upper bound norms provide new sufficient conditions corresponding to the equilibrium point of the globally asymptotic robust stability with respect to the delayed neural networks. The new upper bound norm also yields the optimized minimum results as compared with some existing methods. Numerical examples are given to demonstrate the effectiveness of the proposed results obtained through the new upper bound norm method.

This article discusses the fixed-time stability (FTS) of a kind of delayed discontinuous system (DS) in Filippov sense. Based on the set-valued map, the FTS analysis of the general solution is first transformed into the zero solution of the differential inclusion. Second, the new criteria of the Lyapunov-Krasovskii functional (LKF) are given and LKF is proved to possess the indefinite derivatives by using the simple integral inequalities. In addition, the FTS of the considered delayed DS is achieved and the new settling time is estimated. Third, to demonstrate the applicability of the new FTS theorems, the FTS control of a class of discontinuous inertial neural networks (DINNs) with time-varying delays is solved. Finally, two numerical examples are given to examine the theoretical results and simulations are also provided to make some illustrations.

In this article, the extended dissipative performance of distributed parameter systems (DPSs) with stochastic disturbances and multiple time-varying delays is studied by using a new fuzzy aperiodic intermittent sampled-data control strategy. Different from the previous fuzzy sampled-data control results, the state sampling of the proposed sampled-data controller occurs only in space and is intermittent rather than continuous in the time domain. By introducing a novel multitime-delay-dependent switched Lyapunov functional to explore the dynamic characteristics of the controlled system, and by means of the famous Jensen’s inequality with reciprocally convex approach, Wirtinger’s inequality, the criterion of the system’s mean square stabilization is established based on the LMI technique, which quantitatively reveals the relationship between the control period, the control length, and the upper bound of the control sampling interval. Especially, the optimal control gain is given by designing an optimized algorithm in the article, which greatly reduces the cost. Finally, two numerical examples are presented to demonstrate the effectiveness and superiority of the proposed approach.

This article aims to propose time-delayed and simplified inequality conditions and establish more novel fixed-time (FXT) stability principles of delayed Filippov systems. First, the sign function is used to unify the orders of the Lyapunov–Krasovskii functional, and the time-delayed term is introduced in the inequality conditions, then some new FXT stability theorems are established and new estimations of the settling time involving delayed parameter are given that are absolutely different from the previous ones. The traditional inequality conditions$\dot{V}(z)\leq -aV^\alpha (z)-bV^\beta (z)$is optimized and improved. For the purpose of illustrating the applicability, a class of delayed discontinuous fuzzy Cohen–Grossberg neural networks (DDFCGNNs) is studied. Some new criteria are derived, and the FXT stabilization of the addressed DDFCGNNs is achieved. Finally, a representative example and simulations are provided to examine the correctness.

Based on extensive applications of the time-variant quadratic programming with equality and inequality constraints (TVQPEI) problem and the effectiveness of the zeroing neural network (ZNN) to address time-variant problems, this article proposes a novel finite-time ZNN (FT-ZNN) model with a combined activation function, aimed at providing a superior efficient neurodynamic method to solve the TVQPEI problem. The remarkable properties of the FT-ZNN model are faster finite-time convergence and preferable robustness, which are analyzed in detail, where in the case of the robustness discussion, two kinds of noises (i.e., bounded constant noise and bounded time-variant noise) are taken into account. Moreover, the proposed several theorems all compute the convergent time of the nondisturbed FT-ZNN model and the disturbed FT-ZNN model approaching to the upper bound of residual error. Besides, to enhance the performance of the FT-ZNN model, a fuzzy finite-time ZNN (FFT-ZNN), which possesses a fuzzy parameter, is further presented for solving the TVQPEI problem. A simulative example about the FT-ZNN and FFT-ZNN models solving the TVQPEI problem is given, and the experimental results expectably conform to the theoretical analysis. In addition, the designed FT-ZNN model is effectually applied to the repetitive motion of the three-link redundant robot and image fusion to show its potential practical value.

In this article, a class of discontinuous inertial neural networks (DINNs) with parameter uncertainties and time delays is studied. The main aim is to investigate the new fixed-time stability (FTS). In order to achieve the targets, first, by introducing the generalized variable transformation and differential inclusions theory, two kinds of drive–response differential inclusion systems are established. Based on the definition of FTS and inequality technologies, by constructing the Lyapunov–Krasovskii functional (LKF), whose derivative is allowed to be indefinite, new delay-dependent criteria shown by some simple inequalities are derived for the purposing of achieving the FTS based on the designed discontinuous control strategies. Moreover, the new settling time (ST) is given. Compared to the previous stability results on INNs, the results established and the approaches applied are absolutely new. Finally, examples are given to show the effectiveness of the established results.

This paper is concerned with the problem of event-triggered optimized control for uncertain nonlinear Itô-type stochastic systems with time-delay and unknown dynamic. By using fuzzy logic systems to approximate two unknown nonlinear functions with the delayed state and current state, respectively. The adaptive identifier is constructed to determine the stochastic system, and the optimized control is designed by using the identifier and adaptive dynamic programming (ADP) of actor-critic architecture. Almost all of the works are concentrated on ADP-based optimal control and it will inevitably cause the complexity of computation and requirements of persistence excitation (PE) assumption. In this paper, the ADP algorithm is obtained based on the negative gradient of a simple positive function (equivalent to the HJB equation), and so the proposed optimal control is simple and can release the PE assumption. Moreover, the event-triggered control approach is proposed to reduce computing burden and communication resources. Furthermore, we prove that the states of system and FLSs parameter errors are semi-globally uniformly ultimately bounded (SGUUB) in mean square via the adaptive identifier and the Lyapunov direct method as well as identifier-actor-critic architecture-based ADP algorithm. Finally, the effectiveness of the proposed method is illustrated through two numerical examples.

This article aims to analyze the fixed-time synchronization of a class of discontinuous fuzzy inertial neural networks with time-varying delays based on the new improved fixed-time stability lemmas. First of all, by using the generalized variable transformation and Filippov solution theory, the discontinuities of the considered neural system can be coped with, and the error system is established. By relaxing the conditions of the$C$-regular Lyapunov function, two new fixed-time stability lemmas are proved via simple inequality techniques. The setting times are also estimated and are more accurate in comparison with the previous ones. Finally, one typical numerical example is carried out to verify the correctness and the advantages of the main results.

This article focuses on the intermittent nonfragile control problem for a class of stochastic neutral-type time-varying delay systems with randomly occurring uncertainties. First, the problem is transformed into the intermittent stabilization problem of generalized systems by variable substitution. Second, based on the dynamic characteristics of the intermittent controlled generalized systems, the time-dependent switching Lyapunov functional is introduced, and the convex combination technique is applied to provide sufficient conditions for the stability of the systems. Then, it is proved that the conditions can be transformed into a feasible solution of a group of linear matrix inequalities. Finally, several numerical examples are provided to verify the effectiveness and advantages of the proposed method.

In this short note, we consider time-varying stochastic functional differential systems with distributed-delay dependent impulsive effects. Such systems arise from a large number of applications, such as financial markets and population dynamics. By developing some inequality techniques and then combining stochastic analysis theory, Lyapunov approach, some stability criteria for such systems are established. The feature of the criteria shows that derivatives of the Razumikhin functions are allowed to be indefinite, and the restrictions with respect to the system parameters is very loose. Finally, we carry out two numerical experiments to show the usefulness and significance of the criteria.

In this paper, the problem of the exponential stability criterion for stochastic delayed systems with actuator failures is investigated via weighted relaxed integral inequality. A suitable Lyapunov-Krasovskii functional (LKF) candidate is adapted to derive the sufficient conditions that guarantee the exponential stability of the considered stochastic system. The main concerned problem is to estimate stronger upper bounds than the conventional ones for the integral terms induced through the derivative LKF. For this estimation process, combining the weighted integral inequality together with the reciprocal convex lemma, a new type of relaxed-based integral inequality is introduced to bound the integral term based on the weighted integral inequality. By making the use of derived inequality, the desired exponential stability conditions are established by means of linear matrix inequalities (LMIs). Lastly, the applicability and superiority of the proposed theoretical results over the existing ones are examined in virtue of numerical examples.

Throughout this article, we study the mean square exponential stabilization of stochastic retarded systems described by stochastic functional differential equations (SFDEs). Different from the traditional feedback controls with continuous observation of state, we put forward a novel sampled-data feedback control depending on the discrete observation of state and time delay. It greatly enlarges the probability of finding discrete-time feedback controls for stochastic retarded systems. In addition, the novel sampled-data feedback control succeeds in handling the delays involved in SFDEs. As applications, we provide two examples with simulation figures to illustrate the main result.

Abstract This article presents a class of neutral‐type Cohen‐Grossberg neural networks with discontinuous activations and mixed time delays. Based on the functional differential inclusions theory, inequality technique, and nonsmooth analysis theory with Lyapunovlike approach, some new sufficient criteria are given to ascertain the existence, uniqueness, and globally exponential stability of the antiperiodic solution. Finally, two topical numerical examples and the corresponding computer simulations are delineated to substantiate the correctness of our theoretical predictions. The obtained results of this article are new and complement some related earlier works.

This paper focuses on the dynamical behavior for a class of memristor-based bidirectional associative memory neural networks (BAMNNs) with additive time-varying delays in discrete-time case. The necessity of the proposed problem is to design a proper state estimator such that the dynamics of the corresponding estimation error is exponentially stable with a prescribed decay rate. By constructing an appropriate Lyapunov-Krasovskii functional (LKF) and utilizing Cauchy-Schwartz-based summation inequality, the delay-dependent sufficient conditions for the existence of the desired estimator are derived in the absence of uncertainties which are further extended to available uncertain parameters of the prescribed memristor-based BAMNNs in terms of linear matrix inequalities (LMIs). By solving the proposed LMI conditions the estimation gain matrices are obtained. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed results.

This paper deals with a state-feedback control scheme for nonlinear stochastic systems with Markovian switching. First, we present the results on the practically p -moment exponential stability with respect to an additional disturbance and the practically p -moment asymptotic stability relying on a specific event. However, elements in this event are hard to be observed directly. The main aim of this paper is to develop a self-triggered sampling rule to overcome this difficulty. By applying the improved monotone growth condition, Itô's formula, Fubini's theorem, Gronwall inequality, and comparison lemma, we establish a novel lemma to estimate the lower bound and upper bound of second-moment for state and error, respectively. Moreover, we also establish the practically asymptotic stability in mean square with the help of Jensen's inequality technique, properties of K -function and result on p -moment input-to-state stability. Furthermore, from Lipschitz continuity and monotonicity of functions, we obtain the value of the maximum triggering interval based on lasted-observed state. Finally, we give some remarks and discussions to show the significance of our results by comparing with those in the previous literature.

This brief investigates nonautonomous stochastic reaction-diffusion neural-network models with S-type distributed delays. First, the existence and uniqueness of mild solution are studied under the Lipschitz condition without the linear growth condition. Due to the existence of a nonautonomous reaction-diffusion term and the infinite dimensional Wiener process, the criteria for the well-posedness of the models are established based on the evolution system theory. Then, the S-type distributed delay, which is an infinite delay, is handled by the truncation method, and sufficient conditions for the global exponential stability are obtained by constructing a simple Lyapunov-Krasovskii functional candidate. Finally, neural-network examples and an illustrative example are given to show the applications of the obtained results.

In this paper, we investigate the dissipativity and passivity of Markovian jump stochastic neural networks involving two additive time-varying delays. Using a Lyapunov-Krasovskii functional with triple and quadruple integral terms, we obtain delay-dependent passivity and dissipativity criteria for the system. Using a generalized Finsler lemma (GFL), a set of slack variables with special structure are introduced to reduce design conservatism. The dissipativity and passivity criteria depend on the upper bounds of the discrete time-varying delay and its derivative are given in terms of linear matrix inequalities, which can be efficiently solved through the standard numerical software. Finally, our illustrative examples show that the proposed method performs well and is successful in problems where existing methods fail.

This paper discusses the issue of stability analysis for a class of impulsive stochastic bidirectional associative memory neural networks with both Markovian jump parameters and mixed time delays. The jumping parameters are modeled as a continuous-time discrete-state Markov chain. Based on a novel Lyapunov-Krasovskii functional, the generalized Itô's formula, mathematical induction, and stochastic analysis theory, a linear matrix inequality approach is developed to derive some novel sufficient conditions that guarantee the exponential stability in the mean square of the equilibrium point. At the same time, we also investigate the robustly exponential stability in the mean square of the corresponding system with unknown parameters. It should be mentioned that our stability results are delay-dependent, which depend on not only the upper bounds of time delays but also their lower bounds. Moreover, the derivatives of time delays are not necessarily zero or smaller than one since several free matrices are introduced in our results. Consequently, the results obtained in this paper are not only less conservative but also generalize and improve many earlier results. Finally, two numerical examples and their simulations are provided to show the effectiveness of the theoretical results.

In this paper, the problem of exponential stability is investigated for a class of stochastic neural networks with both Markovian jump parameters and mixed time delays. The jumping parameters are modeled as a continuous-time finite-state Markov chain. Based on a Lyapunov-Krasovskii functional and the stochastic analysis theory, a linear matrix inequality (LMI) approach is developed to derive some novel sufficient conditions, which guarantee the exponential stability of the equilibrium point in the mean square. The proposed LMI-based criteria are quite general since many factors, such as noise perturbations, Markovian jump parameters, and mixed time delays, are considered. In particular, the mixed time delays in this paper synchronously consist of constant, time-varying, and distributed delays, which are more general than those discussed in the previous literature. In the latter, either constant and distributed delays or time-varying and distributed delays are only included. Therefore, the results obtained in this paper generalize and improve those given in the previous literature. Two numerical examples are provided to show the effectiveness of the theoretical results and demonstrate that the stability criteria used in the earlier literature fail.

This paper is concerned with the problem of exponential stability for a class of markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays and known or unknown parameters. The jumping parameters are determined by a continuous-time, discrete-state Markov chain, and the mixed time delays under consideration comprise both time-varying delays and continuously distributed delays. To the best of the authors' knowledge, till now, the exponential stability problem for this class of generalized neural networks has not yet been solved since continuously distributed delays are considered in this paper. The main objective of this paper is to fill this gap. By constructing a novel Lyapunov-Krasovskii functional, and using some new approaches and techniques, several novel sufficient conditions are obtained to ensure the exponential stability of the trivial solution in the mean square. The results presented in this paper generalize and improve many known results. Finally, two numerical examples and their simulations are given to show the effectiveness of the theoretical results.