Sliding mode control for uncertain fractional-order reaction-diffusion memristor neural networks with time delays.

This paper investigates a sliding mode control method for a class of uncertain delayed fractional-order reaction-diffusion memristor neural networks. Different from most existing literature on sliding mode control for fractional-order reaction-diffusion systems, this study constructs a linear sliding mode switching function and designs the corresponding sliding mode control law. The sufficient theory for the globally asymptotic stability of the sliding mode dynamics are provided, and it is proven that the sliding mode surface is finite-time reachable under the proposed control law, with an estimate of the maximum reaching time. Finally, a numerical test is presented to validate the effectiveness of the theoretical analysis.

Input-to-State Stability of Switched Network Control Systems Under Unknown Deception Attacks.

This article focuses on the stability issue of switched network control systems (SNCSs) under deception attacks described by a Bernoulli process with unknown probability distribution. The false information in deception attacks is unknown but bounded and may be state dependent or state independent. By means of the input-to-state stability (ISS) tool and the convex combination method, an improved lemma is first developed for SNCSs, which facilitates the derivations of our results. After that, some attack-independent sufficient conditions for the ISS of SNCSs are obtained for mode-dependent average dwell time switching and stochastic switching, respectively. Different from existing results, the concerned switching contributes to the stability of SNCSs, which benefits the ISS performance of SNCSs even though the unknown deception attacks cause all subsystems to be non-ISS. The proposed results provide an effective solution with strong robustness to deal with unknown deception attacks or denial-of-service attacks.

Two Novel Noise-Suppression Projection Neural Networks With Fixed-Time Convergence for Variational Inequalities and Applications.

This article proposes two novel projection neural networks (PNNs) with fixed-time ( FIXt ) convergence to deal with variational inequality problems (VIPs). The remarkable features of the proposed PNNs are FIXt convergence and more accurate upper bounds for arbitrary initial conditions. The robustness of the proposed PNNs under bounded noises is further studied. In addition, the proposed PNNs are applied to deal with absolute value equations (AVEs), noncooperative games, and sparse signal reconstruction problems (SSRPs). The upper bounds of the settling time for the proposed PNNs are tighter than the bounds in the existing neural networks. The effectiveness and advantages of the proposed PNNs are confirmed by numerical examples.

Neurodynamic optimization approaches with finite/fixed-time convergence for absolute value equations.

This paper proposes three novel accelerated inverse-free neurodynamic approaches to solve absolute value equations (AVEs). The first two are finite-time converging approaches and the third one is a fixed-time converging approach. It is shown that the proposed first two neurodynamic approaches converge to the solution of the concerned AVEs in a finite-time while, under some mild conditions, the third one converges to the solution in a fixed-time. It is also shown that the settling time for the proposed fixed-time converging approach has an uniform upper bound for all initial conditions, while the settling times for the proposed finite-time converging approaches are dependent on initial conditions. The proposed neurodynamic approaches have the advantage that they are all robust against bounded vanishing perturbations. The theoretical results are validated by means of a numerical example and an application in boundary value problems.

Synchronization of Switched Neural Networks via Attacked Mode-Dependent Event-Triggered Control and Its Application in Image Encryption.

It is challenging to synchronize switched time-delay systems when some modes are uncontrolled and the dwell time (DT) of controlled mode is very small. Therefore, in this article, global exponential synchronization almost surely (GES a.s.) in a cluster of switched neural networks (NNs) with hybrid delays (time-varying delay and infinite-time distributed delay) is investigated, where transition probability (TP)-based random mode-dependent average DT (MDADT) switching is considered. A novel mode-dependent pinning event-triggered controller with nonidentical deception attacks is proposed to save the communication resource and derive less conservative results. The two necessary and restrictive conditions in existing papers that the value of the Lyapunov-Krasovskii functional (LKF) before switching instants should be smaller than that after corresponding instant and the DT of each switching mode is restricted by the sampling intervals of the event trigger are moved. Sufficient conditions in terms of linear matrix inequalities (LMIs) are given to guarantee the GES a.s., even though both synchronizing and nonsynchronizing modes coexist and maybe the minimum DT of synchronizing modes is very small. Numerical examples, including image encryption, are provided to demonstrate the merits of the new technique.

State Estimation of Switched Time-Delay Complex Networks With Strict Decreasing LKF.

State estimation issue is investigated for a switched complex network (CN) with time delay and external disturbances. The considered model is general with a one-sided Lipschitz (OSL) nonlinear term, which is less conservative than Lipschitz one and has wide applications. Adaptive mode-dependent nonidentical event-triggered control (ETC) mechanisms for only partial nodes are proposed for state estimators, which are not only more practical and flexible but also reduce the conservatism of the results. By using dwell-time (DT) segmentation and convex combination methods, a novel discretized Lyapunov-Krasovskii functional (LKF) is developed such that the value of LKF at switching instants is strict monotone decreasing, which makes it easy for nonweighted L2 -gain analysis without additional conservative transformation. The main results are given in the form of linear matrix inequalities (LMIs), by which the control gains of the state estimator are designed. A numerical example is given to illustrate the advantages of the novel analytical method.

H ∞ state estimation of quaternion-valued inertial neural networks: non-reduced order method.

This paper concentrates on the problem of H ∞ state estimation for quaternion-valued inertial neural networks (QVINNs) with nonidentical time-varying delay. Without reducing the original second order system into two first order systems, a non-reduced order method is developed to investigate the addressed QVINNs, which is different from the majority of existing references. By constructing a new Lyapunov functional with tuning parameters, some easily checked algebraic criteria are established to ascertain the asymptotic stability of error-state system with the desired H ∞ performance. Moreover, an effective algorithm is provided to design the estimator parameters. Finally, a numerical example is given out to illustrate the feasibility of the designed state estimator.

Measurement and spatial-temporal analysis of coupling coordination development between green finance and environmental governance in China.

To direct financial resources for achieving the goal of sustainable development, Chinese government has devoted increasing efforts to developing green finance. However, few studies explored the relationship between green finance and environmental governance. Thus, this paper first theoretically discusses the interactive connection between green finance and environmental governance. And then we construct two comprehensive indicator systems and use entropy method to calculate green finance index (GFI) and environmental governance index (EGI) for 30 provinces of China from 2004 to 2020. The theoretical analysis unveils the complementary and mutual reinforcing relationship of the interaction between green finance and environmental governance through green industry. Using the data of GFI and EGI, the coupling coordination degree of green finance and environmental governance (CCDGE) is measured by coupling coordination model. The trend analysis discovers that GFI is increasing over time while EGI starts decreasing from 2013. Although GFI has grown more rapidly than EGI, but the development of green finance still lags behind environmental governance because of its short history. Just because of the uncoordinated development between green finance and environmental governance, CCDGE has been hovering in the moderate coupling coordination stage for a long time and still has a great distance to the high coupling coordination level. These findings imply that the relationship between green finance and environmental governance is still in a state of disorderly development that restricts each other. Furthermore, the findings of spatial-temporal analysis show there are obvious regional differences in GFI and EGI and the interactive effect between green finance and environmental governance. Specifically, GFI and EGI in eastern China are the highest, while CCDGE presents with a ladder decline status of "eastern region > central region > northeast region > west region." Our findings provide vital references for policymakers to promote the coupling coordination development between green finance and environmental governance.

Novel LKF Method on H∞ Synchronization of Switched Time-Delay Systems.

This article investigates H∞ global asymptotic synchronization (GAS) of switched nonlinear systems with delay. By introducing mode-dependent double event-triggering mechanisms (DETMs), the communication resources in both system-controller (S-C) channel and controller-actuator (C-A) channel are saved as much as possible. By designing a new multiple Lyapunov-Krasovskii functional (LKF) with time-varying matrices and developing novel analysis techniques such that the increment of the LKF at switching instant is smaller than one, not only the conservatism of obtained results is greatly reduced but also the nonweighted L2 -gain is convenient to be derived without using any conservative transformation. The exclusion of the Zeno behavior of the DETMs is proved. Synchronization criteria formulated by linear matrix inequalities (LMIs) are given, by which the control gains, event-triggering weights, as well as the minimum L2 -gain are simultaneously designed. Numerical examples demonstrate the low conservatism of the theoretical analysis. Meanwhile, image processing on the basis of the H∞ GAS is provided to further illustrate the perfect performance.

Finite-Time Synchronization of Markovian Coupled Neural Networks With Delays via Intermittent Quantized Control: Linear Programming Approach.

This article is devoted to investigating finite-time synchronization (FTS) for coupled neural networks (CNNs) with time-varying delays and Markovian jumping topologies by using an intermittent quantized controller. Due to the intermittent property, it is very hard to surmount the effects of time delays and ascertain the settling time. A new lemma with novel finite-time stability inequality is developed first. Then, by constructing a new Lyapunov functional and utilizing linear programming (LP) method, several sufficient conditions are obtained to assure that the Markovian CNNs achieve synchronization with an isolated node in a settling time that relies on the initial values of considered systems, the width of control and rest intervals, and the time delays. The control gains are designed by solving the LP. Moreover, an optimal algorithm is given to enhance the accuracy in estimating the settling time. Finally, a numerical example is provided to show the merits and correctness of the theoretical analysis.

Finite-time bipartite synchronization of switched competitive neural networks with time delay via quantized control.

This article tackles the finite-time bipartite synchronization (FTBS) of coupled competitive neural networks (CNNs) with switching parameters and time delay. Quantized control is utilized to achieve the FTBS at a small control cost and with limited channel resources. Since the effects of the time delay and switching parameters, traditional finite-time techniques cannot be directly utilized to the FTBS. By constructing a novel multiple Lyapunov functional (MLF), a sufficient criterion formulated by linear programming (LP) is established for the FTBS and the estimation of the settling time. To further improve the accuracy of the settling time, another MLF is designed by dividing the dwell time. With the aid of convex combination, a new LP is provided, which removes the requirement that the increment coefficient of the MLF at switching instants has to be larger than 1. In addition, to obtain the more precise settling time, an optimal algorithm is provided. Two numerical examples are put forward to demonstrate the reasonableness of the theoretical analysis.

Synchronization of Switched Discrete-Time Neural Networks via Quantized Output Control With Actuator Fault.

This article considers global exponential synchronization almost surely (GES a.s.) for a class of switched discrete-time neural networks (DTNNs). The considered system switches from one mode to another according to transition probability (TP) and evolves with mode-dependent average dwell time (MDADT), i.e., TP-based MDADT switching, which is more practical than classical average dwell time (ADT) switching. The logarithmic quantization technique is utilized to design mode-dependent quantized output controllers (QOCs). Noticing that external perturbations are unavoidable, actuator fault (AF) is also considered. New Lyapunov-Krasovskii functionals and analytical techniques are developed to obtain sufficient conditions to guarantee the GES a.s. It is discovered that the TP matrix plays an important role in achieving the GES a.s., the upper bound of the dwell time (DT) of unsynchronized subsystems can be very large, and the lower bound of the DT of synchronized subsystems can be very small. An algorithm is given to design the control gains, and an optimal algorithm is provided for reducing conservatism of the given results. Numerical examples demonstrate the effectiveness and the merits of the theoretical analysis.

Synchronization of Coupled Time-Delay Neural Networks With Mode-Dependent Average Dwell Time Switching.

In the literature, the effects of switching with average dwell time (ADT), Markovian switching, and intermittent coupling on stability and synchronization of dynamic systems have been extensively investigated. However, all of them are considered separately because it seems that the three kinds of switching are different from each other. This article proposes a new concept to unify these switchings and considers global exponential synchronization almost surely (GES a.s.) in an array of neural networks (NNs) with mixed delays (including time-varying delay and unbounded distributed delay), switching topology, and stochastic perturbations. A general switching mechanism with transition probability (TP) and mode-dependent ADT (MDADT) (i.e., TP-based MDADT switching in this article) is introduced. By designing a multiple Lyapunov-Krasovskii functional and developing a set of new analytical techniques, sufficient conditions are obtained to ensure that the coupled NNs with the general switching topology achieve GES a.s., even in the case that there are both synchronizing and nonsynchronizing modes. Our results have removed the restrictive condition that the increment coefficients of the multiple Lyapunov-Krasovskii functional at switching instants are larger than one. As applications, the coupled NNs with Markovian switching topology and intermittent coupling are employed. Numerical examples are provided to demonstrate the effectiveness and the merits of the theoretical analysis.

Cluster stochastic synchronization of complex dynamical networks via fixed-time control scheme.

By means of fixed-time (FDT) control technique, cluster stochastic synchronization of complex networks (CNs) is investigated. Quantized controller is designed to realize the synchronization of CNs within a settling time. FDT synchronization criteria are established with the help of Lyapunov functional and comparison system methods. It should be noted that the convergence of synchronization is further improved by comparing with existing FDT synchronization results. Numerical simulations are given to illustrate our results.

Synchronization of Time-Delayed Complex Networks With Switching Topology Via Hybrid Actuator Fault and Impulsive Effects Control.

This article investigates global exponential synchronization almost surely (GES a.s.) of complex networks (CNs) with node delay and switching topology. By introducing transition probability (TP) and mode-dependent average dwell time (MDADT) to the switching signal, the considered model is more practical than the systems with average dwell-time (ADT) switching. Controllers with both impulsive effects and actuator fault feedback are considered. New analytical techniques are developed to obtain sufficient conditions to guarantee the GES a.s. Different from the existing results on the synchronization of switched systems, our results show that the GES a.s. can still be achieved even in the case that the upper bound of the dwell time (DT) of uncontrolled nodes is very large and the lower bound of the DT of controlled nodes is very small. Numerical examples demonstrate the effectiveness and the merits of the theoretical analysis.

Exponential synchronization of semi-Markovian coupled neural networks with mixed delays via tracker information and quantized output controller.

In this paper, exponential synchronization of semi-Markovian coupled neural networks (NNs) with bounded time-varying delay and infinite-time distributed delay (mixed delays) is investigated. Since semi-Markov switching occurs by time-varying probability, it is difficult to capture its precise switching signal. To overcome this difficulty, a tracker is used to track the switching information with some accuracy. Then a quantized output controller (QOC) is designed by using the tracked information. Novel Lyapunov-Krasovskii functionals (LKFs) with negative terms and delay-partitioning approach, which reduce the conservativeness of the obtained results, are utilized to obtain LMI conditions ensuring the exponential synchronization. Moreover, an algorithm is proposed to design the control gains. Our results include both those derived by mode-dependent and mode-independent control schemes as special cases. Finally, numerical simulations validate the effectiveness of the methodology.

Fixed-time synchronization criteria for complex networks via quantized pinning control.

In this paper, fixed-time (FDT) synchronization of complex networks (CNs) is considered via quantized pinning controllers (QPCs). New control schemes with logarithmic quantization are designed, which not only can reduce control cost but also can save channel resources. The QPC with sign function can be used more generally than the QPC without sign function, but the QPC without sign function can be utilized to overcome the chattering phenomenon in some existing results. Based on designed Lyapunov function and different control schemes, several FDT synchronization criteria expressed by linear matrix inequalities (LMIs) are presented. Moreover, a numerical example is presented to illustrate the theoretical results.

Finite-time cluster synchronization for a class of fuzzy cellular neural networks via non-chattering quantized controllers.

This paper considers the finite-time cluster synchronization (FTCS) of coupled fuzzy cellular neural networks (FCNNs) with Markovian switching topology, discontinuous activation functions, proportional leakage, and time-varying unbounded delays. Novel quantized controllers without the sign function are designed to avoid the chattering and save communication resources. Under the framework of Filippov solution, several sufficient conditions are derived to guarantee the FTCS by constructing new Lyapunov-Krasovskii functionals and utilizing M-matrix methods. The new analytical techniques skillfully overcome the difficulties caused by time-varying delays and cope with the uncertainties of both Filippov solution and Markov jumping, which enable us determine the settling time explicitly. Numerical simulations demonstrate the effectiveness of the theoretical analysis.

Fixed-Time Stochastic Synchronization of Complex Networks via Continuous Control.

This paper investigates the fixed-time synchronization (FDTS) of complex networks with stochastic perturbations. A new control scheme is designed to realize the synchronization goal. Moreover, the designed controller without sign function is continuous, which means the chattering phenomenon in some previous results can be avoided. By constructing Lyapunov functionals, using the properties of the Weiner process as well as applying a designed comparison system, several FDTS criteria are obtained. Synchronization criteria of this paper are very general and can be utilized in directed and undirected weighted networks. Numerical simulations are given to illustrate the theoretical results.

Synchronization of Coupled Markovian Reaction-Diffusion Neural Networks With Proportional Delays Via Quantized Control.

The asymptotic synchronization of coupled reaction-diffusion neural networks with proportional delay and Markovian switching topologies is considered in this brief where the diffusion space does not need to contain the origin. The main objectives of this brief are to save communication resources and to reduce the conservativeness of the obtained synchronization criteria, which are carried out from the following two aspects: 1) mode-dependent quantized control technique is designed to reduce control cost and save communication channels and 2) Wirtinger inequality is utilized to deal with the reaction-diffusion terms in a matrix form and reciprocally convex technique combined with new Lyapunov-Krasovskii functional is used to derive delay-dependent synchronization criteria. The obtained results are general and formulated by linear matrix inequalities. Moreover, combined with an optimal algorithm, control gains with the least magnitude are designed.