Mean-square Synchronization Research Articles

Aperiodic intermittent dynamic event-triggered synchronization control for stochastic delayed multi-links complex networks

In this work, the exponential synchronization issue of stochastic complex networks with time delays and time-varying multi-links (SCNTM) is discussed via a novel aperiodic intermittent dynamic event-triggered control (AIDE-TC). The AIDE-TC is designed by combining intermittent control with an exponential function and dynamic event-triggered control, aiming to minimize the number of the required triggers. Then, based on the proposed control strategy, the sufficient conditions for exponential synchronization in mean square of SCNTM are obtained by adopting graph theoretic approach and Lyapunov function method. In the meanwhile, it is proven that the Zeno behavior can be excluded under the AIDE-TC, which ensures the feasibility of the control mechanism to realize the synchronization of SCNTM. Finally, we provide a numerical simulation on islanded microgrid systems to validate the effectiveness of main results and the simulation comparison results show that the AIDE-TC can reduce the number of event triggers.

Exponential synchronization of complex networks via intermittent dynamic event-triggered control

In this paper, the exponential synchronization in mean square (ESMS) of complex networks (CNs) under intermittent dynamic event-triggered control strategy (IE-TCS) is discussed. Compared with the existing literature, the intermittent control strategy (ICS) proposed is awakened when a certain situation occurs rather than periodically, which can better improve the control efficiency. The average control rate in this paper is more flexible. Furthermore, we give a positive lower bound for the event-triggered intervals to ensure that Zeno behavior does not occur. Combining the graph-theoretic approach with the Lyapunov method, some criteria for ESMS are obtained. In particular, we also discuss the ESMS of non-strongly connected CNs under IE-TCS. Besides, we combine the self-triggered control strategy (S-TCS) with the ICS, which is called the intermittent S-TCS, to study the ESMS of CNs. For practicability, the theoretical results are applied to research the ESMS of the microgrid system, and some relevant sufficient conditions are derived. Eventually, numerical simulations are put forward to verify the effectiveness of theoretical results.

Lag Synchronization in Mean Square of Stochastic Complex Networks with Multiple Mixed Delays via Impulsive Control

Lag Synchronization in Mean Square of Stochastic Complex Networks with Multiple Mixed Delays via Impulsive Control

Pinning Synchronization for Stochastic Complex Networks With Randomly Occurring Nonlinearities: Tackling Bit Rate Constraints and Allocations.

In this article, the ultimately bounded synchronization problem is investigated for a class of discrete-time stochastic complex networks under the pinning control strategy. Communication between system nodes and the remote controller is facilitated via wireless networks subject to bit rate constraints. The system model is distinguished by the inclusion of randomly occurring nonlinearities. A coding-decoding transmission mechanism under constrained bit rates is introduced to characterize the digital transmission process. To achieve synchronization of the network nodes with the unforced target node, a pinning controller is specifically devised based on the information from partially selected nodes. Through the application of the stochastic analysis method, a sufficient condition is derived for ensuring the mean-square boundedness of the synchronization error system. In addition, an optimization algorithm is introduced to address bit rate allocation and the design of desired controller gains. Within the presented theoretical framework, the correlation between the mean-square synchronization performance and bit rate allocation is further elucidated. To conclude, a simulation example is provided to substantiate the efficacy of the recommended pinning control approach.

Optimized Distributed Cooperative Control for Islanded Microgrid Based on Dragonfly Algorithm

This study introduces novel stochastic distributed cooperative control (SDCC) in the context of island microgrids (MGs). A proportional resonant (PR) controller and virtual impedance droop control in stationary reference frames are employed in cooperation with distributed averaging secondary control optimized by the dragonfly algorithm (DA). The suggested approach demonstrates the capability to achieve mean-square synchronization for the voltage and frequency restoration of distributed generators (DGs) to ensure efficient active power sharing. Therefore, a sparse communication network has been used to avoid data congestion and reduce the need for extensive communication and information exchange. The proposed system offers an instinctive compromise between voltage regulation and reactive power sharing. A conventional centralized secondary control with PR droop control is simulated for performance evaluation and comparison purposes. In this study, empirical evidence is demonstrated to support the MG’s ability to confront communication failure and its ability to work reliably during plug-and-play operations.

Mean square [formula omitted] synchronization for time-varying networks with double delays partial differential systems of Markov jump topology

This paper discusses the mean-square exponential synchronization and H∞ synchronization of double time-delays partial differential systems(PDSs) with Markov jump topology. First, based on the Lyapunov functional approach and Dynkins formula, sufficient conditions are obtained for the mean-square synchronization of double time-varying delays PDSs with Markov jump topology and these conditions are presented by linear matrix inequalities (LMIs). Moreover, the mean-square H∞ synchronization of time-delay coupled PDSs with external disturbances is also derived in terms of LMIs, which guarantee the H∞ synchronization of the coupled PDSs with Markov jump topology. Finally, numerical examples of coupled time-delay PDSs are given to illustrate the correctness of the obtained results.

Exponential bipartite synchronisation of stochastic signed networks via intermittent pinning discrete-time state observations control

This paper studies the exponential bipartite synchronisation in mean square (EBS-MS) of stochastic signed networks (SSNs) via periodically intermittent pinning control. It is important to note that intermittent control is an extension of existing literature, which depends on discrete observations instead of continuous observations during the work period. Additionally, only a small percentage of the network nodes are controlled by intermittent control. Several sufficient conditions are established by the Lyapunov method and graph theory. Especially, when the duration τ between two consecutive observations tends to zero, our control will degenerate into common periodically intermittent pinning control. Meanwhile, a corollary about the EBS-MS of SSNs is presented. Besides, theoretical results are applied to a single-link robot arm system and an oscillator system. Finally, numerical simulations are presented to show the feasibility of the theoretical results.

Stochastic Synchronization of Semi-Markovian Switching Cyber-Physical Impulsive Complex Networks via Dynamic Event-Triggered SMC

In this paper, a novel dynamic event-triggered sliding mode control (SMC) scheme is developed to investigate the stochastic synchronization of semi-Markovian switching cyber-physical complex network (SSCCN) with impulsive effects. First of all, the mode-dependent average dwell time (MDADT) and the transition probability (TP) are introduced to express the semi-Markovian switching signal, which makes the proposed model more applicable than other systems where only the average dwell time (ADT) switching is provided. Moreover, to prevent system uncertainty and unnecessary data transmission, a new dynamic event-triggered mechanism is incorporated into the design of SMC. In most of the existing event-triggered SMC strategies, the continuity of sliding mode surfaces for SSCCN is lost due to intermittent impulsive effects and stochastic switching in the system. Considering this problem, a piecewise mode-independent integral sliding function is put forward that takes into account the dynamic properties of the impulses through the proposed dynamic event-triggered mechanism. It can not only obtain the continuous trajectories of the impulsive networked system, but also significantly reduce the number of event triggers. Some rigorous analytical techniques have been developed to obtain the sufficient conditions required to ensure both the mean square synchronization (MSS) and almost sure synchronization (ASS) of SSCCN. Finally, some numerical examples are presented to demonstrate the effectiveness of the theoretical analysis.

A New Estimation Method for Time–Space Sampled-Data Synchronization of RDNNs With Random Delays

The asymptotical synchronization in mean square of reaction–diffusion neural networks (RDNNs) with random delays is studied in this article. By sampling on both the time domain and spatial domain, a time–space sampled-data controller (TSSDC) is designed, which can efficiently save the network communication resources for RDNNs. A new processing method for the TSSDC is provided. Compared with the existing methods, the processing method here can capture more sampling information and is more concise. An extended Poincaré–Wirtinger inequality is proposed, which is in matrix form and less conservative. Then by constructing a sampling-dependent LKF, using the extended Poincaré–Wirtinger inequality and Hölder inequality, new mean square asymptotical synchronization criteria are set up for RDNNs with random delays, and the desired TSSDC gain is obtained. At length, a numerical example is given to verify the effectiveness and superiority of the obtained results.

Stochastic synchronization for semi-Markovian complex dynamic networks with partly unknown transition rates

This paper investigates the synchronization of complex dynamic networks with time-varying delay and general semi-Markovian jump. The general transition rates include completely unknown and uncertain but bounded as two special cases. First, by introducing auxiliary vectors with a few nonorthogonal polynomials, two free-matrix-based integral inequalities are developed, which encompass some existing ones as special cases. Second, an integral- based delay-product-type Lyapunov-Krasovskii functional is constructed, which fully considers the information of time delay. By utilizing a deley-dependent controller, two sufficient conditions are derived to realize the global stochastic mean-square synchronization by employing the established inequalities to evaluate the infinitesimal generator of the functional. This paper takes all possibilities into consideration and divides the general transition rates into five cases, which is never investigated before. Finally a numerical example is given to show the effectiveness and practicality of the presented method.

Synchronization of hybrid switching diffusions delayed networks via stochastic event-triggered control

In this paper, the synchronization problem of stochastic complex networks with time delays and hybrid switching diffusions (SCNTH) is concerned based on event-triggered control. Therein, a new class of event-triggered function is proposed for the control design. Particularly, different from the existing work, the triggered instant generated by event-triggered control in this paper is a stochastic sequence instead of a number sequence to be more realistic for stochastic systems, which is a breakthrough. Furthermore, some sufficient conditions are derived to guarantee asymptotical synchronization in mean square, exponential synchronization in mean square and almost surely exponential synchronization of SCNTH based on sampled-data control, event-driven control theory and stability analysis. Meanwhile, the Zeno phenomenon can be avoided. Then, the synchronization of single-link robot arms is investigated in detail as a practical application of the obtained results. Ultimately, a numerical example is given for demonstration.

Mean-square synchronization of fractional-order stochastic complex network via pinning control

In this paper, the mean-square synchronization problem is considered for the fractional-order stochastic complex network (FOSCN) via pinning control. Firstly, suppose that the dynamics of the node are modeled by continuous-time nonlinear fractional stochastic differential equations (FSDEs). Next, the pinning nodes are selected according to the low-dimensional pinning criteria. Furthermore, the controller is designed for each pinning node, and a set of sufficient conditions are given to guarantee the mean-square synchronization. Then, the convergence analysis of the closed-loop system is finished by directly utilizing the properties of the integral solution. It proved that the mean-square synchronization of FOSCN can be achieved with the designed controller under some conditions. In addition, the synchronization problem of general fractional-order complex networks (FOCN) without stochastic noise is solved by using a similar method. Finally, compared simulation examples are performed to demonstrate the effectiveness of the proposed methods.

Mean-Square Synchronization and Stochastically Passive Synchronization of Delayed Gene Regulatory Networks With Markovian Switching

Mean-Square Synchronization and Stochastically Passive Synchronization of Delayed Gene Regulatory Networks With Markovian Switching

Synchronization for stochastic Lévy noise systems on a time-varying multi-weights network via delay intermittent control

In previous papers, either the time-varying coupling structure or multi-weights have been considered into networks. However, few scholars have paid attention to networks with both time-varying coupling structure and multi-weights. In this paper, we formulate and probe stochastic Lévy noise delayed systems on a time-varying multi-weights network (SLDSTN) for the first time. In order to solve the synchronization problem of SLDSTN, we design a novel class of delay intermittent control. Different from previous intermittent control based on current state, delay intermittent control is based on past state. Then, by means of Lyapunov method, graph theory and some techniques of inequalities, sufficient conditions for exponential synchronization in mean square of SLDSTN are proposed. Therein, we relax the condition of processing the time-varying coupling term successfully. Furthermore, for presenting the superiorities of delay intermittent control, delay feedback control and aperiodically intermittent control also are applied to solve the synchronization problem of SLDSTN. To demonstrate the effectiveness of the theoretical results, a class of single-link robot arms is considered as a practical application. Finally, some numerical simulations are provided.

Robust synchronization of uncertain Markovian jumping complex interconnected neural networks via adaptive fault-tolerant control

This article inspects the problem of robust synchronization for uncertain Markovian jumping complex interconnected neural networks with randomly occurring uncertainties and time delays. The uncertainties considered here occur randomly and are assumed to follow certain mutually uncorrelated Bernoulli distributed white noise sequences. The presence of sensor faults may cause degradation or even instability of the entire network. Therefore, control laws are designed with sensor faults to ensure the controlled synchronization of the complex interconnected neural networks. Three types of fault-tolerant controls are designed based on the Lyapunov stability theory and adaptive schemes which include passive and adaptive fault-tolerant control laws. By constructing a new Lyapunov-Krasovskii functional (LKF) and by using Jensen’s inequality with a free-weighting matrix approach, some new delay-dependent synchronization criteria are obtained in terms of linear matrix inequalities (LMIs). By using the Lyapunov stability theory, the existence condition for the adaptive controller that guarantees the robust mean-square synchronization of complex interconnected neural networks in terms of LMIs are derived. Finally, a numerical example is presented to demonstrate the performance of the developed approach.

Intermittent Dynamic Event-Triggered Control for Synchronization of Stochastic Complex Networks

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

Neural network based asynchronous synchronization for fuzzy hidden Markov jump complex dynamical networks

This paper investigates the drive-response synchronization problem of Takagi–Sugeno fuzzy hidden Markov jump complex dynamical networks. More precisely, a novel asynchronous synchronization control strategy is developed for coping with mismatched hidden jumping modes. Furthermore, the neural network is adopted with online learning laws for unknown function approximation. By taking advantage of Lyapunov method, sufficient conditions are established to ensure mean-square synchronization performance with disturbances. Based on the synchronization criterion, asynchronous controller gains are designed in terms of linear matrix inequalities. An illustrative example is finally given to validate the effectiveness of the proposed synchronization techniques.

Synchronization of neural networks with memristor-resistor bridge synapses and Lévy noise

In this paper, a kind of memristor-resistor bridge synapses are applied to neural networks, which makes the connection weights of networks continuously adjustable. A novel model for this new kind of neural networks is established, in which the memory characteristic of memristors is retained. The state synchronization of the model with the influence of Lévy noise is investigated. By making use of the Itô formula for Lévy process and Lyapunov method, a sufficient condition is obtained for exponentially state synchronization in mean square of the drive and response networks. Moreover, by applying controller to each synapse, the complete synchronization of the drive and response networks is achieved. Finally, numerical examples are carried out to illustrate the feasibility of theoretical results.

Synchronization Analysis for Stochastic Inertial Memristor-Based Neural Networks with Linear Coupling

This paper concerns the synchronization problem for a class of stochastic memristive neural networks with inertial term, linear coupling, and time-varying delay. Based on the interval parametric uncertainty theory, the stochastic inertial memristor-based neural networks (IMNNs for short) with linear coupling are transformed to a stochastic interval parametric uncertain system. Furthermore, by applying the Lyapunov stability theorem, the stochastic analysis approach, and the Halanay inequality, some sufficient conditions are obtained to realize synchronization in mean square. The established criteria show that stochastic perturbation is designed to ensure that the coupled IMNNs can be synchronized better by changing the state coefficients of stochastic perturbation. Finally, an illustrative example is presented to demonstrate the efficiency of the theoretical results.

Almost sure exponential synchronization of drive-response stochastic memristive neural networks

Abstract This paper concerns with the almost sure exponential synchronization for some general classes of drive-response stochastic memristive neural networks (SMNNs) with nonidentical nodes under state feedback controllers. The SMNNs considered may include networks which are asymmetrically nondelayed and delayed coupled simultaneously, and state-dependent or even those that are subject to exogenous stochastic perturbations representatively. The main results of this paper are a collection of generic sufficient conditions for guaranteed almost sure exponential synchronization of these SMNNs, which performs great advantages compared with mean-square synchronization. Furthermore, some practical corollaries are also obtained from the main results that may be directly applied to some smaller subclasses of these networks. In particular, a simpler and more effective way of almost surely exponentially synchronizing SMNNs without delays follows by considering them as a special case of SMNNs with delays. Some numerical simulations are given to illustrate our main theoretical findings.