Synchronization Criteria Research Articles

Sampled-data controller scheme for multi-agent systems and its Application to circuit network

The objective of this study is to investigate the synchronization criteria under the sampled-data control method for multi-agent systems (MASs) with state quantization and time-varying delay. Currently, a looped Lyapunov–Krasovskii Functional (LKF) has been developed, which integrates information from the sampling interval to ensure that the leader system synchronizes with the follower system, resulting in a specific condition in the form of Linear Matrix Inequalities (LMIs). The LMIs can be easily solved using the LMI Control toolbox in Matlab. Finally, the proposed approach’s feasibility and effectiveness are demonstrated through numerical simulations and comparative results.

Uniform ultimate boundedness and approximate synchronization of coupled reaction-diffusion systems with parameter mismatches

We present a framework for studying the uniform ultimate boundedness and approximate synchronization of coupled systems. The individual subsystems of the coupled systems are described by general reaction-diffusion (RD) systems, and we account for parameter mismatches between individual subsystems while considering a general coupling scheme. We derive several criteria for the uniform ultimate boundedness of coupled RD systems under different assumptions regarding the properties of the reaction terms and coupling schemes. Using M-matrix theory and iterative methods, we establish an approximate synchronization criterion for the coupled RD systems. This criterion allows the coupled systems to synchronize with synchronization errors arising from parameter mismatches, and perfect synchronization is achieved when there are no parameter mismatches. Moreover, the criterion provides an estimated bound for the synchronization error, which decreases as the degree of inhomogeneity caused by parameter mismatches reduces. To demonstrate the effectiveness of our approaches, we apply our theories to the FitzHugh-Nagumo (FHN) neuron model.

Unified synchronization and fault‐tolerant anti‐disturbance control for synchronization of multiple memristor‐based neural networks

SummaryThis work primarily concentrates on the design of fault‐tolerant anti‐disturbance control for synchronization of multiple memristor‐based neural networks subject to time delay, matched and mismatched disturbances. Moreover, in the addressed network model, we consider parameter uncertainties and actuator faults. Firstly in order to estimate the matched disturbances generated by the exogenous system, a disturbance observer is devised. Whereas, the mismatched part is tackled by employing the mixed and passivity performance indexes. Subsequently, a unified controller is designed by incorporating error feedback control and the disturbance estimate. Further, with the assistance of Lyapunov stability theory and linear matrix inequality technique, an adequate criteria is procured to ascertain the required synchronization criteria for the assayed network model with the mixed and passivity performance indexes. Following this, by basing on the established conditions, the explicit form of the controller and observer gain matrices is obtained. In the end, a numerical example with simulation results is shown to confirm the potential and usefulness of the conclusions acquired from the theoretical analysis.

Secure synchronisation for multiple coupled complex networks with time-varying delays under DoS attacks

This paper investigates the secure synchronisation for multiple coupled complex networks with time-varying delays under Denial-of-Service attacks, in which the attacks are considered in the controller-to-actuator channel. A synchronisation criterion is established to ensure the secure synchronisation of the presented networks based on the designed adaptive topology observer, controller and Lyapunov function. Furthermore, the result adapts to study the synchronisation of complex networks without and with multiple time-varying delays. Finally, two numerical examples are provided to illustrate the availability of the derived theoretical results.

Synchronization of fractional-order delayed coupled networks with reaction–diffusion terms and Neumann boundary value conditions

This paper investigates the adaptive pinning strategies for achieving synchronization of fractional-order delayed coupled networks with reaction–diffusion terms and a digraph topology by incorporating Neumann boundary value conditions. By employing the inf–sup method, a novel fractional-order inequality is proved. The classical Poincaré inequality is also extended by utilizing the Hölder inequality. Two types of control laws are developed to achieve synchronization: one with control gains dependent solely on time, and another with control gains dependent on both space and time. For each case, adaptive control laws and synchronization criteria based on matrix inequalities are proposed. Finally, the effectiveness of the synchronization results is demonstrated through two numerical examples.

Event‐triggered pinning control for passivity and synchronization of directly coupled delayed reaction‐diffusion neural networks

SummaryThis article solves event‐triggered pinning control for passivity and synchronization problems of directly coupled delayed reaction‐diffusion neural networks (CDRDNNs). Outer coupling matrix of the presented model can be direct, while previous literature referred to reaction‐diffusion neural networks usually assumed this matrix undirected simply. First, through exploiting appropriate event‐triggered pinning protocol, passivity and synchronization criteria are acquired for directly CDRDNNs on account of Lyapunov functional and inequality techniques. After that, we also deal with event‐triggered pinning passivity and synchronization for undirected CDRDNNs. In the end, the effectiveness of these obtained results is verified by given examples.

Exponential synchronization of delayed coupled neural networks with delay-compensatory impulsive control

This paper studies the exponential synchronization problem for a class of delayed coupled neural networks with delay-compensatory impulsive control. A Razumikhin-type inequality involving some destabilizing delayed impulse gains and a new idea of delay-compensatory that shows two critical roles for system stability are presented, respectively. Based on the constructed inequality and the presented delay-compensatory idea, sufficient stability and synchronization criteria for globally exponential synchronization (GES) of coupled neural networks (CNNs) are presented. Compared with existing results, the uniqueness of the presented results lies in that impulse delays can be fetched and integrated to compensate for instantaneous unstable impulse dynamics caused by destabilizing gains. Moreover, constraints between system delay and impulsive delay are relaxed, and the interval of impulses no longer constrains the system delay. Comparisons and a practical application are given to demonstrate the superior performance of the presented novel control methods

Further results on synchronization of chaotic Lur’e systems based on aperiodic time-triggered intermittent control

Aperiodic time-triggered intermittent control (ATIC) is presented to investigate the exponential synchronization issue of chaotic Lur’e systems (CLSs). In our work, for CLSs, the mathematical expression of ATIC is put forward initially. Different from time-triggered intermittent control (TIC), ATIC allows aperiodic sampling. The aperiodic sampling characteristic of ATIC makes it more flexible and adaptable in complex environments, which greatly increases its applications. Then, for the deduced ATIC error system, a key lemma is established, which demonstrates that, on control or free time intervals, the bound of the error vector norm at any instance can be described by the multiple of its norm at initial instance. Further, based on the lemma and a mixed time-dependent Lyapunov functional (MTLF), the exponential stability theorem is given for the deduced ATIC error system. Consequently, the exponential synchronization criterion with less conservativeness is obtained for CLSs via ATIC. With its aid, the design method of ATIC is proposed. Finally, the validity and superiority of ATIC are verified by a simulation example.

Event-triggered impulsive cluster synchronization of coupled reaction–diffusion neural networks and its application to image encryption

This paper investigates the cluster synchronization of coupled neural networks with reaction–diffusion terms. With the help of impulsive control strategies, some cluster synchronization criteria are proposed by an appropriate event-triggered mechanism. A numerical example is given to verify the validity of the theoretical results. Additionally, the proposed event-triggered impulsive synchronization is successfully applied to image encryption with encouraging cryptanalysis results demonstrating its strong ability to efficiently encrypt images.

Lp synchronization of shunting inhibitory cellular neural networks with multiple proportional delays

In this paper, synchronization control of shunting inhibitory cellular neural networks with multiple proportional delays is studied. Firstly, a controller is designed to ensure Lp synchronization between the response and drive shunting inhibitory cellular neural networks. Then, a method based on system solutions is proposed to obtain Lp synchronization criteria. On the one hand, the synchronization criteria obtained by this method only contain some simple inequalities, and hence the calculation amount is greatly reduced. On the other hand, the method does not require the establishment of any Lyapunov–Krasovskii functional. The obtained Lp synchronization criteria are simpler and can be tested by standard software tools. Finally, a numerical example is given to illustrate the superiority of the proposed Lp synchronization criteria. It is worth emphasizing that the Lp synchronization control problem is analyzed for the first time in this paper.

Synchronization sampled-data control of uncertain neural networks under an asymmetric Lyapunov–Krasovskii functional method

This paper investigates the synchronization control of neural networks (NNs) considering parameter uncertainties by utilizing an improved asymmetric Lyapunov–Krasovskii functional (ALKF) method. Firstly, an uncertain NNs model with discrete and distributed delays is developed. To synchronize the master–slave system, a memory sampled-data controller is designed. Secondly, an improved ALKF is constructed, in which the positive-definite and symmetric restrictions of matrices are relaxed. Furthermore, improved synchronization criteria are established by linear matrix inequalities (LMIs), which are based on the ALKF method and the integral inequality technique. Finally, two simulation examples are conducted to demonstrate the feasibility and superiority of the established stability conditions in reaching a maximum sampling period.

Bipartite synchronization of multilayer signed networks under aperiodic intermittent-based adaptive dynamic event-triggered control

This article addresses the exponential bipartite synchronization (EBS) of multilayer signed networks with time-varying coupling (MSNs) under aperiodic intermittent-based adaptive dynamic event-triggered control (AAIDETC). Firstly, to increase the elasticity, a novel AAIDETC strategy is presented, whose superiority is that the control gains and the triggering parameters can vary with the evolution of the considered networks. Meanwhile, concerning the aperiodic intermittent control, a new definition of average control ratio (ACR) is put forward, which is more rigorous compared with the relevant results. Then, by the method of ACR, graph theory and Lyapunov approach, the simpler synchronization criterion is gained, which avoids the topology structure of MSNs. Moreover, the EBS issues of Chua’s circuits and neural networks established on MSNs are studied, which are two practical applications of our theoretical results. Finally, corresponding numerical simulations are presented to verify the availability of the obtained results.

Finite-time synchronization and topology identification of stochastic multi-layer networks with Markovian switching

The finite-time synchronization and topology identification problems of stochastic multi-layer networks with Markovian switching are investigated in this paper. Compared with previous studies, Markovian switching is considered in stochastic multi-layer networks. First, by using Kirchhoff’s matrix tree theorem in graph theory, the Lyapunov function of the coupling system is constructed indirectly from the Lyapunov function of the vertex system. In view of finite-time stability theory and stochastic analysis technique, some finite-time synchronization criteria of stochastic multi-layer networks are proposed. Moreover, the intra-layer and inter-layer topological structures are successfully identified in finite time. Then, using the pinning control technique, the unknown partial topological structures are also identified in finite time. In the end, two examples for whole and partial topology identification of two-layer small-world networks are given.

Novel Single Bounded Input Control Synchronization Criterion for a Category of Hyperchaotic and Chaotic Systems in Presence of Uncertainties

Abstract Dynamical systems that have a chaotic underlying structure have a sensitive dependency on the initial conditions and the values of their parameters. In this piece of work, a straightforward method for solving the synchronization issue in master–slave arrangement for a category of chaotic or hyperchaotic systems, in which perturbations are present in the parameters of the response system, is discussed. The desired control signal is bounded by the initial state when the controller is activated. There is just one control input that is used, and it is derived from Lyapunov's concept of stability. In general, it is tricky to synchronize hyperchaotic or chaotic systems with single controller, and the work turns out to be significantly more complex when the parameters of the slave system are perturbed. The feedback controller using single input that has been constructed makes certain that the state variables of the response system are in synchronization with the state variables that correspond to them in the drive system. In order to attain the desired level of synchronization, the required conditions that must be satisfied to do so have been identified utilizing Lyapunov's stability analysis in a simple manner. In addition, numerical illustrations have been provided in order to support and confirm the theoretical findings of the paper.

Synchronization analysis of nabla fractional-order fuzzy neural networks with time delays via nonlinear feedback control

This paper is committed to explore synchronization issues for a class of nabla fractional-order fuzzy neural networks with time delays. First, we establish two useful nabla fractional inequalities by feat of the theory of nabla fractional calculus and N-transform together with nabla convolution. Next, we design two distinctive controllers including nonlinear delay feedback controller and hybrid nonlinear delay controller, some easily verified quasi-synchronization (QS) criteria and complete synchronization (CS) criteria are derived by virtue of newly proposed inequalities therein and some inequality techniques. Finally, the correctness of theoretical results is indicated finally through numerical simulations. What is more important, theoretical results therein can offer some new avenues about QS and CS analysis for nabla fractional dynamical networks.

Saturation function-based continuous control on fixed-time synchronization of competitive neural networks

Currently, through proposing discontinuous control strategies with the signum function and discussing separately short-term memory (STM) and long-term memory (LTM) of competitive artificial neural networks (ANNs), the fixed-time (FXT) synchronization of competitive ANNs has been explored. Note that the method of separate analysis usually leads to complicated theoretical derivation and synchronization conditions, and the signum function inevitably causes the chattering to reduce the performance of the control schemes. To try to solve these challenging problems, the FXT synchronization issue is concerned in this paper for competitive ANNs by establishing a theorem of FXT stability with switching type and developing continuous control schemes based on a kind of saturation functions. Firstly, different from the traditional method of studying separately STM and LTM of competitive ANNs, the models of STM and LTM are compressed into a high-dimensional system so as to reduce the complexity of theoretical analysis. Additionally, as an important theoretical preliminary, a FXT stability theorem with switching differential conditions is established and some high-precision estimates for the convergence time are explicitly presented by means of several special functions. To achieve FXT synchronization of the addressed competitive ANNs, a type of continuous pure power-law control scheme is developed via introducing the saturation function instead of the signum function, and some synchronization criteria are further derived by the established FXT stability theorem. These theoretical results are further illustrated lastly via a numerical example and are applied to image encryption.

Global Asymptotic Stability and Synchronization of Fractional-Order Reaction–Diffusion Fuzzy BAM Neural Networks with Distributed Delays via Hybrid Feedback Controllers

In this paper, the global asymptotic stability and global Mittag–Leffler stability of a class of fractional-order fuzzy bidirectional associative memory (BAM) neural networks with distributed delays is investigated. Necessary conditions are obtained by means of the Lyapunov functional method and inequality techniques. The hybrid feedback controllers are then developed to ensure the global asymptotic synchronization of these neural networks, resulting in two additional synchronization criteria. The derived conditions are applied to check the fractional-order fuzzy BAM neural network’s Mittag–Leffler stability and synchronization. Three examples are given to demonstrate the effectiveness of the achieved results.

Application of linear ordinary differential equations to the stability control of long time lag networks

Abstract Optimal control based on the exact synchronization of linear ordinary differential equations can provide conditions for the existence of optimal control of long-time lag network stability. In this paper, we first generalize network control systems, time lag systems, and modern control system stability theory to discuss long-time lag network stability analysis and control problems. The numerical solution method for solving ordinary differential equations with boundary conditions is proposed by combining the numerical solution method for initial value problems of differential equations and the iterative method for solving nonlinear equations. Finally, the fixed-time synchronization problem of complex networks with time-varying time lags under periodic intermittent control is studied. Two intermittent control strategies are designed based on the linear ordinary differential equation algorithm, and the convergence analysis of the synchronization error and the synchronization criterion are given. Numerical values show that the synchronization error converges to zero (< 1.0e − 5) in 0.32s, while the convergence times are 0.55s and 0.90s. The fixed times of the three methods are calculated to be T * = 0.52, T 1 = 0.71 and T 2 = 1.32, respectively, and the synchronization error system converges faster under the method in the paper. The numerical simulation results verify the effectiveness of linear ordinary differential equations in controlling the stability of long-time lag networks.

Novel Synchronization Criteria for Non-Dissipative Coupled Networks with Bounded Disturbances and Time-Varying Delays of Unidentified Bounds via Impulsive Sampling Control

The μ−synchronization issues of non-dissipative coupled networks with bounded disturbances and mixed delays are studied in this article. Different from existing works, three kinds of time delays, including internal delays, coupling delays, and impulsive sampling delays, have unidentified bounds and even evolve towards infinity over time, making the concerned network more practical. Considering μ−stability theory and impulse inequality techniques, a hybrid non-delayed and time-delayed impulsive controller including both current and historical state information is designed, and several novel sufficient conditions are derived to make nonlinear complex networks achieve μ−synchronization. Moreover, not only can the constriction of dissipative coupling conditions on network topology be relaxed, but also the restriction of various time delays on impulsive intervals can be weakened, which makes the theoretical achievements in this article more general than the previous achievements. Ultimately, numerical simulations confirm the effectiveness of our results.

Tradeoff analysis between synchronization time and energy consumption for multi-layer networks

Based on finite-time (FNT) synchronization and energy consumption estimation of multi-layer networks, the tradeoff problem of synchronization time and energy consumption are discussed in this paper. Firstly, by establishing a switching controller without sign function, a sufficient criterion for the finite time synchronization of the error system is obtained. Then, the upper bound of the energy is estimated. Furthermore, by establishing the normalized evaluation index function, the tradeoff between control time and energy consumption is analyzed, and the optimal control gain of the switching controller is obtained, which can realize FNT synchronization with lower energy cost in a shorter time. Finally, the validity of the results is supported by numerical simulation.