Nonlinearly Coupled Complex Networks Research Articles

Resolution‐Dependent State Estimation for a Class of Nonlinear Coupled Complex Networks With Stochastic Communication and Correlated Noises

ABSTRACTThis article proposes the design of the resolution‐dependent variance‐constrained state estimation (RDVCSE) algorithm for a class of time‐varying nonlinear coupled complex networks (TVNCCNs) with stochastic communication and correlated noises. Specifically, a continuous‐differentiable nonlinear function with bounded first partial derivative is considered during the exchange among different coupled units and a resolution‐limited model is taken into account to embody the limited data‐processing capabilities of sensors. In order to describe the principle of random allocation in engineering, a stochastic strategy is employed in the sensor/estimator shared channel. An augmented RDVCSE method is developed such that the error covariance upper bound of state estimation (ECUBSE) can be guaranteed and obtained first. Then, the estimator parameter can be concretized via optimizing the trace of ECUBSE. In addition, a sufficient criterion is provided to verify the uniform boundedness of the presented RDVCSE algorithm. Finally, a comparative simulation is carried out to illustrate the validity of the introduced RDVCSE algorithm.

Clustering Component Synchronization of Nonlinearly Coupled Complex Networks via Pinning Control

In this paper, the problem of clustering component synchronization of nonlinearly coupled complex networks with nonidentical nodes and asymmetric couplings is investigated. A pinning control strategy is designed to achieve the clustering component synchronization with respect to the specified components. Based on matrix analysis and stability theory, clustering component synchronization criteria are established. Two numerical simulations are also provided to show the effectiveness of the theoretical results.

Aperiodically intermittent event-triggered pinning control on cluster synchronization of directed complex networks

This paper is dedicated to investigating the exponential cluster synchronization in a class of nonlinearly coupled complex networks with non-identical nodes and an asymmetrical coupling matrix. A novel aperiodically intermittent pinning control (APIPC) protocol is presented, which takes full account of the cluster-tree topology structure of the networks and pins only the nodes in the current cluster that have directional links to neighboring clusters. Since it is difficult to precisely determine the intermittent control instants and rest instants of APIPC in advance, the event-triggered mechanism (ETM) is thus proposed. Based on the concept of the minimal control ratio and the segmentation analysis method, sufficient requirements for realizing the exponential cluster synchronization are derived. Moreover, the Zeno behavior of ETM is excluded by rigorous analysis. Eventually, the effectiveness and advantages of the established theorems and control strategies are demonstrated by two numerical simulations.

Dynamic Event-triggered State Estimation for Nonlinear Coupled Output Complex Networks Subject to Innovation Constraints

This letter investigates the recursive state estimation (RSE) problem for a class of coupled output complex networks via the dynamic event-triggered communication mechanism (DETCM) and innovation constraints (ICs). Firstly, a DETCM is employed to regulate the transmission sequences. Then, in order to improve the reliability of network communication, a saturation function is introduced to constrain the measurement outliers. A new RSE method is provided such that, for all output coupling, DETCM and ICs, an upper bound of state estimation error covariance (SEEC) is presented in a recursive form, whose trace can be minimized via parameterizing the state estimator gain matrix (SEGM). Moreover, the theoretical analysis is given to guarantee that the error dynamic is uniformly bounded. Finally, a simulation example is illustrated to show the effectiveness of the proposed RSE method.

Recursive state estimation for a class of nonlinear uncertain coupled complex networks subject to random link failures and packet disorders

This paper is concerned with the recursive state estimation (RSE) problem under minimum mean-square error sense for a class of nonlinear complex networks (CNs) with uncertain inner coupling, random link failures and packet disorders. Firstly, a set of random variables obeying the Bernoulli distribution is adopted to characterize whether there are connections between different network units, i.e., there is no random link failure when the random variable is equal to 1, otherwise the random link failure occurs. In addition, the inner coupling strength is assumed to be varying within a given interval and the phenomenon of packet disorders caused by the random transmission delay (RTD) is also taken into account. In our study, the nonlinearity satisfies the continuously differentiable condition, which can be linearized by resorting to the Taylor expansion. The focus of the addressed RSE problem is on the design of an RSE approach in the mean-square error sense such that, for all uncertain inner coupling, random link failures and packet disorders, a suboptimal upper bound of the state estimation error covariance is obtained and minimized by parameterizing the state estimator gain with explicit expression form. Furthermore, a sufficient condition with respect to the uniform boundedness of state estimation error in mean-square sense is elaborated. Finally, a numerical experiment is introduced to demonstrate the validity of the presented RSE approach.

Formula omitted] filtering for nonlinearly coupled complex networks subjected to unknown varying delays and multiple fading measurements

In this paper, the robust filtering problem for uncertain complex networks with time-varying state delay and stochastic nonlinear coupling based on H∞ performance criterion is studied. The random connections of coupling nodes are represented by utilizing independent random variables and the multiple fading measurements phenomenon is characterized by introducing diagonal matrices with independent stochastic elements. Moreover, the probabilistic time-varying delays in the measurement outputs are described by white sequences with the Bernoulli distributions. Furthermore, All system’s matrices are supposed to have uncertainty and a quadratic bound is assumed for nonlinear part of the network. This bound can be obtained by solving a sum of squares (SOS) optimization problem. By applying the Lyapunov theory, we design a robust filter for each node of the network so that the filtering error system is asymptomatically stable and the H∞ performances are met. Then, the parameters of the filters are achieved by solving a linear matrix inequality (LMI) feasibility problem. Finally, the applicability and performance of the proposed H∞ filtering approach are demonstrated via a practical example.

Pinning Impulsive Synchronization of Complex Networks with Multiple Sizes of Delays via Adaptive Impulsive Intervals

The leader-following issue for a class of nonlinearly coupled complex networks with multiple time-varying delays was investigated in this study. A distributed controller was introduced for realizing the exponential synchronization of the complex network with different delay scales that are known in advance. The Lyapunov stability theorem and mathematical induction method were used to obtain delay-dependent criteria for global impulsive synchronization. Additionally, an adaptive strategy was adopted to establish appropriate impulsive intervals suitable for various delays. The fact that the proposed adaptive scheme is more general and less conservative enables the effective release of the constriction caused by unknown delay scales. Furthermore, the pinning impulsive control method enables the control cost to be further reduced. Finally, several numerical simulations were performed to evaluate the effectiveness of the mathematical deductions.

Secure synchronization of complex networks under deception attacks against vulnerable nodes

Secure synchronization for a class of nonlinearly coupled complex networks with deception attacks is investigated in this paper. False data caused by deception attacks is assumed to be injected into both the sensor-to-controller channels and the controller-to-actuator channels, which is modelled by Bernoulli stochastic variable. A distributed controller combined with impulsive protocol is applied for realizing the secure synchronization. By jointly applying the definition of average impulsive gain, the definition of average impulsive interval and the Lyapunov stability theorem, sufficient criteria are obtained to ensure the secure synchronization within the given error bound. In addition, pinning impulsive method is proposed to describe the attacks on vulnerable systems in complex networks, therefore, the theorem is extended to a less conservative situation. Finally, two numerical examples are presented to illustrate the effectiveness of theoretical results.

Polynomial Lyapunov Functions for Synchronization of Nonlinearly Coupled Complex Networks.

In this article, we search for polynomial Lyapunov functions beyond the quadratic form to investigate the synchronization problems of nonlinearly coupled complex networks. First, with a relaxed assumption than the quadratic condition, a synchronization criterion is established for nonlinearly coupled networks with asymmetric coupling matrices. Compared with the existing synchronization criteria, our results are less conservative and have a wider application. Second, the synchronization problem for polynomial networks is characterized as the sum-of-squares (SOS) optimization one. In this way, polynomial Lyapunov functions can be obtained efficiently with SOS programming tools. Furthermore, it is shown that the local synchronization of certain nonpolynomial networks can also be analyzed by using the SOS optimization method through the Taylor series expansion. Finally, three numerical examples are presented to verify the effectiveness and less conservatism of our analytical results.

Synchronization of nonlinearly coupled complex networks: Distributed impulsive method

Abstract This paper is devoted to discussing the exponential synchronization of a class of nonlinearly coupled complex networks (NCCNs) with time-varying delays and stochastic disturbance. In consideration of the complex networks would subject to certain impulse disturbances, a kind of distributed controller combining with pinning control and impulsive control schemes is designed. Based on the concept of average impulsive interval and comparison principles, sufficient conditions for achieving the exponential synchronization are derived. In addition, the exponential convergence velocities are obtained, respectively, with considering different functions of the impulsive inputs. Finally, a numerical simulation is presented to demonstrate the feasibility of the theoretical deduction.

Recovering node parameters and topologies of uncertain non‐linearly coupled complex networks

Node dynamics and network topologies play vital roles in determining dynamical behaviours and features of complex networks. Thus it is of great theoretical significance and practical value to identify the node parameters and topologies of uncertain complex networks. This study presents adaptive anticipatory synchronisation-based approaches to identify the unknown node parameters and topologies of uncertain non-linearly coupled complex networks perturbed by stochastic noise. Moreover, during the identification process, the authors proposed scheme guarantees anticipatory synchronisation between the uncertain drive and constructed response network simultaneously. In particular, their methods can be used to recover node parameters and topologies of complex networks in several special cases, such as cases without node delay or coupling delay. Furthermore, numerical simulations are provided to verify the applicability and effectiveness of their methods for recovering node parameters and topologies of uncertain non-linearly coupled complex networks.

Finite-Time Cluster Synchronization of Lur’e Networks: A Nonsmooth Approach

This paper is devoted to the finite-time cluster synchronization issue of nonlinearly coupled complex networks which consist of discontinuous Lur’e systems. On the basis of the definition of Filippov regularization process and the measurable selection theorem, the discontinuously nonlinear function is mapped into a function-valued set, then a measurable function is accordingly selected from the Filippov set to ensure the existence of the solution for the discontinuous system. By designing the finite-time pinning controller, some sufficient conditions are obtained for cluster synchronization of the identical and nonidentical Lur’e networks, respectively. In addition, the settling time for achieving the cluster synchronization is estimated by applying the finite-time stability theory. And finally, a numerical example is presented to illustrate the validity of theoretical analysis.

Adaptive Synchronization of Fractional-Order Nonlinearly Coupled Complex Networks With Time Delay and External Disturbances

This paper considers both local and global synchronizations of fractional-order nonlinearly-coupled complex networks with time delay and unknown external disturbances. Here, neither delayed or non-delayed configuration matrices are necessarily irreducible or symmetric. Combined with the fractional order compare theorem and fractional order stability theory, some novel sufficient conditions are obtained that guarantee the realization of local and global asymptotic synchronization via adaptive control and pinning control. The network model and conclusion in this paper are more practical and general than those in the existing literature. The experimental results show the feasibility of our theoretical analysis.

Synchronization of delayed complex networks via intermittent control with non-period

In this paper, a pinning synchronization scheme of nonlinear coupled complex networks is investigated via non-periodically intermittent control method, in which dynamical system is delayed nonlinear system, and its coupling matrices can be nonsymmetric. In the case that control ratio of control width to total time width is equal in any time interval, the control scheme is studied, and some sufficient conditions are given to ensure global exponential synchronization. Furthermore, two main corollaries are derived. At last, numerical simulations show effectiveness of the synchronization scheme.

State estimation for nonlinearly coupled complex networks with application to multi-target tracking

This paper is concerned with the state estimation problem for a class of nonlinearly coupled complex networks with random coupling strengths. The coupling strengths are assumed to be chosen from a set of uniform distributions with non-negative means. The estimator is developed for each node by using the structure of the extended Kalman filter, where the gain matrix is determined by optimizing an upper bound matrix for the estimation error covariance despite the linearization errors and coupling terms. It is shown that the gain matrix can be derived separately for each node by solving two Riccati-like difference equations. By using the stochastic analysis technique, a sufficient condition is established which guarantees the boundedness of the estimation errors. As an application, we show how the nonlinearly coupled complex networks can be used to describe the target motions with interacting behaviors and the proposed estimator can be used to derive the state estimates of the targets. A numerical example is provided to verify the effectiveness of the proposed estimator.

Variance-Constrained State Estimation for Nonlinearly Coupled Complex Networks.

This paper studies the state estimation problem for nonlinearly coupled complex networks. A variance-constrained state estimator is developed by using the structure of the extended Kalman filter, where the gain matrix is determined by optimizing an upper bound matrix for the estimation error covariance despite the linearization errors and coupling terms. Compared with the existing estimators for linearly coupled complex networks, a distinct feature of the proposed estimator is that the gain matrix can be derived separately for each node by solving two Riccati-like difference equations. By using the stochastic analysis techniques, sufficient conditions are established which guarantees the state estimation error is bounded in mean square. A numerical example is provided to show the effectiveness and applicability of the proposed estimator.

Finite-time synchronization of multi-layer nonlinear coupled complex networks via intermittent feedback control

This paper addresses the problem of finite-time synchronization for a class of multi-layer nonlinear coupled complex networks via intermittent feedback control. Firstly, based on finite-time stability theory, some novel criteria are given to guarantee that the error system of drive-response systems is still finite-time stable under an inherently discontinuous controller. Then, by proposing two kinds of intermittent feedback control laws, sufficient conditions of finite-time synchronization of two kinds of multi-layer complex networks are derived, respectively. The time delay between different layers is also taken into consideration. Finally, a numerical example is provided to verify the effectiveness of the proposed methods.

Almost sure cluster synchronization of Markovian switching complex networks with stochastic noise via decentralized adaptive pinning control

This paper investigates the issue of almost sure cluster synchronization in nonlinearly coupled complex networks with nonidentical nodes and time-varying delay. These networks are modulated by a continuous-time Markov chain and disturbed by a Brownian movement. The decentralized adaptive update law and pinning control protocol are employed in designing controllers for guaranteeing almost sure cluster synchronization. By constructing a novel stochastic Lyapunov–Krasovskii function and using the stochastic Lasalle-type invariance theorem, some sufficient conditions for almost sure cluster synchronization of the networks are derived. Finally, a numerical example is given to testify the effectiveness of the theoretical results.

Exponential synchronization of nonlinearly coupled complex networks with hybrid time-varying delays via impulsive control

This paper investigates the issue of exponential synchronization for a class of nonlinearly coupled complex networks with hybrid time-varying delays by applying impulsive control protocol. It should be mentioned we need not to assume the synchronization state since it may be difficult to find an appropriate function or dynamics to describe the synchronization manifold. By employing the Lyapunov method combined with average impulsive interval as well as the comparison principle, a set of simple and easily verifiable sufficient conditions are derived to guarantee the exponential synchronization for any initial values. Meanwhile, the exponential convergence rate can be specified through the analysis of the networks. Additionally, some numerical examples are given to verify the effectiveness of our theoretical results.

Pinning synchronization of nonlinearly coupled complex networks with time-varying delays using M-matrix strategies

In this paper, we investigate the global synchronization problem for a class of nonlinearly-coupled complex networks (NCCNs) with mixed time-varying delays by using an M-matrix approach. The M-matrix strategy allows many synchronization problems with much relaxed conditions to be considered and can be used to derive sufficient conditions for this new class of NCCNs by pinning control. We also propose an effective way of adapting the coupling strengths of complex networks and give numerical examples to illustrate the effectiveness of our theoretical results.