Uncertain Complex Networks Research Articles

Event‐triggered sampled‐data synchronization of complex networks with uncertain inner coupling and time‐varying delays

AbstractThis paper focuses on event‐triggered sampled‐data synchronization of uncertain complex networks with time‐varying coupled delays. First of all, a discrete event‐triggered sampled‐data control scheme is adopted, which not only makes the state of the system be monitored in discrete time, but also the sampling information is effectively transmitted. The proposed event‐triggered mechanism effectively prevents Zeno behavior. In addition, we also use some novel piecewise time‐dependent Lyapunov–Krasovskii and Wirtinger inequality to handle the time‐varying delays and parameter uncertainties of complex networks. Then, synchronization criteria are given for uncertain complex networks. Finally, the simulation results show that the control scheme can significantly reduce the number of transmitted signals while maintaining the uncertain complex networks synchronization.

Research Progress of Complex Network Modeling Methods Based on Uncertainty Theory

A complex network in reality contains a large amount of information, but some information cannot be obtained accurately or is missing due to various reasons. An uncertain complex network is an effective mathematical model to deal with this problem, but its related research is still in its infancy. In order to facilitate the research into uncertainty theory in complex network modeling, this paper summarizes and analyzes the research hotspots of set pair analysis, rough set theory and fuzzy set theory in complex network modeling. This paper firstly introduces three kinds of uncertainty theories: the basic definition of set pair analysis, rough sets and fuzzy sets, as well as their basic theory of modeling in complex networks. Secondly, we aim at the three uncertainty theories and the establishment of specific models. The latest research progress in complex networks is reviewed, and the main application fields of the three uncertainty theories are discussed, respectively: community discovery, link prediction, influence maximization and decision-making problems. Finally, the prospect of the modeling and development of uncertain complex networks is put forward.

Robust H ∞ state estimation for a class of complex networks with dynamic event-triggered scheme against hybrid attacks

We investigate the dynamic event-triggered state estimation for uncertain complex networks with hybrid delays suffering from both deception attacks and denial-of-service attacks. Firstly, the effects of time-varying delays and finite-distributed delays are considered during data transmission between nodes. Secondly, a dynamic event-triggered scheme (ETS) is introduced to reduce the frequency of data transmission between sensors and estimators. Thirdly, by considering the discussed plant, dynamic ETS, state estimator, and hybrid attacks into a unified framework, this framework is transferred into a novel dynamical model. Furthermore, with the help of Lyapunov stability theory and linear matrix inequality techniques, sufficient condition to ensure that the system is exponentially stable and satisfies H ∞ performance constraints is obtained, and the design algorithm for estimator gains is given. Finally, two numerical examples verify the effectiveness of the proposed method.

Finite-time lag synchronization for uncertain complex networks involving impulsive disturbances

This paper focuses on the finite-time lag synchronization (FTLS) of uncertain complex networks involving impulsive disturbance effects. By designing two different controllers, some Lyapunov-based conditions are established in terms of linear matrix inequalities to ensure the FTLS of impulsive systems, where the upper bound of the synchronizing times can be estimated via constructing Lyapunov functions. It is interesting to discover that the synchronizing time depends not only on the initial value but also on the impulse sequences, which implies that different impulses will lead to different synchronization times. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed FTLS criterion.

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.

Distributed Dynamic Self-Triggered Control for Uncertain Complex Networks With Markov Switching Topologies and Random Time-Varying Delay

This paper studies the synchronization of complex networks with probabilistic interval delay and Markov switching topologies by using a novel dynamic self-triggered control (DSTC) scheme. Employing the probability distribution information of the input time-delay, the control protocol is transformed into a new rule with stochastic parameters. Also, a more general case of switching topologies, Markov switching topologies with partial information on transition rate, is discussed. By introducing a free-connection weighting matrix scheme and using the stability theory, a less conservative synchronization result is derived. It is shown by a numerical example that the DSTC method can reduce the sampling frequency apparently, and the tolerable delay upper bound can also be relaxed. In addition, continuous communication and the Zeno-behavior can be avoided.

Resilient state estimation for time‐varying uncertain dynamical networks with data packet dropouts and switching topology: an event‐triggered method

In this study, the recursive state estimation method based on the event-triggered protocol is given for time-varying uncertain complex networks with switching topology (ST), data packet dropouts (DPDs), and randomly occurring non-linearities (RONs). The event-triggered strategy is given to regulate the communications and then save the limited network resources when the measurement information is transmitted. The phenomena of RONs, ST, and DPDs are depicted by some random variables obeying the Bernoulli distribution. Besides, the estimator gain perturbations are dealt with. The major aim of this study is to present a new state estimation algorithm for addressed time-varying uncertain complex networks such that, for all STs, DPDs, and RONs, a minimal upper bound of state estimation error covariance matrix is derived by designing an optimal estimator gain matrix. Finally, a numerical simulation is presented to show the effectiveness of the provided time-varying state estimation method.

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.

Resilient Set-membership State Estimation for Uncertain Complex Networks with Sensor Saturation under Round-Robin Protocol

This article gives primarily attention to the resilient set-membership state estimation problem for a class of discrete time-varying complex networks with distributed delays, uncertain inner coupling and sensor saturation under the round-robin (RR) protocol. The process and measurement noises are unknown but bounded, which are confined to the ellipsoidal sets. The RR protocol is utilized to assign the priority of accessing to the communication network to nodes in terms of a fixed circular order. By means of the recursive linear matrix inequality (RLMI) technique, a sufficient criterion is established to guarantee that the one-step ahead estimation error is confined to the ellipsoidal set. In term of the convex optimization approach and the recursive algorithm, the desired estimator gains can be derived by utilizing the sufficient condition and optimizing the corresponding constraint matrices. Finally, a simulation example is used to verify the effectiveness of the designed resilient set-membership state estimation scheme.

Robust Partial-Nodes-Based State Estimation for Complex Networks Under Deception Attacks.

In this paper, the partial-nodes-based state estimators (PNBSEs) are designed for a class of uncertain complex networks subject to finite-distributed delays, stochastic disturbances, as well as randomly occurring deception attacks (RODAs). In consideration of the likely unavailability of the output signals in harsh environments from certain network nodes, only partial measurements are utilized to accomplish the state estimation task for the addressed complex network with norm-bounded uncertainties in both the network parameters and the inner couplings. The RODAs are taken into account to reflect the compromised data transmissions in cyber security. We aim to derive the gain parameters of the estimators such that the overall estimation error dynamics satisfies the specified security constraint in the simultaneous presence of stochastic disturbances and deception signals. Through intensive stochastic analysis, sufficient conditions are obtained to guarantee the desired security performance for the PNBSEs, based on which the estimator gains are acquired by solving certain matrix inequalities with nonlinear constraints. A simulation study is carried out to testify the security performance of the presented state estimation method.

Trajectory Tracking on Uncertain Complex Networks via NN-Based Inverse Optimal Pinning Control.

A new approach for trajectory tracking on uncertain complex networks is proposed. To achieve this goal, a neural controller is applied to a small fraction of nodes (pinned ones). Such controller is composed of an on-line identifier based on a recurrent high-order neural network, and an inverse optimal controller to track the desired trajectory; a complete stability analysis is also included. In order to verify the applicability and good performance of the proposed control scheme, a representative example is simulated, which consists of a complex network with each node described by a chaotic Lorenz oscillator.

Identifying topologies and system parameters of uncertain time-varying delayed complex networks

Node dynamics and network topologies play vital roles in determining the network features and network dynamical behaviors. Thus it is of great theoretical significance and practical value to recover the topology structures and system parameters of uncertain complex networks with available information. This paper presents an adaptive anticipatory synchronization-based approach to identify the unknown system parameters and network topological structures of uncertain time-varying delayed complex networks in the presence of noise. Moreover, during the identification process, our proposed scheme guarantees anticipatory synchronization between the uncertain drive and constructed auxiliary response network simultaneously. Particularly, our method can be extended to several special cases. Furthermore, numerical simulations are provided to verify the effectiveness and applicability of our method for reconstructing network topologies and node parameters. We hope our method can provide basic insight into future research on addressing reconstruction issues of uncertain realistic and large-scale complex networks.

Local [formula omitted] synchronization of uncertain complex networks via non-fragile state feedback control

This paper is concerned with local H∞ synchronization control of uncertain complex networks, in which there are nonlinear coupling functions between network nodes, and the coupling terms as well as network nodes are subject to time-varying delays. In order to make a complex network achieve H∞ synchronization, a non-fragile state feedback control scheme is used. By employing the Lyapunov functional method, a sufficient condition on the existence of H∞ non-fragile controllers is derived. This condition can not only guarantee the asymptotic stability of each network node, but also ensure a prescribed robust H∞ performance level for the synchronization error system under study. The effectiveness of the proposed method is finally verified through a numerical example.

Synchronization of uncertain hybrid switching and impulsive complex networks

• Hybrid switches and impulses are characterized by dwell-time constraint. • Dwell-time partitioning and convex combination techniques are used. • Results unify synchronizing and desynchronizing impulses. • Unsynchronized networks can be synchronized by desynchronizing impulses. This paper considers the asymptotic synchronization problem for a class of uncertain complex networks (CNs) with hybrid switching and impulsive effects. The switches and impulses occur by following a time sequence which is characterized by dwell-time constraint. By designing Lyapunov function with time-varying matrix parameter, two general synchronization criteria formulated by matrix inequalities are first given, which unify synchronizing and desynchronizing impulses. Then specific conditions in terms of linear matrix inequalities (LMIs) are given by partitioning the dwell time and using convex combination technique. Compared with those criteria which are only applicable to pure synchronizing impulses or pure desynchronizing impulses, our results are more practical. It is shown that the switched impulsive CNs (SICNs) can be synchronized by desynchronizing impulses even though CNs without impulse are unsynchronized. Numerical examples are given to show the effectiveness of our new results.

Synchronization Control of Complex Dynamical Networks Based on Uncertain Coupling

In recent years, the study of complex networks has been a focus subject of technology fields. In this paper, we consider the adaptive control and synchronization of uncertain complex networks. By using the adaptive control techniques with the linear feedback updated law and the well-known invariant principle on dynamical system theory, some simple yet generic criteria are derived. Furthermore, the result is applied to typical chaotic cellular neural networks (CNN). Finally, numerical simulations are presented to demonstrate the feasibility and effectiveness of the proposed techniques.

Synchronization of Uncertain Complex Networks with Time‐Varying Node Delay and Multiple Time‐Varying Coupling Delays

AbstractThis paper investigates the synchronization problem of a class of complex dynamical networks via an adaptive control method. It differs from existing works in considering intrinsic delay and multiple different time‐varying coupling delays, and uncertain couplings. A simple approach is used to linearize the uncertainties with the norm‐bounded condition. Simple but suitable adaptive controllers are designed to drive all nodes of the complex network locally and globally synchronize to a desired state. In addition, several synchronization protocols are deduced in detail by virtue of Lyapunov stability theory and a Cauchy matrix inequality. Finally, a simulation example is presented, in which the dynamics of each node are time‐varying delayed Chua chaotic systems, to demonstrate the effectiveness of the proposed adaptive method.

Modified function projective lag synchronization of uncertain complex networks with time-varying coupling strength

In this article, we investigate the issue on modified function projective lag synchronization (MFPLS) of dynamical complex networks with disturbance and unknown parameters, the dynamical network is a complex network model containing uncertainty and coupling delay, the coupling strength is time-varying in the complex networks. Theoretical analysis and numerical simulations about MFPLS of uncertain complex networks are presented, not only unknown parameters of the networks are estimated, but also unknown bounded disturbances can be simultaneously conquered by adaptive laws and adaptive coupling strength obtained from Lyapunov stability theory.

Exponentially impulsive projective and lag synchronization between uncertain complex networks

This paper is concerned with exponentially projective and lag synchronization between general complex networks via impulsive control. Presented general complex networks are uncertain with time-varying delays in both coupled and uncoupled terms. Different dynamics for each node is taken into account in order to cover the practical needs. Based on the impulsive control theory, the global exponential synchronization of complex networks is analyzed and some new sufficient conditions are derived. Moreover, two numerical examples are presented to demonstrate the effectiveness of the proposed method, first one is devoted to synchronization of networks with self-excited attractor and second one is for networks with hidden attractor.

Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay

Based on the stability theory of fractional-order systems, synchronization of general fractional-order uncertain complex networks with delay is investigated in this paper. By the inequality of the fractional derivative and the comparison principle of the linear fractional equation with delay, synchronization of complex networks with delay is realized under adaptive control. Some sufficient criteria ensuring local asymptotical synchronization under adaptive control and global asymptotical synchronization under adaptive pinning control are derived, respectively. Finally, numerical simulations are presented to demonstrate the validity and feasibility of the proposed synchronization criteria.

Structure Identification of Uncertain Complex Networks Based on Anticipatory Projective Synchronization.

This paper investigates a method to identify uncertain system parameters and unknown topological structure in general complex networks with or without time delay. A complex network, which has uncertain topology and unknown parameters, is designed as a drive network, and a known response complex network with an input controller is designed to identify the drive network. Under the proposed input controller, the drive network and the response network can achieve anticipatory projective synchronization when the system is steady. Lyapunov theorem and Barbǎlat’s lemma guarantee the stability of synchronization manifold between two networks. When the synchronization is achieved, the system parameters and topology in response network can be changed to equal with the parameters and topology in drive network. A numerical example is given to show the effectiveness of the proposed method.