Discrete-time Complex Networks Research Articles

Random temporal connections promote network synchronization.

We report a phenomenon of collective dynamics on discrete-time complex networks: a random temporal interaction matrix even of zero or/and small average is able to significantly enhance synchronization with probability one. According to current knowledge, there is no verifiably sufficient criterion for the phenomenon. We use the standard method of synchronization analytics and the theory of stochastic processes to establish a criterion, by which we rigorously and accurately depict how synchronization occurring with probability one is affected by the statistical characteristics of the random temporal connections such as the strength and topology of the connections as well as their probability distributions. We also illustrate the enhancement phenomenon using physical and biological complex dynamical networks.

Dynamic event-triggered mechanism for H∞ non-fragile state estimation of complex networks under randomly occurring sensor saturations

In this paper, the problem of non-fragile H∞ state estimation is investigated for a class of discrete-time complex networks subject to randomly occurring sensor saturations (ROSSs) under a dynamic event-triggered mechanism (DETM). The ROSS phenomenon is taken into account in the network measurements as a reflection of the probabilistic limitation of the physical sensors, and the DETM is implemented to govern the signal transmission from the sensor to its corresponding state estimator. The objective of the problem addressed is to design an H∞ non-fragile state estimator under the DETM that can tolerate the possible gain perturbations, thereby possessing the desired non-fragility. By constructing a novel Lyapunov function, a sufficient condition is established such that the estimation error dynamics is exponentially mean-square stable with a prescribed H∞ performance level, and then the estimator gains are parameterized according to certain matrix inequalities. A simulation example is provided to demonstrate the effectiveness of the proposed state estimation scheme.

Pinning event‐triggered control for stochastic discrete‐time complex networks with time‐varying delay

In this study, the distributed event-triggered control strategy is found to cope with the pinning control problem of stochastic discrete-time complex networks with time-varying delay. Under the devised mechanism, exponential mean-square synchronisation can be implemented in the directed networks. By utilising the Lyapunov functional method and the stochastic analysis, several sufficient conditions are established. Moreover, the issue of average synchronisation is investigated. For the stochastic complex networks without reference state, it is demonstrated that all nodes can converge to a time-varying weighted average exponentially by a suitable distributed event-triggered controller. Finally, some numerical examples are presented to indicate the effectiveness of the devised control strategies.

Delayed‐impulsive control for difference systems with actuator saturation and its synchronisation application

This study focuses on the problem of time-delayed impulsive control with actuator saturation for discrete-time dynamical systems. By establishing a delayed-impulsive difference inequality, combining with convex analysis and inequality techniques, some sufficient conditions are obtained to ensure exponential stability for discrete-time dynamical systems via time-delayed impulsive controller with actuator saturation. And those results are also used in the problem of synchronisation of the discrete-time complex networks. The designed controller admits the existence of some transmission delays in impulsive feedback law, and the control input variables are required to stay within an availability zone. Several numerical simulations are also given to demonstrate the effectiveness of the proposed results.

Synchronization for discrete-time complex networks with probabilistic time delays

This paper investigates the problem of adaptive synchronization for discrete-time complex dynamical networks with random delays. In such complex systems, there occurs two kinds of nonidentical probability delays, i.e. self-feedback delays and coupling delays, and these delays are assumed to take values in a given finite sets with probability distributions. By means of the Lyapunov theory, discrete-time Jensen inequality and reciprocal convex combination approach, several delay-probability-distribution-dependent conditions are derived in the linear matrix inequality (LMI) format such that the discrete-time complex dynamical networks with random delays are globally synchronization in mean square. In addition, we use Watts–Strogatz (WS) random complex networks and regular Rulkov networks as two numerical examples to illustrate the effectiveness of our theoretical analysis.

Locally Exponential Stability of Discrete-time Complex Networks with Impulsive Input Saturation

In this paper, the problem of exponential stabilization for a class of discrete-time complex network with saturated impulse input is investigated. Based on the inductive method, convex analysis, and auxiliary matrix, several Lyapunov-type stability criteria are derived for exponential stability of discrete-time complex network with impulsive input saturation. Two examples are also presented to illustrate the effectiveness and the feasibility of the obtained results.

A Partial-Nodes-Based Information fusion approach to state estimation for discrete-Time delayed stochastic complex networks

This paper is concerned with the information-fusion-based state estimation problem for a class of discrete-time complex networks with time-varying delays and stochastic perturbations. The measurement outputs available for state estimation are from a fraction of network nodes, and the addressed problem is therefore referred to as the so-called Partial-Nodes-Based (PNB) state estimation problem. By employing the Lyapunov stability theory, a novel framework is established to cope with the PNB state estimation problem by the measurement outputs collected from partial network nodes. By constructing specific Lyapunov-Krasovskii functionals, sufficient criteria are derived for the existence of the desired exponentially ultimately bounded state estimator in mean square for the complex networks. Moreover, a special case is considered where the complex network under investigation is free of stochastic perturbations and the corresponding analysis issue is discussed to ensure the existence of an exponential state estimator. In addition, the explicit expressions of the gains of the desired estimators are characterized. Finally, a numerical illustrative example is presented to demonstrate the effectiveness of the obtained theoretical results.

Event-Based Time-Interval Pinning Control for Complex Networks on Time Scales and Applications

This paper studies the synchronization problem for linear complex dynamical networks (CDNs) on time scales. An intermittent dynamic time-interval pinning control strategy is designed to achieve synchronization for CDNs with the isolated node. Based on the Lyapunov approach and the theory of time scales, synchronization criteria are established for CDNs on general time scales. The main results in the paper show that, by controlling a proportion of the network nodes, the exponential synchronization can be achieved. Moreover, the infinitely fast switching of the pinning node set is avoided by means of the event-triggered strategy. According to our selection algorithm, the number of pinning nodes will be updated online at each pinning time. The modeling framework investigated in this paper is a unification and generalization of many existing continuous-time and discrete-time complex network models. Three numerical examples are given to illustrate the effectiveness and priority of the obtained results. Finally, the analytical results are applied to the distributed auxiliary control of microgrids and formation control of spacecraft.

Finite-time outer-synchronization for complex networks with Markov jump topology via hybrid control and its application to image encryption

This paper investigates the problem of finite-time outer-synchronization for discrete-time complex networks with Markov jump topology in the presence of communication delays and possible information losses and its application to image encryption. A hybrid control, which is subject to both stochastic jumps and deterministic switches, is proposed to realize finite-time and stochastic outer-synchronization for the concerned networks. By utilizing a stochastic Lyapunov functional combined with the average dwell-time method, sufficient conditions are found such that the synchronization error dynamical system is stochastically stable in finite-time. Two numerical examples are presented to illustrate the effectiveness of the proposed method. Finally, the complex network consists of four coupled Lorenz systems are utilized to generate chaotic sequences and a new chaotic image cryptosystem is constructed to transmit encrypted images based on the synchronized drive-response complex networks. Experiments are conducted by using numerical simulation, and the security is analyzed in terms of key space, key sensitivity, histogram distributions, correlation coefficients, information entropy and differential attack measures. The experimental results show that the proposed chaotic image cryptosystem has the advantages of high security against some classical attacks.

Exponential synchronization of discrete-time impulsive dynamical networks with time-varying delays and stochastic disturbances

Abstract In this paper, based on the discrete-time delayed impulsive system theory, exponential synchronization of discrete-time complex networks with both time-varying delays and stochastic disturbances is investigated. By applying an iterative Lyapunov function in combination with the linear matrix inequality (LMI) technique, a new synchronization criterion based on topology matrices and impulsive conditions is developed. Some numerical simulations are provided to verify the theoretical results.

Event-triggered H∞ state estimation for state-saturated complex networks subject to quantization effects and distributed delays

This paper is concerned with the event-triggered H∞ state estimation problem for a class of discrete-time complex networks subject to state saturations, quantization effects as well as randomly occurring distributed delays. A series of Bernoulli distributed random variables is utilized to model the random occurrence of distributed delays. For the energy-saving purpose, an event-triggered mechanism is proposed to decide whether the current quantized measurement should be transmitted to the estimator or not. For the state-saturated complex networks, our aim is to design event-triggered state estimators that guarantee both the exponential mean-square stability of and the H∞ performance constraint on the error dynamics of the state estimation. Stochastic analysis is conducted, in combination with the Lyapunov functional approach, to derive sufficient conditions for the existence of the desired estimators whose gain matrices are obtained by solving a set of matrix inequalities. An illustrative example is exploited to show the usefulness of the estimator design algorithm proposed.

Recursive filtering for complex networks using non‐linearly coupled UKF

This study is concerned with the recursive filtering problem for a class of discrete-time complex networks with non-linearly coupled terms. A coupled unscented Kalman filter (UKF) is developed, where the sigma points of the UKF are propagated by introducing the coupled terms. By using the stochastic analysis technique, a sufficient condition is established to guarantee the boundedness of the estimation errors, where an upper bound for the coupling strength is derived. It is shown that the upper bound of the coupling strength is inversely proportional to the number of nodes. A numerical example involving tracking of multiple interacting targets is provided to verify the effectiveness of the proposed filter.

Non-fragile $H_{\infty}$ state estimation for discrete-time complex networks with randomly occurring time-varying delays and channel fadings

Non-fragile $H_{\infty}$ state estimation for discrete-time complex networks with randomly occurring time-varying delays and channel fadings

Synchronization of stochastic discrete-time complex networks with partial mixed impulsive effects

In this paper, the synchronization problem is studied for a class of stochastic discrete-time complex networks with partial mixed impulsive effects. The involving impulsive effects, called partial mixed impulses, can be regarded as local and time-varying impulses, which means that impulses are not only injected into a fraction of nodes in networks but also contain synchronizing and desynchronizing impulses at the same time. In order to handle this case, several mathematical techniques are proposed to tackle mixed impulsive effects in discrete-time dynamical systems. Based on the variation of parameters formula, several sufficient criteria are derived to ensure that synchronization of the addressed networks can be achieved in mean square. The obtained criteria not only rely on the strengths of mixed impulses and the impulsive intervals, but also can reduce conservativeness. Finally, a numerical example is presented to show the effectiveness of our results for neural networks.

Finite‐horizon bounded synchronisation and state estimation for discrete‐time complex networks: local performance analysis

This study is concerned with the finite-horizon bounded H ∞ synchronisation and state estimation for the discrete-time complex networks with missing measurements based on the local performance analysis. First, a new local description of the bounded H ∞ synchronisation performance index is proposed, which considers only the synchronisation errors among neighbours. In addition, a more general sector-bounded condition is presented, where the parameter matrices are different for different node. Next, by establishing the vector dissipativity-like for the complex network dynamics, the H ∞ synchronisation criterion is derived in term of the locally coupled conditions for each node. These conditions implemented in a cooperative manner can judge whether the complex network reaches synchronisation. Similarly, the existence conditions for the estimator on each node are obtained, and then the estimator parameters are designed via the recursive linear matrix inequalities. Notably, these conditions on each node by cooperation among neighbours can achieve the desirable performance index. The distinctive features of the authors' algorithms are low complexity, scalability, and distributed execution. At last, two numerical examples are utilised to verify the effectiveness and applicability of the proposed algorithms.

Synchronisation of discrete‐time complex networks with delayed heterogeneous impulses

In this study, the synchronisation problem is investigated for discrete-time complex networks with delayed heterogeneous impulses. Heterogeneous impulses are a form of inhomogeneous impulse, which means that the impulsive strengths depend on both time and space domains. To describe more appropriately impulsive effects, both heterogeneous impulsive effects and impulsive input delays are considered. Employing the Razumikhin theorem and constructing a time-dependent Lyapunov function, several sufficient criteria are derived to ensure exponential synchronisation of the discrete-time complex networks with delayed heterogeneous impulsive effects. The derived criteria are formulated in terms of linear matrix inequalities, in which the impulsive intervals, impulsive input delays and impulsive strengths play an important role. Finally, an example is delivered to illustrate the effectiveness of the proposed synchronisation criteria.

An Event-Triggered Approach to State Estimation for a Class of Complex Networks With Mixed Time Delays and Nonlinearities.

In this paper, the state estimation problem is investigated for a class of discrete-time complex networks subject to nonlinearities, mixed delays, and stochastic noises. A set of event-based state estimators is constructed so as to reduce unnecessary data transmissions in the communication channel. Compared with the traditional state estimator whose measurement signal is received under a periodic clock-driven rule, the event-based estimator only updates the measurement information from the sensors when the prespecified "event" is violated. Attention is focused on the analysis and design problem of the event-based estimators for the addressed discrete-time complex networks such that the estimation error is exponentially bounded in mean square. A combination of the stochastic analysis approach and Lyapunov theory is employed to obtain sufficient conditions for ensuring the existence of the desired estimators and the upper bound of the estimation error is also derived. By using the convex optimization technique, the gain parameters of the desired estimators are provided in an explicit form. Finally, a simulation example is used to demonstrate the effectiveness of the proposed estimation strategy.

Delayed impulsive synchronization of discrete-time complex networks with distributed delays

In this paper, a novel delayed impulsive control strategy is proposed for synchronization of discrete-time complex networks with distributed delays. Different from the existing results, the involving time delays include distributed delays and impulsive input delays. Employing the Razumikhin theorem and the mathematical induction method, several sufficient criteria are derived in terms of algebraic conditions, which depend on impulsive input delays and impulsive control gains. Meanwhile, the derived criteria also reveal the relationship between the bounds of impulsive intervals and impulsive input delays. Finally, two examples are given to illustrate the effectiveness of the proposed approach.

Non‐fragile mixed ℋ ∞ / l 2 − l ∞ synchronisation control for complex networks with Markov jumping‐switching topology under unreliable communication links

This study is concerned with the non-fragile mixed ℋ∞/l 2 − l ∞ synchronisation control problem for discrete-time complex networks with Markov jumping-switching topology under unreliable communication links. The network topology under consideration is assumed to be governed by a Markov chain with time-varying transition probabilities (TPs). The variation of TPs is subject to a kind of slow switching signals; that is, the average dwell time (ADT) switching. The focus is on the design of non-fragile mixed mode-dependent/-independent controllers such that the underlying network reaches stochastic mean-square synchronisation with a mixed ℋ∞/l 2 − l ∞ performance level for an admissible switching signal with ADT. By using a new mixed ℋ∞/l 2 − l ∞ performance index, combined with the switched control method, the solutions to the considered problem are formulated. Finally, simulation results demonstrate the effectiveness of our proposed approach.

Exponential synchronization of impulsive discrete-time complex networks with time-varying delay

In this paper, the exponential synchronization of discrete-time complex networks with time-varying delay is investigated. Based on the Lyapunov function method and the Razumikhin technique, several synchronization criteria are derived for exponential synchronization of impulsive discrete-time complex networks. Using the concept of “average impulsive interval”, the derived results are proved to be effective in dealing with synchronizing and desynchronizing impulses. Several numerical simulation examples are provided to demonstrate the effectiveness of the proposed approach. Moreover, the simulation results show that the criteria are less conservative than the existing results considering the upper or lower of impulsive intervals.