Time-varying Coupling Strength Research Articles

Event-Triggered Multiagent Consensus Under Relative Output Sensing.

Event-triggered (ET) consensus of linear multiagent systems with relative output sensing on undirected graphs is studied. Two output-feedback protocols with static and time-varying coupling strengths, respectively, are proposed, which, different from the existing results in relative output sensing, integrate effective ET strategies to reduce the communication burdens between agents. To ensure the closed-loop consensus, design conditions about the gain matrices, coupling strengths, and event-triggering functions are derived. Zeno behaviors are also shown to be excluded from the triggering process. In addition, recursive algorithms are devised for computing the continuous-time relative signals required by the event-triggering functions, so that continuous monitoring of neighbors is circumvented. Numerical examples finally demonstrate the effectiveness of the proposed design method.

Cooperative Control of Multi-Time-Scale Agent Networks Under Digraphs

This paper addresses cooperative control for a class of multi-agent networks. An interesting feature of such network is that each agent possesses the characteristic of multi-time-scale. By developing the relative states or the relative outputs based consensus protocols, some well-conditioned consensus criteria in terms of linear matrix inequalities are derived successively based on the ε-strict Lyapunov function. Compared with undirected graphs or strongly connected digraphs in existing works, a more general digraph that it contains at least a directed spanning tree is considered herein. Moreover, a fully distributed consensus protocol with time-varying coupling strength is proposed to avoid using global information. Finally, the obtained theoretical results are validated by two examples including standard and nonstandard agents.

Stochastic synchronisation of nonlinear networks with additive measurement noise

Stochastic synchronisation of complex networks has recently attracted considerable attention because of the ubiquitousness of random noise in real-world complex systems. Previous works have mainly considered noise-corrupted communication by ignoring intrinsic dynamics of nodes. This work provides a systematic study of complex networks by taking into account both additive noise and nonlinear dynamics of nodes, examining their stochastic synchronisation problems. We model the deterministic diffusive coupling and noisy additive coupling with the time-invariant strength and the time-varying strength, respectively. Using the stochastic Lyapunov technique, this framework enables an analytical treatment of the problem, ultimately leading to sufficient conditions for the onset of synchronisation. For symmetrical/asymmetrical connections, the synchronisation condition for the time-invariant coupling strength can be stated elegantly in terms of node dynamics and network topology, whereas that for the time-varying coupling strength is described as a robust condition. Finally, two simulation examples are carried out to illustrate the effectiveness of theoretical findings.

Uncertainty meets fixed-time control in neural networks

The fixed-time stability on uncertain neural networks with adaptive coupling strength is addressed in this paper. To beign with, a new time-varying coupling strength is introduced, which is based on the projective transform of quantized error systems. Next, to address various disturbances in master-slave systems, inhomogeneous uncertainty is taken into consideration. Then, a multi-quantized fixed-time controller is put forward to ensure that the systems reach to a prescribed trajectory in the settling time. Afterward, sufficient synchronization criteria are derived on the strength of the Lyapunov stability theorem. Finally, simulation examples are given to validate the theoretical analysis.

Event-triggered control of interconnected nonlinear systems subjected to cyber-attacks and time-varying coupling

This paper addresses the problem of efficient control of nonlinear distributed networked control systems in the presence of stochastic deception attacks and time-varying coupling strength. A strategy combining model-based and event-triggered control to reduce the number of transmissions over a network thereby, saving network resources is proposed. In this strategy, a plant model at the controller end is used to estimate the state of each subsystem. Further, the control law between the two adjacent triggering instants changes in accordance with dynamics of the plant model. The nonlinearities present in each subsystem are approximated via neural network. The neural network weights and feedback signal are updated only when the event-triggering condition at the sensor end is violated. Also, a lower bound on the inter-event time is computed to avoid the occurrence of Zeno phenomena. Finally, the efficacy of the proposed methodology are verified through simulation examples.

Recursive state estimation for nonlinear coupling complex networks with time-varying topology and round-robin protocol

This paper is devoted to solving the recursive state estimation (RSE) issue for a class of complex networks (CNs) with Round-Robin (RR) protocol and switching nonlinearities (SNs). A random variable obeying the Bernoulli distribution with known statistical properties is introduced to describe the switching phenomenon between two nonlinear functions. A Gaussian noise and time-varying outer coupling strength are adopted to show the changeable network topology (CNT). The RR protocol is applied to regulate signal transmissions, which determines that the element in measurement output has access to the communication networks at each step. The purpose of this paper is to construct a recursive state estimator such that, for all SNs, time-varying topology and RR protocol, the expected state estimation performance is guaranteed. Specifically, based on two recursive matrix equations, the covariance upper bound (CUB) of state estimation error is obtained firstly and then minimized via designing estimator gain in a proper way. Moreover, a feasible criterion is given to guarantee that the trace of obtained CUB is bounded and a monotonicity relationship is established between state estimation error and time-varying outer coupling strength. Lastly, a simulation experiment is illustrated to verify the feasibility of the addressed estimation method.

Emergence of extreme events in coupled systems with time-dependent interactions

We present a class of extreme events manifested in dynamical systems involving time-dependent attractive and repulsive couplings. We consider two cases of time-varying coupling strengths -(i) explicit time-dependence (periodically varying) and (ii) implicit time dependence (distance-dependent coupling). In both of these cases, the coupled systems generate quasi-stable equilibrium points, which in turn are responsible for the generation of extreme events. In the explicit time-dependent case, the quasi-stable equilibrium points are periodically created whenever the amplitude of the external force is higher than the threshold value. In the implicit time-dependent case, they exist whenever the distance between the trajectories is below a critical distance. We demonstrate the results with the examples of two, three, and a network of hundred coupled Stuart–Landau oscillators. We also show the prevalence of this phenomenon in other dynamical systems (van der Pol oscillator) and highlight its applications in natural systems.

Adaptive synchronization of fractional-order complex-valued coupled neural networks via direct error method

In this paper, without dividing the fractional-order complex-valued coupled neural networks (FCVCNNs) into two real-valued systems, the problem of synchronization is investigated for FCVCNNs with time-varying coupling strength. To achieve synchronization, by updating coupling strength, two feasible adaptive protocols are designed, 1) a fractional-order adaptive strategy depending on global information; 2) a fractional-order adaptive law relying on the local information based on the connected dominating set theory. Additionally, instead of making the weighted average technique or the solution of the isolated node equation as synchronization reference value, direct error method is adopted to realize synchronization, which offers a flexible way in analysis of FCVCNNs. At last, a numerical simulation is provided to illustrate the validity of theoretical results.

Cluster Synchronization in Delayed Networks With Adaptive Coupling Strength via Pinning Control

Many previous studies have indicated that pinning control and adaptive feedback control are two of most effective strategies for achieving synchronization. In this paper, we present a mixed method integrating the two control strategies to realize cluster synchronization in delayed networks with directed couplings. Based on Lyapunov stability theory and matrix theory, several criteria on cluster synchronization are obtained. Compared with the previous results on cluster synchronization, the obtained criteria can be applied to delayed network with nonidentical nodes, directed couplings and time-varying coupling strength. Finally, numerical simulations are performed to verify the theoretical results.

Quasi-synchronization of neural networks with diffusion effects via intermittent control of regional division

In this paper, we investigate the quasi-synchronization issue of an array of Diffusion Effects Neural Networks (DENNs) with time-varying coupling strength. Two kinds of quasi-synchronization scenarios are discussed. One is self-synchronization and the other is tracking-synchronization. In order to lower the communication loads and reduce the control resource consumption, we propose a new control scheme called intermittent control of reginal division to make the synchronization error within a bounded scope. In this novel control scheme, the non-negative real region is divided into three subregions in advance and an auxiliary Lyapunov function is imported to decide the work time and the rest time by its relationship with three subregions. Moreover, by using rigorous mathematic analysis, we obtain sufficient conditions for the two kinds of quasi-synchronization modes of DENNs under the as-proposed control scheme. Nonidentical term in the network is viewed as external disturbance about to be compensated by the controller. The result shows that the upper bound of synchronization error will be progressively regulated by the parameters in chosen divided region. Several numerical examples are also presented to verify the validity of our theory.

Adaptive event-triggered prescribed performance learning synchronization for complex dynamical networks with unknown time-varying coupling strength

In this paper, we focus on investigating the prescribed performance synchronization problems of complex dynamical networks with unknown time-varying coupling strength by learning control method. An event-triggered control protocol is designed, and a sufficient condition of synchronization is also given based on Lyapunov stability theory, which can ensure that the sates of all nodes synchronize to the specified target trajectory, and the synchronization errors meet the prescribed performance requirements. The main advantage of the protocol is not only to ensure the transient performance and convergence of synchronization errors of complex dynamic networks with unknown time-varying coupling strength, but also to avoid the continuous communication among network nodes under the event-triggered communication mechanism which can reduce the number of information updates. In addition, the Zeno behavior is avoided in communication process of the networks. At last, the effectiveness of the proposed theoretic results obtained is verified via the applications of the complex dynamical networks with Chua’s circuit and a simple pendulum dynamics.

Stabilization of stochastic time-varying coupled systems with delays and Lévy noise on networks based on aperiodically intermittent control

The aim of this paper is to research the stabilization of stochastic time-varying coupled systems with delays and Lévy noise on networks (STSDLN) via aperiodically intermittent control. It is worth pointing out that the time-varying coupling is considered into Lévy noise systems in the first time. Then, by means of a graph-theoretic approach, Lyapunov method and some techniques of inequalities, some stabilization criteria are obtained to guarantee exponentially stability in mean square for STSDLN. Therein, we weaken the sufficient condition for dealing with the time-varying coupling compared to the existing literature, which can reduce the conservation of the conclusions. Additionally, the intensity of control is closely related to the perturbed intensity of noise and the time-varying coupling strength. In particular, as a practical application of our theoretical results, the stabilization of stochastic time-varying coupled oscillators with delays and Lévy noise on networks is studied. Finally, a numerical example is provided to illustrate the validity of the results obtained.

Volatility Flocking by Cucker–Smale Mechanism in Financial Markets

We analyze empirical evidence of flocking stock volatilities according to the Cucker–Smale (C–S) mechanism. By using daily realized volatilities of stocks listed on Dow Jones Industrial Average from January, 2007 to December, 2009, we calibrate key parameters such as time-varying coupling strength, communication weight and stochastic noise in coupling of a benchmark C–S model in Bae et al. (Math Models Methods Appl Sci 25:1299–1335, 2015). Our numerical solutions show that the flocking mechanism explains average volatility dynamics better than a stochastic volatility model without the mechanism over the sample period. The model’s empirical implications are found from cyclicality of Volatility Flocking Index (VFI), an aggregate measure of differences between volatilities. Results from Granger causality tests after vector autoregression estimation show that VFI helps us predict the implied volatility index, and weighted average return of S&P500 Index.

Complex projection synchronization of fractional order uncertain complex-valued networks with time-varying coupling

In this paper, the complex projection synchronization problem of fractional complex-valued dynamic networks is investigated. Considering the time-varying coupling and unknown parameters of the fractional order complex network, several decentralized adaptive strategies are designed to adjust the coupling strength and controller feedback gain in order to investigate the complex projection synchronization problem of the system. Moreover, based on the designed identification law, the uncertain parameters in the network can be estimated. Using adaptive law which balances the time-varying coupling strength and the feedback gain of the controller, some sufficient conditions are obtained for the complex projection synchronization of complex networks. Finally, numerical simulation examples are provided to illustrate the efficiency of the complex projection synchronization strategies of the fractional order complex dynamic networks.

Projective synchronization via adaptive pinning control for fractional-order complex network with time-varying coupling strength

This paper presents an adaptive projective pinning control method for fractional-order complex network. First, based on theories of complex network and fractional calculus, some preliminaries of mathematics are given. Then, an analysis is conducted on the adaptive projective pinning control theory for fractional-order complex network. Based on the projective synchronization control method and the combined adaptive pinning feedback control method, suitable projection synchronization scale factor, adaptive feedback controller and the node selection algorithm are designed to illustrate the synchronization for fractional-order hyperchaotic complex network. Simulation results show that all nodes are stabilized to equilibrium point. Theoretical analysis and simulation results demonstrate that the designed adaptive projective pinning controllers are efficient.

Adaptive Aperiodically Intermittent Synchronization for Complex Dynamical Network with Unknown Time-Varying Outer Coupling Strengths

In this paper, exponential synchronization problem of complex dynamical networks with unknown periodically coupling strengths was investigated. An aperiodically intermittent control synchronization strategy is proposed. Based on Lyapunov exponential stability theory, inequality techniques, and adaptive learning laws design, some sufficient exponential synchronization criteria for complex dynamical network with unknown periodical coupling weights are obtained. The numerical simulation example is presented to illustrate the feasibility of theoretical results.

Distributed leader-following consensus of heterogeneous second-order time-varying nonlinear multi-agent systems under directed switching topology

Abstract This paper focuses on studying the distributed leader-following consensus problem of heterogeneous second-order time-varying nonlinear multi-agent systems (HSTN_MASs) under directed switching topology. Firstly, based on the relative position and relative velocity measurements among neighborhood agents, a class of distributed tracking protocols are proposed. Then the state transformations are provided to solve the time-varying nonlinearity and translate the leader-following problem into the stabilization control problem. By constructing the topology-dependent Lyapunov function and choosing appropriate time-varying regulation factor and coupling strength, it is shown that the exponential tracking of HSTN_MASs can be achieved. Moreover, this paper discusses the distributed leaderless consensus problem of HSTN_MASs. Finally, several simulation examples are given to illustrate the validity of theoretical results.

Measurement-induced multipartite entanglement for distant four-level atoms in Markovian and non-Markovian environments

In this paper, we propose a scheme for generating multipartite entanglement of distant four-level atoms separately trapped in individual cavities, each of which is coupled to a non-Markovian reservoir. The entanglement of atoms is generated by measuring the photons leaking from cavities. In non-Markovian environments, we derive dynamical evolution of the entanglement and obtain the condition of generating the long-living multipartite maximally entangled state. When the condition is not satisfied, by introducing a time-varying coupling strength, the maximal multipartite entangled state can also be generated.

Synchronization control in multiplex networks of nonlinear multi-agent systems.

This paper is concerned with synchronization control of a multiplex network, in which two different kinds of relationships among agents coexist. Hybrid coupling, including continuous linear coupling and impulsive coupling, is proposed to model the coexisting distinguishable interactions. First, by adding impulsive controllers on a small portion of agents, local synchronization is analyzed by linearizing the error system at the desired trajectory. Then, global synchronization is studied based on the Lyapunov stability theory, where a time-varying coupling strength is involved. To further deal with the time-varying coupling strength, an adaptive updating law is introduced and a corresponding sufficient condition is obtained to ensure synchronization of the multiplex network towards the desired trajectory. Networks of Chua's circuits and other chaotic systems with double layers of interactions are simulated to verify the proposed method.

Hybrid adaptive synchronization strategy for linearly coupled reaction–diffusion neural networks with time-varying coupling strength

Abstract In this article, the adaptive synchronization control for an array of coupled reaction diffusion neural networks with time-varying coupling strength and delays is considered. A novel hybrid adaptive learning law consists of discrete updating law for the unknown time-varying coupling coefficient and continuous adaptive law for the unknown time-invariant parameter is derived, which extends the adaptive synchronization control for the constant coupling coefficient to the time-varying one. Through constructing a novel Lyapunov–Krasovskii functional, the synchronization controller and criterion are presented. Furthermore, to take the disturbance into consideration, the H∞ synchronization criterion is presented, also. Finally, a numerical example is given and some comparisons are performed to demonstrate the effectiveness of the synchronization strategies.