Pinning Synchronization Research Articles

Pinning Event-Triggered Scheme for Synchronization of Delayed Uncertain Memristive Neural Networks

To reduce the communication and computation overhead of neural networks, a novel pinning event-triggered scheme (PETS) is developed in this paper, which enables pinning synchronization of uncertain coupled memristive neural networks (CMNNs) under limited resources. Time-varying delays, uncertainties, and mismatched parameters are all considered, which makes the system more interpretable. In addition, from the low energy cost point of view, an algorithm for pinned node selection is designed to further investigate the newly event-triggered function under limited communication resources. Meanwhile, based on the PETS and following the Lyapunov functional method, sufficient conditions for the pinning exponential stability of the proposed coupled error system are formulated, and the analysis of the self-triggered method shows that our method can efficiently avoid Zeno behavior under the newly determined triggered conditions, which contribute to better PETS performance. Extensive experiments demonstrate that the PETS significantly outperforms the existing schemes in terms of solution quality.

Asymptotic pinning synchronization of nonlinear multi-agent systems: Its application to tunnel diode circuit

This work proposes a pinning state-feedback control technique for synchronizing non-linear multi-agent systems (MASs) with time delays. A collection of switching-directed graphs describes the communication exchanges between all of the agents. The challenge of asymptotic stability analysis for some error systems is translated into the construction of a leader-following synchronization of the relevant MASs. The closed-loop system could be acquired by building a convenient Lyapunov–Krasovskii functional (LKF) that has two integral terms, and by using Kronecker product qualities combined with matrix inequality techniques. When these conditions are met, a state-feedback pinning controller can be built with linear matrix inequalities (LMIs), which can be derived easily from a number of efficient optimization algorithms. Further, the performance of the proposed control design system is verified based on a tunnel diode circuit (TDC) by numerical simulations.

Effect of large delay on pinning impulsive synchronization control: A strict comparison principle

SummaryOver the past decades, various successful results have shown the discoveries and progress of impulsive synchronization. Yet, little attention has been devoted to the effects of the impulsive elasticity coefficient on network synchronization for both impulsive control problems and impulsive disturbance problems. In this work, we study impulsive pinning synchronization for coupled neural networks from a large delay perspective. Some flexible synchronization criteria are derived based on the average impulsive interval method. It has shown that synchronization of coupled neural networks with arbitrarily finite delay can be achieved via controlling a small fraction of nodes. Specifically, by applying a strict comparison principle for impulsive delayed neural networks, the effects of the impulsive elasticity coefficient on synchronization are revealed to be dissimilar from the case of delay‐free neural networks. One can verify that increasing the elasticity coefficient may bring a desynchronizing impact on the original synchronized networks. More ulteriorly, the generated criteria will still hold if the delay is sufficiently large, which implies that the delay is independent of the size of the impulsive interval. Our work is an essential step toward investigating the role of the elasticity coefficient on synchronization. Furthermore, the synchronization region of different impulsive weights, impulsive intervals, and impulsive control proportions are described thoroughly.

Intermittent pinning synchronization between two hyperbolic coupled networks with time-varying delays

This paper is devoted to synchronization between two hyperbolic coupled networks (HCNs) with time-varying delays via aperiodically intermittent pinning control (AIPC). Based on the Lyapunov function with a piecewise continuous function, sufficient criteria of HCNs with internal delays only and with hybrid delays are obtained, separately. And it is found that the convergence speed of synchronization of HCNs with hybrid delays is slower than that with internal delays only. Furthermore, two simulation results are presented to verify the theoretical results.

Sampled-Data-Based $\mathcal {H}_{\infty }$ Fuzzy Pinning Synchronization of Complex Networked Systems With Adaptive Event-Triggered Communications

In this article, the fuzzy pinning adaptive event-triggered control (FPAETC) problem related to complex networked systems is investigated. In light of the fact that the underlying controllers are fuzzy pinning, and the threshold parameters can flexibly update their states based on the latest and current sampled signals rather than transmitted signals, a novel state-dependent FPAETC protocol is devised to reduce the frequency of event-triggering and save more communication resources. Moreover, a more general time-dependent AETC protocol is proposed compared to the existing related results. Then, in combination with the graph theory, looped Lyapunov functional method, and fuzzy logic pinning technique, some relaxed criteria that establish the relationship between the synchronization and desired <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance for the considered system are derived. Simulation results validate the superiority of derived theoretical results.

Pinning a Complex Network to Follow a Target System With Predesigned Control Inputs

In this paper, the global pinning synchronization problem is studied for a complex dynamical network to follow a dynamic target system. A distinguished feature of the present network model is that the target system may have some predesigned control inputs. This implies that, when pinning synchronization is guaranteed, the states of the nodes within such a pinning-controlled dynamical network may approach a specified trajectory which does not satisfy the system equation of the uncoupling individual node system within the network. The practical constraint that the external control inputs acting on the target system are unknown to any node in the considered network poses a big challenge in solving such a pinning synchronization problem. The designed scheme for achieving pinning synchronization is executed in two steps. Specifically, the first step is to select some nodes to pin such that the augmented interaction topology has at least one directed spanning tree rooted at the node describing the target system, while the second step is to construct a coupling law to synchronize all the states of nodes within the network. Moreover, two kinds of discontinuous coupling laws with static and adaptive coupling gains are, respectively, proposed to achieve pinning synchronization. Meanwhile, by utilizing nonsingular ${M}$ -matrix theory and Lyapunov stability analysis for nonsmooth system, some efficient criteria are established for guaranteeing synchronization in the pinning-controlled networks. Numerical simulations on pinning synchronization of networking Chua’s circuit systems are finally given to verify the analytic results.

Pinning Synchronization of Complex Dynamical Networks with Variable-Delayed Coupling by Periodically Intermittent Control

This paper studied the adaptive pinning synchronization in complex networks with variable-delay coupling via periodically intermittent control. Theoretical analysis is included by means of Lyapunov functions and linear matrix inequalities (LMI) to make all nodes reach complete synchronization. Moreover, the synchronization criteria do not impose any restriction on the size of time delay. Numerical examples including the regular, Watts–Strogatz and scale-free BA random topological architecture are provided to illustrate the importance of our theoretical analysis.

Pinning synchronization of weighted bipartite networks with time-varying delays via aperiodic intermittent control

Bipartivity has been revealed as an important topological feature of many real networks. In this paper, we first propose a model of weighted bipartite networks with time-varying delays, where both internal delay and communication delay are incorporated, and meanwhile the delayed coupling contains only one single transmittal delay. Then we investigate its pinning synchronization problem via aperiodic intermittent control. By utilizing the Lyapunov functional method and mathematical induction, a generic global exponential synchronization criterion is established. Moreover, based on the theory of linear algebra, two easy verifiable low-dimensional synchronization conditions are obtained. It is shown that the network nodes with the highest degrees should be pinned successively. Finally, numerical simulations are given to verify the validity of the theoretical analysis.

Compartmentalization Strategy for the Optimal Economic Operation of a Hybrid AC/DC Microgrid

In this paper, a compartmentalization strategy is proposed for the economic operation of a hybrid AC/DC microgrid. The hybrid AC/DC microgrid will be compartmentalized into several independently controlled and coordinated AC and DC nanogrids. Accordingly, the optimal economic operation of the microgrid consists of two segments, including the optimal power sharing among local DERs in individual nanogrids and the optimal power sharing among interconnected nanogrids. For each AC/DC nanogrid, the optimal power sharing and frequency/voltage restoration are realized simultaneously without the need for any real-time communication. In the compartmentalized microgrid, each nanogrid will communicate with neighboring nanogrids through a sparse communication network to regulate power exchanges among nanogrids. In islanded mode, incremental costs of nanogrids are unified for realizing the optimal economic operation of the microgrid. In grid-connected mode, the external electricity price (i.e., purchase/sale electricity price set by the utility grid) is the desired incremental cost, which would be imposed on some pinned nanogrids and propagated among the remaining nanogrids. Then, the optimal power sharing of nanogrids within the grid-connected microgrid would be modeled as a pinning synchronization problem. The proposed compartmentalization strategy ensures that the optimal economic operation of the hybrid AC/DC microgrid is achieved under both island and grid-connected modes while the utilized communication structure is simplified and the dependency on communication networks is reduced. The performance of the proposed compartmentalization strategy is tested and verified through time-domain simulations in PSCAD/EMTDC for a hybrid AC/DC microgrid located at Illinois Institute of Technology (IIT).

Intermittent pinning synchronization of reaction–diffusion neural networks with multiple spatial diffusion couplings

This paper addresses the intermittent pinning synchronization problem of spatial diffusion coupled reaction–diffusion neural networks (RDNNs). Initially, the synchronization error signals are quantized before transmission to save both channel resource and control cost. Subsequently, utilizing intermittent pinning control scheme, only a small fraction of network nodes are selected to be controlled in various time periods, which further reduces the control cost. On the basis of the constructed controller, sufficient conditions that guarantee the synchronization of the coupled RDNNs are derived via Lyapunov direct method. Finally, the efficacy of the developed control approach is demonstrated by numerical simulation studies of three examples.

Adaptive Pinning Synchronization of Fractional Complex Networks with Impulses and Reaction–Diffusion Terms

In this paper, a class of fractional complex networks with impulses and reaction–diffusion terms is introduced and studied. Meanwhile, a class of more general network structures is considered, which consists of an instant communication topology and a delayed communication topology. Based on the Lyapunov method and linear matrix inequality techniques, some sufficient criteria are obtained, ensuring adaptive pinning synchronization of the network under a designed adaptive control strategy. In addition, a pinning scheme is proposed, which shows that the nodes with delayed communication are good candidates for applying controllers. Finally, a numerical example is given to verify the validity of the main results.

Global pinning synchronization of stochastic delayed complex networks

In this paper, the global pinning synchronization problem of a class of complex dynamical networks with hybrid couplings, time delays, random data packet dropouts and multiple stochastic disturbances is investigated. The hybrid couplings are portrayed in three forms: constant couplings, discrete-delay couplings and distributed-delay couplings. The phenomenon of random packet dropouts is described as a binary random variable which obeys the Bernoulli distribution taking values of 0 and 1 with a certain probability. Multiple noisy processes herein are characterized by Brownian motions, which act on all coupling terms as well as the overall dynamics equation. By applying the Lyapunov method and stochastic analysis technique, sufficient conditions are established to ensure the considered stochastic delayed complex network to globally synchronize to a reference trajectory in the mean-square sense via the developed randomly occurring pinning control strategy. The obtained criteria are within the framework of linear matrix inequations. Finally, a simulation example is presented to verify the feasibility and effectiveness of the derived theoretical results.

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.

Design of Distributed Observers in the Presence of Arbitrarily Large Communication Delays.

This paper focuses on the construction of distributed observers in the presence of arbitrarily large communication time delays. In contrast with the traditional centralized observer with the ability to acquire full output of the plant, we design a set of distributed observers, each having access to partial output of the plant through a distributed sensor network. More specifically, each observer obtains partial plant output and communicates with its neighboring observers through consensus protocols. The communication among the network is subject to arbitrarily large time delays. We consider three representative network topologies and for each topology establish conditions to guarantee the observation error systems be exponentially stable. We also consider the design of a pinning synchronization problem as a dual problem of the design of distributed observers. Numerical simulation is carried out to verify the effectiveness of our theoretical analysis.

Analysis and pinning control for passivity of coupled reaction-diffusion neural networks with nonlinear coupling

This paper addresses the passivity and passivity-based synchronization problems of an array model of nonlinearly coupled neural networks (NCNNs) with reaction-diffusion terms. Several sufficient conditions are established to guarantee the passivity of the considered network model by exploiting the Lyapunov functional method and some inequality techniques. Additionally, pinning control is an efficient technique for the investigation of passivity of complex networks. Because of this, the passivity of the proposed model is further studied by designing suitable pinning controller, and some pinning passivity criteria are also presented. On the other hand, the relationship between stability and (pinning) passivity is also analyzed. Several criteria for (pinning) synchronization are established by taking advantage of the relationship between exponential stability and (pinning) passivity. In the last, we provide two examples to elucidate the effectiveness of the theoretical results.

Weighted Average Pinning Synchronization for a Class of Coupled Neural Networks with Time-Varying Delays

This paper deals with the pinning synchronization problem for a class of neural networks with time-varying delay and nonsymmetrical coupling. The weighted average of all the node states is selected as the controlled synchronization state. A pinning feedback controller is proposed, and some sufficient conditions are derived to guarantee the global asymptotical synchronization by use of the Lyapunov–Krasovskii function method. Consequently, the adaptive pinning synchronization is also investigated. Finally, a numerical example is given to show the effectiveness of the main results.

Impulsive pinning synchronization of discrete-time network

Combining impulsive and pinning control, we investigate the synchronization problem of discrete-time network. In the proposed pinning control scheme, the controlled nodes are chosen according to the norm of the synchronization errors at different impulsive instants. Based on the Lyapunov function method and mathematical analysis technique, two synchronization criteria with respect to the impulsive gains and intervals are analytically derived. Both undirected and directed discrete-time networks coupled with Chirikov standard maps are performed in numerical examples to verify the effectiveness of the derived results.

Graph Theory-Based Pinning Synchronization of Stochastic Complex Dynamical Networks.

This paper is concerned with the adaptive pinning synchronization problem of stochastic complex dynamical networks (CDNs). Based on algebraic graph theory and Lyapunov theory, pinning controller design conditions are derived, and the rigorous convergence analysis of synchronization errors in the probability sense is also conducted. Compared with the existing results, the topology structures of stochastic CDN are allowed to be unknown due to the use of graph theory. In particular, it is shown that the selection of nodes for pinning depends on the unknown lower bounds of coupling strengths. Finally, an example on a Chua's circuit network is given to validate the effectiveness of the theoretical results.

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.

Synchronization analysis of linearly coupled delayed neural networks with discontinuous activations

In this study, without assuming the symmetry or irreducibility of the coupling configuration matrix, we investigate the synchronization of linearly coupled dynamical systems with discontinuous identical nodes and time delay. First, we design a feedback controller to realize the complete synchronization and exponential synchronization of discontinuous complex networks using a generalized Lyapunov approach. Second, we propose a set of adaptive controllers and adaptive laws to achieve complete synchronization. Third, we study the adaptive pinning synchronization of the discontinuous complex networks. The results of numerical simulations are presented to demonstrate the effectiveness of the controllers and the correctness of the theoretical results.