Analysis and pinning control for generalized synchronization of delayed coupled neural networks with different dimensional nodes

This paper investigate the generalized synchronization and pinning adaptive generalized synchronization for delayed coupled different dimensional neural networks with hybrid coupling, respectively. First, some sufficient conditions for reaching the generalized synchronization and pinning generalized synchronization of the considered network are acquired by using some inequality techniques and Lyapunov functional method. Second, because the precise parameter values of network cannot be obtained in some situations, we also purse the study on the generalized synchronization analysis and pinning control for the case of coupled different dimensional neural networks with parameter uncertainties. Third, two numerical examples are provided for substantiating the effectiveness of the derived results.     

Cluster synchronization for directed coupled inertial reaction-diffusion neural networks with nonidentical nodes via non-reduced order method

The cluster synchronization issues are investigated for directed coupled inertial reaction-diffusion neural networks (CIRDNNs) with nonidentical nodes by imposing two effective pinning control. A novel Lyapunov-Krasovskii functional (LKF) is established to directly analyze the dynamic behavior of CIRDNNs and deal with reaction-diffusion term, inertia term and coupling term. Moreover, based on different desired cluster synchronization states including a set of un-decoupled trajectories and the particular solutions of the decoupled node systems, two class of synchronization criteria in view of algebraic inequalities are derived under two different communication topologies, respectively. Finally, two typical examples are given to verify the theoretical results.     

Pinning and impulsive synchronization control of complex dynamical networks with non-derivative and derivative coupling

In this paper, the problem of pinning and impulsive synchronization between two complex dynamical networks with non-derivative and derivative coupling is investigated. A hybrid controller, which contains a pinning controller and a pinning impulsive controller, is proposed simultaneously. Based on the Lyapunov stability theory and mathematical analysis technique, some novel criteria of synchronization are derived, which can guarantee that the response network asymptotically synchronizes to the drive network by combining pinning control and pinning impulsive control. Moreover, the restrictions about non-derivative coupling matrix, impulsive intervals and the number of pinned nodes are removed. Numerical examples are presented finally to illustrate the effectiveness of the theoretical results.     

A survey on global pinning synchronization of complex networks

In practice, it is almost impossible to directly add a controller on each node in a complex dynamical network due to the high control cost and the difficulty of practical implementation, especially for large-scale networks. In order to address this issue, a pinning control strategy is introduced as a feasible alternative. The objective of this paper is first to recall some recent advancements in global pinning synchronization of complex networks with general communication topologies. A systematic review is presented thoroughly from the following aspects, including modeling, network topologies, control methodologies, theoretical analysis methods, and pinned node selection and localization schemes (pinning strategies). Fully distributed adaptive laws are proposed subsequently for the coupling strength as well as pinning control gains, and sufficient conditions are obtained to synchronize and pin a general complex network to a preassigned trajectory. Moreover, some open problems and future works in the field are also discussed.     

Static group synchronization of second-order multi-agent systems via pinning control

This paper investigates the expected static group synchronization problem of the second-order multi-agent systems via pinning control. For directed communication topology with spanning tree, based on Gershgorin disk theorem and the matrix property, a static pinning control protocol with fixed gains is first introduced and some sufficient and necessary static group synchronization criteria are also established. It is worth mentioning that a rigorous proof is also given that only one pinning node is needed to guarantee static group synchronization, which could be inferred that our protocol might be more economical and effective in large scale of multi-agent systems. Then, for weakly connected directed communication topology with nodes of zero in-degree, an adaptive pinning control applied to the node with zero in-degree is also proposed to achieve static group synchronization. Finally, the efficiency of the proposed protocols is verified by two simulation examples.     

Pinning synchronization of fractional-order memristor-based neural networks with multiple time-varying delays via static or dynamic coupling

This paper investigates global asymptotical synchronization between fractional-order memristor-based neural networks (FMNNs) with multiple time-varying delays (MTDs) by pinning control. Two classes of coupling manners, static manner and dynamic manner, are introduced into the pinning controller respectively. For the case of static coupling, to make the controller exclude fraction, 1-norm Lyapunov function and fractional Halanay inequality in MTDs case are utilized for synthesis of controller and convergence analysis of synchronization error. For the case of dynamic coupling, a fractional differential inequality is proved and discussed in an elaborate way, and then global asymptotical synchronization is analyzed by means of Lyapunov-like function and the newly-proved inequality. Lastly, numerical simulations are carried out to show the practicability of the pinning controllers and the feasibility of the obtained synchronization criteria.     

Synchronization of linear dynamical networks under stochastic impulsive coupling protocols

This paper investigates a stochastic impulsive coupling protocol for synchronization of linear dynamical networks based on discrete-time sampled-data. The convergence of the networks under the proposed protocol is discussed, and some sufficient conditions are showed to guarantee almost sure exponential synchronization. Moreover, this coupling protocol with a pinning control scheme is developed to lead the state of all nodes to almost sure exponentially converge to a virtual synchronization target. It is shown that the almost sure exponential synchronization can be achieved by only interacting based on the stochastic feedback information at discrete-time instants. Some numerical examples are finally provided to present the effectiveness of the proposed stochastic coupling protocols.     

Adaptive synchronization of complex networks with general distributed update laws for coupling weights

This paper discusses adaptive synchronization control for complex networks interacted in an undirected weighted graph, and aims to provide a novel and general approach for the design of distributed update laws for adaptively adjusting coupling weights. The proposed updating laws are very general in the sense that they encompass most weight update laws reported in the literature as special cases, and also provide new insights in the analysis of network system evolution and graph weight convergence. We show a rigorous proof for the synchronization stability of the overall complex network to a synchronized state, and demonstrate the convergence of adaptive weights for each edge to some bounded constants. A detailed comparison with available results is provided to elaborate the new features and advantages of the proposed adaptive strategies as compared with conventional adaptive laws. The effectiveness of the proposed approach is also validated by several typical simulations.     

Delay-dependent cluster synchronization of time-varying complex dynamical networks with noise via delayed pinning impulsive control

This paper investigates the problem of cluster synchronization of complex dynamical networks with noise and time-varying delays by using a delayed pinning impulsive control scheme. Different from the traditional impulsive control schemes without the effects of input delays, it designs a pinning impulsive control scheme to successfully address the aforementioned problem subject to impulsive input delays. By employing a time-dependent Lyapunov function and the mathematical induction, some novel criteria are established to guarantee the cluster synchronization of the noisy complex networks, revealing the closed relationship between the synchronization performance and the related factors, including the impulsive input delays, the number of the pinned nodes, the frequency and strength of the impulsive control, and the noisy perturbations. Some numerical examples and computer simulations are presented to illustrate the effectiveness of the theoretical results.     

Synchronization of dynamical networks with nonlinearly coupling function under hybrid pinning impulsive controllers

In this paper, the globally exponential synchronization problem of dynamical networks with nonlinearly coupling function is considered. Hybrid pinning control strategies are established to force the states of the network to follow some objective trajectory. The impulsive pinning controllers are used to control a fringe of nodes at the impulsive instants, while during the impulsive instants, pinning state-feedback controllers are designed to achieve the control objective. Finally, the validity of the developed techniques is evidenced by an illustrative example.     

Generalized lag synchronization of multiple weighted complex networks with and without time delay

The generalized lag synchronization of multiple weighted complex dynamical networks with fixed and adaptive couplings is investigated in this paper, respectively. By designing appropriate controller, several synchronization criteria are presented for multiple weighted complex dynamical networks with and without time delay based on the selected Lyapunov functional and inequality techniques. Moreover, an adaptive scheme to update the coupling weights is also developed for ensuring the generalized lag synchronization of multiple weighted complex dynamical networks with and without time delay. Finally, two numerical examples are provided in order to validate effectiveness of the proposed generalized lag synchronization criteria.     

Synchronization of multiplex networks with stochastic perturbations via pinning adaptive control

This paper investigates the synchronization problems for the multiplex networks with both inter-layer and intra-layer couplings subject to the stochastic perturbations. In particular, the topologies of all layers are not the same, so the model can represent a class of multiplex networks. To synchronize the multiplex networks onto the trajectory of a virtual leader, a pinning adaptive protocol is proposed and some pinning criteria are derived for guaranteeing complete synchronization. Furthermore, when the results are extended to the systems with time delays, the pinning adaptive strategy is still proved to be effective. Finally, a two-layer network and a three-layer network are selected for numerical simulations to illustrate the theoretical results.     

Integral predictor based prescribed performance control for multi-motor driving servo systems

An integral predictor-based dynamic surface control scheme is developed with prescribed performance (IPPDSC) for multi-motor driving servo systems in this paper. By employing a novel finite-time performance function and an improved error transformation, the tracking error is limited within a prescribed zone in any preset time without having the overrun and the singularity problem. Furthermore, integral state predictors are designed to update neural network weights to handle high-frequency oscillations under large adaptive gains. Different from the existing approaches, an integral term of prediction error is introduced to eliminate the steady-state error and avoid chattering. In addition, a synchronization controller based on the mean relative coupling structure is proposed to solve the coupling problem between synchronization and tracking. Finally, simulation and experimental results are presented to demonstrate the effectiveness of the designed approach.     

Pinning synchronization and adaptive synchronization of complex-valued inertial neural networks with time-varying delays in fixed-time interval

This article concentrates on pinning synchronization and adaptive synchronization problems of complex-valued inertial neural networks with time-varying delays in fixed-time interval. First, regarding complex-valued inertial neural networks model as an entirety instead of reducing this system to first-order differential equation, separating the real and imaginary parts of this system into an equivalent real-valued one, and establishing a novel Lyapunov function, the fixed-time stability for the closed-loop error system is guaranteed via partial nodes controlled directly by a new pinning controller which involves the state derivatives and other proper terms. Then, from the point of saving cost and avoiding resources waste, a new pinning adaptive controller is further developed and sufficient condition ensuring the adaptive fixed-time stability for the closed-loop error system is also derived. In the end, the effectiveness of these results is verified by a numerical example.     

Stop and Go adaptive strategy for synchronization of delayed memristive recurrent neural networks with unknown synaptic weights

Although the drive-response synchronization problem of memristive recurrent neural networks (MRNNs) has been widely investigated, all the existing results are based on the assumption that the parameters of the drive system are known in prior, which are difficult to implement in real-life applications. In the present paper, a Stop and Go adaptive strategy is proposed to investigate the synchronization control of chaotic delayed MRNNs with unknown memristive synaptic weights. Firstly, by defining a series of measurable logical switching signals, a switched response system is constructed. Subsequently, by utilizing the logical switching signals, several suitable parameter update laws are proposed, then some different adaptive controllers are devised to guarantee the synchronization of unknown MRNNs. Since the parameter update laws are weighted by the logical switching signals, they will work or stop automatically with the switch of the unknown weights of drive system. Finally, two numerical examples with their computer simulations are provided to illustrate the effectiveness of the proposed adaptive synchronization schemes.     

Fixed-time pinning synchronization for delayed complex networks under completely intermittent control

The present study investigates the fixed-time synchronization issue for delayed complex networks under intermittent pinning control. Different from some existing semi-intermittent controllers for finite/fixed-time synchronization, our pinning controller is designed in a complete intermittent way. In order to address the encountered theoretical analysis difficulties, a new differential inequality lemma is developed, which is suitable for the fixed-time synchronization studies under periodic or aperiodic complete intermittent control. Then, by using Lyapunov theory and pinning control approach, sufficient conditions are proposed which can guarantee the aperiodically completely intermittent-controlled delayed complex networks realizing fixed-time pinning synchronization. Moreover, the settling time is explicitly estimated, which is irrelevant to the initial values of our network systems. Additionally, as a special case, the scenario of periodic complete intermittent control is also discussed. At last, some simulation examples are utilized to confirm our theoretical outcomes.     

Synchronization of hybrid-coupled heterogeneous networks: Pinning control and impulsive control schemes

In this paper, the synchronization control problem is considered for the delayed hybrid-coupled heterogeneous networks, i.e., complex networks with nonidentical dynamical nodes. Some effective control schemes are designed under which the whole network is globally asymptotically synchronized to an arbitrary objective trajectory. By imposing the open-loop control on the whole network together with the feedback control only on a small fraction of the nodes, an easy-to-verify sufficient condition is derived to guarantee the asymptotic synchronization of the complex network under study. Furthermore, to decrease the feedback control gains, the idea of adaptive control scheme is combined together, and the verified conditions are further weakened. Finally, by introducing the impulses to the open-loop network and using the improved Halanay inequality, other novel synchronization criteria are developed for the complex network. Comparisons of the obtained theoretical results as well as the detail pinning schemes are also given. Numerical examples of the undirected scale-free network and the directed small-world network are illustrated to demonstrate the applicability and efficiency of the proposed theoretical results.     

Mean-square pinning control of fractional stochastic discrete-time complex networks

This paper considers the mean-square pinning control problem of fractional stochastic discrete-time complex networks. First, a new fractional stochastic discrete-time complex networks model with stochastic noise is established. Then, some pinning controllers and sufficient conditions are developed for the complex networks. By adopting Lyapunov energy function theory and matrix analysis theory, it proved that the synchronization of the fractional stochastic discrete-time complex networks can be achieved in a mean-square sense via pinning control. In addition, these results are extended to solve the synchronization problem of general fractional discrete-time complex networks without noise. Finally, several numerical examples are given to verify the correctness of the obtained theoretical results.     

Adaptive distributed synchronization of heterogeneous multi-Agent systems over directed graphs with time-Varying edge weights

Time-varying edge weights represent dynamical interactions between any two nodes in multi-agent systems (MASs). In this paper, we consider a synchronization problem for heterogeneous MASs over directed graphs with time-varying edge weights from a control-theoretic perspective. We seek for an adaptive control protocol that drives the synchronization error in the presence of time-varying edge weights to converge in terms of asymptotic stability. We propose a class of observer networks for estimating leaders and output regulation equation solvers built on directed graphs with time-varying edge weights. Finally, we use a simulation study to verify the effectiveness of the proposed protocol.     

Pinning exponential synchronization for inertial coupled neural networks via adaptive aperiodically intermittent control under directed topology

This article is mainly focused on investigating pinning exponential synchronization of inertial coupled neural networks (ICNNs) under different directed topologies. The traditional method of variable substitution is removed and replaced by non-reduced order method to investigate the dynamical behavior of second-order coupled system. Additionally, by constructing Lyapunov-Krasovskii functional and utilizing matrix decomposition theory as well as M-matrix theory, an adaptive aperiodically intermittent controller is introduced to derive several improved sufficient criteria based on linear matrix inequalities (LMIs). Finally, some examples with numerical simulation are exhibited to confirm the availability of the theoretical results.