Iterative learning control-based tracking synchronization for linearly coupled reaction-diffusion neural networks with time delay and iteration-varying switching topology

In this paper, the D-type iterative learning control (ILC) protocol based on the local neighbor information is designed to achieve tracking synchronization for linearly coupled reaction-diffusion neural networks in presence of time delay and iteration-varying switching topology under a repetitive environment. Firstly, based on non-collocated sensors and actuators network, the proposed D-type ILC update law can realize tracking synchronization by utilizing output tracking errors. Then, by virtue of the contraction mapping principle, the sufficient convergence conditions of tracking synchronization errors are presented under the fixed commutation topology. Subsequently, the synchronization conclusions are extended to the iteration-varying commutation topology scenario. Finally, two numerical examples are provided to verify the efficacy of the obtained results.     

Adaptive synchronization of complex dynamic networks with switching parameters subject to state constraints in power system

This paper deals with the synchronization control of power complex networks with switching parameters. In the meantime, the node state constraints are considered during the synchronization process. Admittedly, synchronization problem encountered in power complex networks is becoming progressively important due to the increasing connection and disconnection operations resulting from sustainable energy and controllable load. Hereon, the network model considering switching parameters of each node is established to describe the topology variation of power systems that may be confronted in practical terms. Then, by utilizing the adaptive backstepping technique with a barrier Lyapunov function (BLF), a novel synchronization controller is constructed recursively which accomplishes the nodes full states tracking within the predefined transient behavior. Owing to the characteristic of BLF, the designed controller as well as its adaptive law could guarantee both the constrained state of each node restricted by a prescribed range and the synchronization performance. Meanwhile, the bounded output of the system could track the desired trajectory. Finally, scenario simulations are performed to demonstrate the effectiveness and superiority of the proposed method.     

Synchronized stationary distribution of hybrid stochastic coupled systems with applications to coupled oscillators and a Chua’s circuits network

In this paper, the existence of synchronized stationary distribution for hybrid stochastic coupled systems (HSCSs) (here, also known as stochastic coupled systems with Markovian switching) is concerned. By the existence theory of stationary distribution as well as Lyapunov method and graph theory, two kinds of sufficient criteria are presented to promise the existence of synchronized stationary distribution for HSCSs. Our results exhibit that the existence region of synchronized stationary distribution has a close relationship with the intensity of stochastic perturbation. And when stochastic perturbation vanishes, synchronized stationary distribution will become complete synchronization. Then the proposed theoretical results are successfully applied to stochastic coupled oscillators and a Chua’s circuits network. Some existence criteria of synchronized stationary distribution are also obtained. The corresponding numerical simulations are carried out to verify the validity of the theoretical results.     

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.     

Synchronization of coupled heterogeneous complex networks

By only designing the internal coupling, quasi synchronization of heterogeneous complex networks coupled by N nonidentical Duffing-type oscillators without any external controller is investigated in this paper. To achieve quasi synchronization, the average of states of all nodes is designed as the virtual target. Heterogeneous complex networks with two kinds of nonlinear node dynamics are analyzed firstly. Some sufficient conditions on quasi synchronization are obtained without designing any external controller. Quasi synchronization means that the states of all nonidentical nodes will keep a bounded error with the virtual target. Then the heterogeneous complex network with impulsive coupling which means the network only has coupling at some discrete impulsive instants, is further discussed. Some sufficient conditions on heterogeneous complex network with impulsive coupling are derived. Based on these results, heterogeneous complex network can still reach quasi synchronization even if its nodes are only coupled at discrete impulsive instants. Finally, two examples are provided to verify the theoretical results.     

Event-triggered synchronization control of complex networks with adaptive coupling strength

The event-triggered synchronization control problem is concerned for a class of complex networks with nonlinearly coupling function and adaptive coupling strength. Given a state-based event-trigger mechanism and the threshold, an event-triggered control method is introduced to make complex networks achieve exponential synchronization. By combining the Lyapunov stability theory and the knowledge of graph theory, a sufficient condition is established such that complex networks can achieve exponential synchronization. Then, the feasibility of the event-triggered control is analyzed. Moreover, the second-order Kuramoto oscillators is taken into account. And the event-triggered control strategy is used to make the oscillators achieve exponential synchronization. Meanwhile, two simulation results about the second-order Kuramoto oscillators are given to show the effectiveness of results.     

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.     

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.     

Exponential synchronization for coupled complex networks with time-varying delays and stochastic perturbations via impulsive control

This paper is concerned with the problem of exponential synchronization of coupled complex networks with time-varying delays and stochastic perturbations (CCNTDSP). Different from previous works, both the internal time-varying delay and the coupling time-varying delay are taken into account in the network model. Meanwhile, an impulsive controller is designed to realize exponential synchronization in mean square of CCNTDSP. Combining the Lyapunov method with Kirchhoff’s Matrix Tree Theorem, some sufficient criteria are obtained to guarantee exponential synchronization in mean square of CCNTDSP. Furthermore, we apply the theoretical results to study exponential synchronization of stochastic coupled oscillators with the internal time-varying delay and the coupling time-varying delay. And a synchronization criterion is also obtained. Finally, two numerical examples are given to demonstrate the effectiveness and feasibility of our theoretical results and the superiority of impulsive control.     

Secure chaotic communication based on extreme multistability

Extreme multistability is the coexistence of a large number of attractors which can be reached by varying initial conditions. In this paper we show how this fascinating phenomenon can be used for secure communication. The main advantage of the communication system based on extreme multistability over a conventional chaos-based communication system is its exceptionally high security. The proposed system consists of two identical six-order oscillators; one in the transmitter and another one in the receiver, each exhibiting the coexistence of a large number of chaotic attractors. The oscillators are synchronized using a private channel through one of the system variables, while the information is transmitted via a public channel through another variable. The information is encrypted by varying the initial condition of one of the state variables in the transmitter using a chaotic map, adhering message packages in a staggered form to the coexisting attractors within the same time series of another state variable, which leads to switching among the coexisting chaotic attractors. To ensure communication security, the duration of the packages is shorter than synchronization time, so that synchronization attacks are ineffective.     

Graph-theoretic approach to exponential synchronization of coupled systems on networks with mixed time-varying delays

In this paper, the issue of exponential synchronization for coupled systems on networks with mixed time-varying delays is concerned. An approach combining Kirchhoff’s matrix tree theorem in graph theory with Lyapunov method and periodically intermittent control is taken to investigate the problem. This method is different from the corresponding previous works. Two different kinds of synchronization conditions in the form of Lyapunov-type theorem and coefficients-type criterion are derived. They both reveal synchronization has a close relation with the topology structure of the network. Finally, the feasibility and effectiveness of the proposed method are illustrated by several numerical simulation figures.     

Exponential synchronization of switched genetic oscillators with time-varying delays

This paper addresses the problem of exponential synchronization of switched genetic oscillators with time-varying delays. Switching parameters and three types of nonidentical time-varying delays, that is, the self-delay, the intercellular coupling delay, and the regulatory delay are taken into consideration in genetic oscillators. By utilizing the Kronecker product techniques and ‘delay-partition’ approach, a new Lyapunov–Krasovskii functional is proposed. Then, based on the average dwell time approach, Jensen?s integral inequality, and free-weighting matrix method, delay-dependent sufficient conditions are derived in terms of linear matrix inequalities (LMIs). These conditions guarantee the exponential synchronization of switched genetic oscillators with time-varying delays whose upper bounds of derivatives are known and unknown, respectively. A numerical example is presented to demonstrate the effectiveness of our results.     

Improved results on synchronization of stochastic delayed networks under aperiodically intermittent control

This paper addresses the synchronization of stochastic complex networks with time-varying delay via aperiodically intermittent control (AIC). By proposing the concepts of average control ratio and average control frequency for AIC, some new synchronization conditions are obtained, which relax the constraints of the lower bound of control widths and the upper bound of control periods. And the proportion of rest widths can be any value in (0,1). So the constraints on AIC are loosened and thus the conservativeness is reduced compared with the existing related results. Two types of time delay are investigated: (i) the upper bound of time-varying delay should be smaller than the average control width but can be larger than the lower bound of control widths; (ii) the upper bound of time-varying delay has no relationship with control and rest widths. An example of coupled stochastic oscillators systems is presented to show the effectiveness and superiority of our results.     

Exponential synchronization of stochastic complex networks with multi-weights: A graph-theoretic approach

This paper concerns the exponential synchronization problem of stochastic complex networks with multiple weights (SCNMW). By the method of network split, SCNMW can be modelled as stochastic coupled systems driven by Brownian motion. By combining graph theory, Lyapunov stability theory and state feedback control technique, drive-response synchronization criteria of SCNMW have been obtained. Two kinds of exponential synchronization criteria are obtained, one is given with Lyapunov functions of vertex systems, and the other is shown with the coefficients of SCNMW. The obtained synchronization principles are closely related to the coupling strength of multiple sub-networks and the intensity of noise perturbation. Finally, a numerical example with some simulations is presented to illustrate the theoretical results.     

Robust synchronization of different coupled oscillators: Application to antenna arrays

This paper deals with the synchronization of a chain of nonlinear and uncertain models of nonidentical oscillators. Using Lyapunov's theory of stability, a dynamical controller guaranteeing the synchronization of the oscillators is determined. The problem of synchronization is transformed into a problem of asymptotic stabilization for a nonlinear system and then is formulated as a system of linear matrix inequalities where the parameter variations of the two oscillators and their differences are modeled by polytopic matrices. The theoretical result is successfully applied to an array of transistor-based oscillators used in “smart antenna” systems.     

General synchronization criteria for nonlinear Markovian systems with random delays

It is well known that control of Markovian systems is a difficult problem. This paper considers synchronization control of Markovian coupled nonlinear systems with random delays. A new control scheme is proposed. Sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained such that the coupled system can be asymptotically synchronized onto an isolated system. The synchronization criteria include classical mode-dependent and mode-independent results as special cases. The design method of the control gains is also given. Compared with mode-dependent and mode-independent control methods, our results are more practical and have lower conservatism, respectively. Numerical simulations are given to verify the effectiveness of the theoretical results.     

Resilient observer-based sliding mode control of connected vehicles with denial-of-service attacks

This paper investigates an observer-based sliding mode control (SMC)) for connected vehicles under denial-of-service attacks. The attacks refer to interrupting communication channels between vehicles. Firstly, a reduced order observer is used to estimate the relative acceleration between neighbor vehicles, and a switching communication topology is introduced to model the attack. Then, an observer based sliding mode controller is proposed to achieve desired stability performance. Moreover, a quadratic cost performance is also defined and the cost upper bound is proved. Some sufficient conditions are provided such that the connected vehicles can achieve robust tracking performance, and input-to-state string stability is guaranteed under zero initial errors. Finally, numerical simulations are given to illustrate the validity of the designed controller.     

Leader-following consensus of multi-agent systems with jointly connected topology using distributed adaptive protocols

The leader-following consensus problems for multi-agent systems with a linear and Lipschitz nonlinear dynamics are considered. Distributed adaptive protocols and Lipschitz distributed adaptive protocols are respectively designed for the linear and Lipschitz nonlinear cases, under which leader-following consensus is reached for jointly connected topology. Finally, a simulation example is provided to illustrate the theoretical results.     

A sliding mode approach to H∞ synchronization of master–slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties

In this paper, a sliding-mode approach is proposed for exponential H_∞ synchronization problem of a class of master–slave time-delay systems with both discrete and distributed time-delays, norm-bounded nonlinear uncertainties and Markovian switching parameters. Using an appropriate Lyapunov–Krasovskii functional, some delay-dependent sufficient conditions and a synchronization law, which include the master–slave parameters are established for designing a delay-dependent mode-dependent sliding mode exponential H_∞ synchronization control law in terms of linear matrix inequalities. The controller guarantees the H_∞ synchronization of the two coupled master and slave systems regardless of their initial states. Two numerical examples are given to show the effectiveness of the method.