Pinning Control For Synchronization Research Articles

Finite‐time pinning synchronization control for multi‐layer complex networks

AbstractThe synchronization of multi‐layer networks can greatly improve production and life efficiency, thus having important research significance. In this article, the finite‐time pinning synchronization control strategy is investigated for multi‐layer networks. A new finite‐time pinning controller, which not only considers the intra‐layer coupling connection, but also the inter‐layer coupling connection, is designed. The pinning synchronization criteria for the multi‐layer networks is established based on the finite‐time control protocols. Additionally, the corresponding convergence analysis are also provided. Finally, the effectiveness of the obtained theoretical results is illustrated using three comparison methods in a two‐layer network.

Adaptive memory event-triggered observer-based pinning synchronization control for complex dynamical networks under asynchronous attacks

This article addresses the security synchronization issue of complex dynamical networks under asynchronous cyber and physical attacks within the context of cyber-physical systems. An observer is devised to estimate the system's state using the measured outputs of partial nodes. The integration of a buffer for storing historical information enhances the accuracy of state estimation under asynchronous attacks, enabling the observer-based control scheme to generate more precise control signals during attacks. The robustness against external disturbances is reinforced by introducing disturbance compensation for both the observer and the controller. Additionally, an adaptive memory event-triggered mechanism is designed to conserve network resources. Then, a sufficient condition for the synchronization of complex dynamical networks against asynchronous attacks is obtained, and the gains of the observer and controller are computed based on the linear matrix inequality technique. Finally, a simulated example demonstrates the effectiveness of the suggested strategy.

Adaptive event‐triggered pinning synchronization control for complex networks with random saturation subject to hybrid cyber‐attacks

SummaryThis research is concerned with the problem of pinning based output synchronization control for a complex networks with random saturation vulnerable to hybrid cyber‐attacks via an adaptive event‐triggered scheme (AETS). The output synchronization error systems are subject to suffer from deception attacks, replay attacks, and denial‐of‐service attacks. A novel hybrid cyber‐attack model is first constructed to integrate the three kinds of attacks into a synchronization of complex network. AETSs based on output synchronization errors with the consideration of hybrid cyber‐attacks, have been proposed to reduce the burden of communication. A pinning control strategy is used to decrease the control signal's input. By constructing a Lyapunov functional and using the linear matrix inequality technique, sufficient conditions are provided to ensure the output synchronization error system. Finally, a numerical simulation results are developed to illustrate the efficacy of the proposed theoretical methodology.

Event-Based Pinning Synchronization Control for Discrete-Time Delayed Complex Cyber-Physical Networks Under All-Around Attacks

This paper is concerned with the problem of pinning synchronization control for a class of nonlinear discrete-time delayed complex cyber-physical networks under all-around attacks. To handle the all-around attacks, a constrained hybrid attacks model is established, which incorporates the pattern feature of false data injection attacks and physical attacks. By utilizing the Lyapunov stability theory and the linear matrix inequality technique, a novel dynamic event-triggering pinning synchronization control scheme is developed to cope with the synchronization control task. Subsequently, sufficient conditions are obtained to guarantee that the closed-loop error dynamics are ultimately exponentially bounded. Furthermore, the design procedure of the synchronization controller is presented for the considered complex cyber-physical networks subject to all-around attacks. Finally, an illustrative example is delivered to demonstrate the effectiveness of the proposed method.

Finite-Time Pinning Synchronization Control for T-S Fuzzy Discrete Complex Networks with Time-Varying Delays via Adaptive Event-Triggered Approach.

This paper is concerned with the adaptive event-triggered finite-time pinning synchronization control problem for T-S fuzzy discrete complex networks (TSFDCNs) with time-varying delays. In order to accurately describe discrete dynamical behaviors, we build a general model of discrete complex networks via T-S fuzzy rules, which extends a continuous-time model in existing results. Based on an adaptive threshold and measurement errors, a discrete adaptive event-triggered approach (AETA) is introduced to govern signal transmission. With the hope of improving the resource utilization and reducing the update frequency, an event-based fuzzy pinning feedback control strategy is designed to control a small fraction of network nodes. Furthermore, by new Lyapunov–Krasovskii functionals and the finite-time analysis method, sufficient criteria are provided to guarantee the finite-time bounded stability of the closed-loop error system. Under an optimization condition and linear matrix inequality (LMI) constraints, the desired controller parameters with respect to minimum finite time are derived. Finally, several numerical examples are conducted to show the effectiveness of obtained theoretical results. For the same system, the average triggering rate of AETA is significantly lower than existing event-triggered mechanisms and the convergence rate of synchronization errors is also superior to other control strategies.

Finite‐Time Pinning Synchronization Control for Coupled Complex Networks with Time‐Varying Delays

The finite‐time pinning synchronization control problem is studied for coupled complex networks with time‐varying delays. Based on the finite‐time stability theorem, a finite‐time tractive synchronous controller is designed. In addition, the selection process of tractive nodes is developed to control as few nodes as possible such that all nodes are synchronized in the network in finite time. At the same time, sufficient conditions of the finite‐time constraint synchronization of the drive‐response network are obtained using the Lyapunov stability theory and the matrix inequality method. The effectiveness of the proposed controller is verified by numerical simulation. This approach can be applied to large‐scale complex networks with time‐varying delays.

Pinning synchronization control for stochastic multi-layer networks with coupling disturbance

The pinning synchronization scheme is investigated for stochastic multi-layer networks under the intra-layer coupling disturbance and stochastic noise. To save the control cost, a pinning control scheme is proposed. And some sufficient conditions in the form of the LMI are given, based on Lyapunov theory and stochastic analysis, to make sure that the multi-layer networks synchronize to a desired trajectory. Next, the selection scheme of pinned nodes is designed according to the structure of considered multi-layer networks. Finally, simulation examples are shown to illustrate the feasibility and availability of the designed pinning scheme.

Pinning synchronization control for multi-layer complex networks via adaptive fuzzy logic system

In this paper, the pinning synchronization problem for the multi-layer networks with dynamic uncertainties is studied. The dynamical uncertainties can be approximated by a fuzzy logic system, based on which, the pinning synchronization scheme is proposed. By using Lyapunov stability theorem, the sufficient condition is given that can ensure that the multi-layer networks can synchronize to the reference trajectory with designed adaptive law. Finally, a numerical example is given to verify the effectiveness of the proposed pinning control scheme.

Prescribed performance synchronization for time‐delayed complex dynamical networks under event‐triggered pinning control

AbstractIn this article, a new event‐based pinning synchronization control strategy for complex dynamical networks with internal delay and transmission delay is investigated. By introducing prescribed performance control schemes, the transient and steady performance of synchronization errors are guaranteed simultaneously. The main results in the article show that, not only exponential synchronization is achieved, but also the transient bounded of synchronization errors is guaranteed based on Lyapunov approach. Furthermore, an efficient event‐based mechanism is derived to avoid the infinitely fast switching of the pinning node set. We also develop a new selection‐algorithm to find certain suitable nodes to be controlled and these selected nodes will be updated online at each triggering instant. At last, the simulation examples are made to demonstrate the effectiveness and superiority of the obtained results.

Cost-effective communication network planning considering performance of pinning-based secondary control in microgrids

Driven by the fact that the structural topology of the communication network has a significant effect on the dynamical performance of the related physical network, this paper addresses the communication network planning problem for islanded microgrids (MGs). The optimal communication topology with the lowest communication cost, which supports the desired performance of pinning-based distributed control is designed in the MG planning stage. To achieve that, firstly, pinning synchronization control (PSC) is developed to regulate the voltage and frequency at each distributed generator (DG) to the reference state. Then criteria of the algebraic connectivity of communication network to fulfill the convergence requirement of PSC protocols are derived analytically using spectral graph properties and Lyapunov theory. A communication network planning model is formulated as Mixed Integer Semidefinite Program (MISDP) by using Linear Matrix Inequalities (LMI) techniques. The convergence speed requirement of PSC, communication time delay and the importance of connections between DGs are considered as constraints. The optimal communication network with the lowest communication cost can be acquired and meanwhile the satisfactory dynamical performance of PSC protocols can be guaranteed. The case studies are designed to evaluate how the planning model can practically facilitate the pinning-based control in the islanded MG. The simulation results effectively verify that the dynamical control convergence can be improved under the properly designed communication network. The control performance of the proposed protocol is validated experimentally based on a two-DG MG prototype.

Adaptive Event-Based Non-Fragile Output Pinning Synchronization Control for Complex Networks With Random Saturations and Cyber-Attacks

This paper addresses the adaptive event-triggered non-fragile output pinning synchronization control for complex networks subject to random saturations and cyber-attacks. An adaptive event-triggered scheme (AETS) based on the output synchronization error is proposed to save network bandwidth, and a pinning control strategy is employed to reduce the input of control signal. Considering the effect of AETS, randomly occurring saturations and cyber-attacks on the drive and response systems, we investigate a novel output security synchronization error model, and then design an event-triggered non-fragile controller such that the asymptotic stability of the error system can be guaranteed. Meanwhile, we obtain the controller gains and event-triggered matrices in terms of solving the linear matrix inequalities (LMIs). Finally, a simulation example is provided to verify the design method.

Event-Based Pinning Synchronization Control for Time-Delayed Complex Dynamical Networks: The Finite-Time Boundedness

The paper is concerned with the synchronization control issue for a kind of nonlinear discrete time-delayed complex dynamical networks. To improve energy efficiency, a dynamic event-triggering strategy is introduced to regulate the signal transmission from the controller to the actuator. Then, the event-based pinning feedback control strategy is adopted to control a small fraction of the network nodes with hope to reduce the frequency of updating and communication in control process. Subsequently, a new concept of finite-time boundedness in the mean square is put forward to evaluate the synchronization control performance by means of a settling-like time function. Furthermore, by using the Lyapunov stability theory and the stochastic analysis technique, a sufficient condition is provided to ensure that the synchronization error is finite-time bounded in the mean square with a prescribed error upper bound in the presence of both time-delay and external noise disturbances. By solving an optimization problem with some inequality constraints, the desired controller gain matrix is parameterized to minimize the settling-like time. Finally, a numerical simulation example is carried out to illustrate the effectiveness and usefulness of the obtained theoretical results.

Pinning Synchronization Control for a Class of Dynamical Networks with Coupled Time-Varying Delays: An Interval-Observer-Based Approach

This paper is concerned with the pinning synchronization control issue for a class of discrete-time complex dynamical networks. By resorting to the interval observer approach, a novel pinning synchronization control strategy is adopted to control a small fraction of the network nodes with hope to reduce the implementation cost. By using the Lyapunov stability theorem, some synchronization criteria have been derived to ensure the desired synchronization performance. Finally, a numerical simulation is presented to illustrate the effectiveness and usefulness of the theoretical results.

Pinning synchronization control for a class of discrete-time switched stochastic complex networks under event-triggered mechanism

In this paper, the pinning control problem is considered for the synchronization of a class of nonlinear discrete-time switched stochastic complex networks with identical nodes. The networks we considered are very general that account for nonlinear inner-coupling structures and nonidentical exogenous disturbances. In order to save the communication cost, a pinning controller under the event-triggered scheme is designed to realize the synchronization. The notion of bounded synchronization in probability is introduced to characterize the performance of the controlled dynamical networks in the presence of exogenous disturbances, switching rules and event-triggered schemes. Upper bounds of the states of the switched stochastic complex networks are first provided, and then the controller gain, the event-trigger parameters and the average dwell time are co-designed for switched subsystems. At last, a numerical example is given to illustrate the effectiveness of our results.

Pinning synchronization control of complex networks with partial couplings

In this article, the pinning synchronization problem of complex networks with a target node via sampled-data communications is considered. Due to partial couplings among the nodes in complex networks, a decoupling method is adopted to investigate each channel of complex networks independently. By constructing a time-dependent Lyapunov function, it is proved that the pinning synchronization of complex networks with a target node can be achieved if the control parameters are appropriately selected. Furthermore, further study is needed to investigate the pinning synchronization of complex networks in the presence of constant delay. A novel criterion is obtained using Jensen’s inequality and Wirtinger’s inequality. It is worth noting that the lower and upper bounds of the sampling intervals can be calculated by linear matrix inequality box of MATLAB. Theoretical results are well verified through a numerical simulation.

Event-based aperiodically intermittent pinning synchronization control strategy for linearly coupled complex networks

In this paper, a kind of event-based aperiodically intermittent pinning synchronization control strategies for linearly coupled complex networks over the directed topology is proposed. With the prescribed convergence performance dynamic, an event-triggered mechanism is presented to guarantee the globally exponential synchronization of the complex networks. Furthermore, a global and robust event-based mechanism is derived by some approximation techniques to handle with the measurement noises of the states and the exponential synchronization is achieved. Simultaneously, with the limitation of information transmission over the networks, through constructing a nonlinear filter dynamic, a robust event-triggered mechanism which is only dependent on the states of the pinned nodes is presented to asymptotically synchronize the complex networks. Moreover, to eliminate the conservation of the constant feedback gains, a synthetic design of the adaptive feedback law and event-triggered mechanism is proposed. It is proved that the asymptotical synchronization of the complex network and the boundedness of the adaptive feedback gains are guaranteed. With rigorous analysis, for all of the presented event-based mechanisms, the Zeno phenomenon is excluded. Finally, a numerical example is performed over the directed scale-free network to demonstrate the effectiveness of the algorithms.

Robust Pinning Constrained Control and Adaptive Regulation of Coupled Chua’s Circuit Networks

This paper addresses the problems of pinning synchronization control and regulation and its circuit realization of a class of perturbed coupled Chua’s circuit networks. Robust constrained control strategies for pinned circuits and adaptive regulation schemes for couplings are developed to eliminate the impact of bounded time-varying perturbations and nonlinearities. Bounded synchronization results of the closed-loop Chua’s circuit networks are obtained based on Lyapunov stability theory. Furthermore, the control strategies and adaptive regulation schemes are implemented physically by circuits to construct the closed-loop Chua’s circuit networks reality. Comparison results based on MULTISIM and MATLAB softwares are given to verify the effectiveness of the proposed control and regulation circuits.

Robust pinning synchronization of complex cyberphysical networks under mixed attack strategies

SummaryThis paper is concerned with the robust pinning synchronization control problem in complex cyberphysical networks under mixed attacks. The channels for transmitting control input signals and receiving information agent are assumed to be independent of each other and both can be destroyed by frequently occurred attacks. After the attacks, a repairing cell will be instantly activated until the communication topology is restored to the initial state. Assume that broken‐down nodes remain partial function. Moreover, feedback gain matrices and coupling strengths will be designed by some algorithms. By dint of geometrical method and inequality technique, sufficient conditions are established to guarantee robust synchronization for the complex cyberphysical networks. Finally, a simulation example is utilized to illustrate the obtained results.

Pinning Synchronization Control of Two Fuzzy Complex Dynamical Networks based on Output Signals

In recent years, researchers found that the complex dynamical network is an effective tool to describe and understand the complex nonlinear systems. Because of the difficulty in establishing accurate mathematical models for nonlinear systems, the classical linear control methods are difficult to be applied to them. T-S fuzzy model has been proved to be an all-purpose approximation for nonlinear system, and has ability to combine linear control theory with fuzzy theory. In this paper, a scheme for synchronization between two fuzzy networks based on output signals under pinning control is proposed. Unlike other common methods,it only requires output signals to be transmitted from driving network to response network, and part of nodes in response network to be controlled. The synchronization criteria is given by using Lyapunov stability theory and linear matrix inequality technology, and the number of pinning nodes can be calculated by using the proposed synchronization theorem. Finally, a simulation example is given to verify the effectiveness of this scheme.

Adaptive Pinning Synchronization Control of the Fractional-Order Chaos Nodes in Complex Networks

Adaptive pinning synchronization control is studied for a class of fractional-order complex network systems which are constructed depending on small-world network algorithm. Based on the fractional-order stability theory, the suitable adaptive control scheme is designed to guarantee global asymptotic stability of all the nodes in complex network systems and the node selected algorithm is given. In numerical implementation, it is shown that the numerical solution of the fractional-order complex network systems can be obtained by applying an improved version of Adams-Bashforth-Moulton algorithm. Furthermore, simulation results are provided to confirm the validity and synchronization performance of the advocated design methodology.