Adaptive Synchronization Problem Research Articles

Adaptive Output Synchronization of Coupled Fractional-Order Memristive Reaction-Diffusion Neural Networks

This article discusses the adaptive output synchronization problem of coupled fractional-order memristive reaction-diffusion neural networks (CFOMRDNNs) with multiple output couplings or multiple output derivative couplings. Firstly, by using Lyapunov functional and inequality techniques, an adaptive output synchronization criterion for CFOMRDNNs with multiple output couplings is proposed. Then, an adaptive controller is designed for ensuring the output synchronization of CFOMRDNNs with multiple output derivative couplings. Finally, two numerical examples are given to verify the effectiveness of the theoretical results.

An almost globally stable adaptive phase‐locked loop for synchronization of a voltage source converter to a weak grid

AbstractIn this article, we are interested in the problem of adaptive synchronization of a voltage source converter with a possibly weak grid with unknown angle and frequency. To guarantee a suitable synchronization with the angle of the three‐phase grid voltage we design an adaptive observer for such a signal requiring measurements only at the point of common coupling. Then we propose an alternative certainty‐equivalent, adaptive phase‐locked loop that ensures the angle estimation error goes to zero for almost all initial conditions. Although well‐known, for the sake of completeness, we also present a PI controller with feedforward action that ensures the converter currents converge to an arbitrary desired value. Relevance of the theoretical results and their robustness to variation of the grid parameters are thoroughly discussed and validated in the challenging scenario of a converter connected to a grid with low short‐circuit‐ratio.

Adaptive Exponential Synchronization of Complex Networks With Nondifferentiable Time-Varying Delay.

In recent years, the adaptive exponential synchronization (AES) problem of delayed complex networks has been extensively studied. Existing results rely heavily on assuming the differentiability of the time-varying delay, which is not easy to verify in reality. Dealing with nondifferentiable delay in the field of AES is still a challenging problem. In this brief, the AES problem of complex networks with general time-varying delay is addressed, especially when the delay is nondifferentiable. A delay differential inequality is proposed to deal with the exponential stability of delayed nonlinear systems, which is more general than the widely used Halanay inequality. Next, the boundedness of the adaptive control gain is theoretically proved, which is neglected in much of the literature. Then, the AES criteria for networks with general delay are established for the first time by using the proposed inequality and the boundedness of the control gain. Finally, an example is given to demonstrate the effectiveness of the theoretical results.

Adaptive Global Synchronization for a Class of Quaternion-Valued Cohen-Grossberg Neural Networks with Known or Unknown Parameters

In this paper, the adaptive synchronization problem of quaternion-valued Cohen–Grossberg neural networks (QVCGNNs), with and without known parameters, is investigated. On the basis of constructing an appropriate Lyapunov function, and utilizing parameter identification theory and decomposition methods, two effective adaptive feedback schemes are proposed, to guarantee the realization of global synchronization of CGQVNNs. The control gain of the above schemes can be obtained using the Matlab LMI toolbox. The theoretical results presented in this work enrich the literature exploring the adaptive synchronization problem of quaternion-valued neural networks (QVNNs). Finally, the reliability of the theoretical schemes derived in this work is shown in two interesting numerical examples.

Finite-time complete periodic synchronization of memristive neural networks with mixed delays

In this paper we study the oscillatory behavior of a new class of memristor based neural networks with mixed delays and we prove the existence and uniqueness of the periodic solution of the system based on the concept of Filippov solutions of the differential equation with discontinuous right-hand side. In addition, some assumptions are determined to guarantee the globally exponentially stability of the solution. Then, we study the adaptive finite-time complete periodic synchronization problem and by applying Lyapunov–Krasovskii functional approach, a new adaptive controller and adaptive update rule have been developed. A useful finite-time complete synchronization condition is established in terms of linear matrix inequalities. Finally, an illustrative simulation is given to substantiate the main results.

Adaptive finite-time synchronization of fractional-order delayed fuzzy cellular neural networks

The adaptive finite-time synchronization problems are investigated for a class of fractional-order delayed fuzzy cellular neural networks (FODFCNNs). First, with the aid of the properties of the Mittag-Leffler function and the Laplace transform with the parameter, some novel fractional-order differential inequalities are established to provide new perspective to explore finite-time synchronization of fractional-order systems. Second, based on these inequalities and the designed adaptive controller, some novel sufficient conditions are given to guarantee the adaptive finite-time synchronization of FODFCNNs. Finally, the effectiveness of the results is demonstrated by a numerical example.

Adaptive Synchronization for Delayed Chaotic Memristor-Based Neural Networks.

This article considers the adaptive synchronization problem of delayed chaotic memristor-based neural networks (MNNs). Note that MNNs are modeled as continuous systems in the flux-voltage-time (ϕ,x,t) domain where memristors are viewed as continuous systems based on HP memristors. New adaptive controllers of MNNs are proposed, where controllers are both on memristors in the flux-time (ϕ,t) domain and neurons in the voltage-time (x,t) domain. Based on the Lyapunov method, Barbalat's lemma, differential mean value Theorem, and other inequality techniques, completed synchronization criteria for delayed chaotic MNNs are derived. In the end, two examples are given to demonstrate the validity of the derived results.

Neural network-based adaptive synchronization for second-order nonlinear multiagent systems with unknown disturbance.

This paper handles the distributed adaptive synchronization problem for a class of unknown second-order nonlinear multiagent systems subject to external disturbance. It is supposed to be an unknown one for the underlying external disorder. First, the neural network-based disturbance observer is developed to deal with the impact induced by the strange disturbance. Then, a new distributed adaptive synchronization criterion is put forward based on the approximation capability of the neural networks. Next, we propose the necessary and sufficient condition on the directed graph to ensure the synchronization error of all followers can be reduced small enough. Then, the distributed adaptive synchronization criterion is further explored because it is difficult to obtain the relative velocity measurements of the agents. The distributed adaptive synchronization criterion without the velocity measurement feedback is also designed to fulfill the current investigation. Finally, the simulation example is performed to verify the correctness and effectiveness of the proposed theoretical results.

Distributed Adaptive Attitude Synchronization of Multiple Spacecraft With Event-Triggered Communication

This article investigates the distributed adaptive attitude synchronization problem for multiple rigid spacecraft with unknown inertial matrices and event-triggered communication. Under a directed topology condition, two distributed event-based adaptive attitude synchronization schemes are proposed. By introducing a reference system for each spacecraft, a distributed adaptive control algorithm is first developed, based on which a group of rigid spacecraft can be synchronized at a common attitude with zero angular velocity. Then, the case without angular velocity measurements is considered. By redesigning the reference system and resorting to a pseudovelocity filter, an event-based adaptive output feedback attitude synchronization algorithm is presented. It is shown that with the proposed control schemes, all the closed-loop signals are uniformly bounded and the attitude synchronization can be achieved, while Zeno behavior in each spacecraft can be excluded. Simulation results are provided to illustrate the effectiveness of the proposed control schemes.

Signal Transmission by Sampled-time Adaptive Synchronization of Time-varying Chaotic Systems

In the paper, the adaptive synchronization problem is studied for a class of time-varying nonlinear systems. The only assumption imposed is the boundedness of the rate of change of the controlled system parameters, while the initial uncertainty can be quite large. The adaptation algorithms in the discrete-time form are derived based on adaptive control of nonlinear time-varying systems with an explicit reference model. As the result, the estimate of the limiting deviation of the solution of the closed-loop system from that of the reference model was obtained. It is shown that with sufficiently slow changes in the parameters and a small initial uncertainty, the limiting error in the system can be made arbitrarily small despite a possibly big range of system parameter values. The systems based on a direct approach are considered. The procedure for the synthesis of a sampled-time adaptive controller and analysis of the synthesized system is illustrated by an example of the signal transmission system. The results obtained allow one to build and analyze a wide class of adaptive systems with reference models under time-varying conditions.

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.

Adaptive Event-Triggered Synchronization of Uncertain Fractional Order Neural Networks with Double Deception Attacks and Time-Varying Delay.

This paper investigates the problem of adaptive event-triggered synchronization for uncertain FNNs subject to double deception attacks and time-varying delay. During network transmission, a practical deception attack phenomenon in FNNs should be considered; that is, we investigated the situation in which the attack occurs via both communication channels, from S-C and from C-A simultaneously, rather than considering only one, as in many papers; and the double attacks are described by high-level Markov processes rather than simple random variables. To further reduce network load, an advanced AETS with an adaptive threshold coefficient was first used in FNNs to deal with deception attacks. Moreover, given the engineering background, uncertain parameters and time-varying delay were also considered, and a feedback control scheme was adopted. Based on the above, a unique closed-loop synchronization error system was constructed. Sufficient conditions that guarantee the stability of the closed-loop system are ensured by the Lyapunov-Krasovskii functional method. Finally, a numerical example is presented to verify the effectiveness of the proposed method.

Adaptive synchronization in the complex heterogeneous networks of Hindmarsh–Rose neurons

• The limit set for trajectories of the heterogeneous Hindmarsh–Rose network is defined. • Sufficient conditions of synchronization in the heterogeneous Hindmarsh–Rose networks with linear couplings are obtained. • The relationship between connectivity of the topological graph and synchronization is established. • The simulation coincides with the obtained theoretical results. This paper is devoted to the adaptive synchronization problem in the heterogeneous Hindmarsh–Rose neuronal networks. Heterogeneity is a natural property of biological neuronal networks, as each neuron has its own physiological characteristics, which may differ from other neurons within the population. Therefore, the study of the effect of heterogeneity on the synchronization in the biological neuronal network is an important problem. In order to solve this problem, the ultimate boundedness of the network trajectories is established, and also the limit set is defined for these trajectories. Based on the boundedness analysis and the Speed Gradient method, the adaptive algorithm for adjusting the coupling strength is developed. It is proved mathematically that the developed algorithm provides synchronization in the network under study. The obtained theoretical results are confirmed by the simulations.

Adaptive Event-Triggered Synchronization of Networked Neural Networks with Time-Varying Delay Subject to Actuator Saturation

This paper discusses the adaptive event-triggered synchronization problem of a class of neural networks (NNs) with time-varying delay and actuator saturation. First, in view of the limited communication channel capacity of the network system and unnecessary data transmission in the NCSs, an adaptive event-triggered scheme (AETS) is introduced to reduce the network load and improve network utilization. Second, under the AETS, the synchronization error model of the delayed master-slave synchronization system is constructed with actuator saturation. Third, based on Lyapunov–Krasovskii functional (LKF), a new sufficient criterion to guarantee the asymptotic stability of the synchronization error system is derived. Moreover, by solving the stability criterion expressed in the form of a set of linear matrix inequalities (LMIs), some necessary parameters of the system are obtained. At last, two examples are expressed to demonstrate the feasibility of this method.

Adaptive and Exponential Synchronization of Uncertain Fractional-Order T-S Fuzzy Complex Networks With Coupling Time-Varying Delays via Pinning Control Strategy

This article investigates the adaptive and exponential synchronization problems of fractional-order Takagi-Sugeno (T-S) fuzzy complex networks (FOTSFCN) with coupling time-varying delays and uncertainty. Firstly, the FOTSFCN model is established by embedding T-S fuzzy logic to reduce the complexity and robustness of the FOTSFCN. Secondly, based on the adaptive pinning control strategy, we obtain the asymptotic synchronization and exponential synchronization criteria to achieve synchronous control of FOTSFCN. Furthermore, according to the Lyapunov stability theory, we prove that the FOTSFCN controlled by the proposed controller is robust stable and the effect of coupling time-varying delays and uncertain disturbances on the tracking error can be subsided in view of the linear matrix inequalities (LMIs). Finally, the effectiveness and applicability of the theoretical results are presented through two illustrative examples.

Distributed Adaptive Event-Triggered Fault-Tolerant Synchronization for Multiagent Systems

This article investigates the fully distributed observer-based adaptive fault-tolerant synchronization problem (SP) of multiagent systems with event-triggered control mechanisms. First, a nonlinear and discontinuous adaptive observer-based event-triggered fault-tolerant controller is proposed for each agent to overcome the occurrence of unknown faults and unmeasurable full states of the controlled system. Besides, an adaptive triggering function consisting of state-dependent and time-dependent threshold is developed to adjust the parameter of triggering threshold online. Then, a modified nonlinear and continuous observer-based controller with adaptive ETC strategy is developed to overcome the chattering phenomenon from the discontinuous controller. It is proved that under two controllers, the SP not only can be achieved in a fully distributed way without continuous communication for both the controller updates and the triggering condition detecting but also exclusion of “Zeno behavior” can be realized. Finally, the effective algorithms can be verified by giving numerical simulations related to mobile robots.

Exponential and adaptive synchronization of inertial complex-valued neural networks: A non-reduced order and non-separation approach

This paper mainly deals with the problem of exponential and adaptive synchronization for a type of inertial complex-valued neural networks via directly constructing Lyapunov functionals without utilizing standard reduced-order transformation for inertial neural systems and common separation approach for complex-valued systems. At first, a complex-valued feedback control scheme is designed and a nontrivial Lyapunov functional, composed of the complex-valued state variables and their derivatives, is proposed to analyze exponential synchronization. Some criteria involving multi-parameters are derived and a feasible method is provided to determine these parameters so as to clearly show how to choose control gains in practice. In addition, an adaptive control strategy in complex domain is developed to adjust control gains and asymptotic synchronization is ensured by applying the method of undeterminated coefficients in the construction of Lyapunov functional and utilizing Barbalat Lemma. Lastly, a numerical example along with simulation results is provided to support the theoretical work.

具有随机扰动和Markov切换的中立型耦合神经网络的自适应同步

The adaptive synchronization problem of neutral-type neural networks with time-varying delays and stochastic perturbations was discussed. Stochastic perturbations were described as the Brownian motion. Through the Lyapunov stability theory, the LMI analysis techniques and the matrix theory were used to study the adaptive synchronization of neutral-type neural networks with stochastic perturbations and Markovian jumpings. The sufficient conditions for the system synchronization were given and proved. The criterion for adaptive synchronization of neutral-type neural networks with time-varying delays and stochastic perturbations was obtained. Finally, numerical examples show the effectiveness and applicability of the proposed approach.

Adaptive finite-time cluster synchronization of neutral-type coupled neural networks with mixed delays

This paper investigates the adaptive finite-time cluster synchronization problem of the neutral-type coupled neural networks (NCNNs) with mixed delays. Compared with the traditional neural networks, the model of NCNNs is more general in some sense, due to that it involves state delays, distributed delays and coupling delays. In this paper, a novel, adaptive and closed-loop control control algorithm is proposed to achieve the finite-time cluster synchronization of NCNNs with mixed delays. In addition, the sufficient conditions on the control parameters for stabilizing the closed-loop system are derived by leveraging the Lyapunov stability argument. Finally, the simulation results are carried out to illustrate the validity and feasibility of the proposed algorithm.

Adaptive synchronization of memristor-based complex-valued neural networks with time delays

This paper mainly deals with the adaptive synchronization problem of memristor-based complex-valued neural networks with time delays. In order to make the system itself adjust to achieve stable synchronization, the concept of adaptive control technology is used, a specific feedback controller is designed to achieve synchronization. The obtained results are more reliable and improve some existing achievements on the synchronization of real-valued memristor-based neural networks. Two numerical examples are given to illustrate the effectiveness of the theoretical results.