Finite-time Stochastic Synchronization Research Articles

Finite-time non-fragile control for synchronization of fractional-order stochastic neural networks

This study concerned with the synchronization problem over a finite-time domain for a class of fractional-order stochastic neural networks via non-fragile controller with discontinuous activation functions. Specifically, the suggested state feedback controller sequentially cope with non-fragile scheme for gain scheduling process. Notably, the main objective of this work is to obtained the finite-time synchronization criterion for the resulting synchronized error system over finite bound with the developed non-fragile controller. For that, some consignment of sufficient conditions is derived systematically by implementing Lyapunov’s indirect method and finite-time stability theory which ensures the finite-time stochastic synchronization of the stipulated neural networks. Later on, the controller gain fluctuations that obeying certain white noise sequels derived from Bernoulli distribution are formulated in terms of linear matrix inequalities. Eventually, the illustrated study are substantiated through two numerical examples and the simulation results manifest the advantage and accuracy of the proposed synchronization criteria.

Finite-time stochastic synchronization of fuzzy bi-directional associative memory neural networks with Markovian switching and mixed time delays via intermittent quantized control

<abstract><p>We are concerned in this paper with the finite-time synchronization problem for fuzzy bi-directional associative memory neural networks with Markovian switching, discrete-time delay in leakage terms, continuous-time and infinitely distributed delays in transmission terms. After detailed analysis, we come up with an intermittent quantized control for the concerned bi-directional associative memory neural network. By designing an elaborate Lyapunov-Krasovskii functional, we prove under certain additional conditions that the controlled network is stochastically synchronizable in finite time: The $ 1 $st moment of every trajectory of the error network system associated to the concerned controlled network tends to zero as time approaches a finite instant (the settling time) which is given explicitly, and remains to be zero constantly thereupon. In the meantime, we present a numerical example to illustrate that the synchronization control designed in this paper is indeed effective. Since the concerned fuzzy network includes Markovian jumping and several types of delays simultaneously, and it can be synchronized in finite time by our suggested control, as well as the suggested intermittent control is quantized which could reduce significantly the control cost, the theoretical results in this paper are rich in mathematical implication and have wide potential applicability in the real world.</p></abstract>

A Novel Method of Realizing Stochastic Chaotic Secure Communication by Synchrosqueezed Wavelet Transform: The Finite-Time Case

This paper is concerned with the finite-time stochastic synchronization of a chaotic system without linear term and its application in secure communication based on synchrosqueezed wavelet transform (SWT). In order to improve the anti-jamming ability of chaotic systems and forecast the synchronization time, proper controllers are designed to achieve finite-time stochastic synchronization for the chaotic system with random perturbation. Based on the proposed chaotic synchronization systems, we present secure communication scheme about secondary encryption to enhance the level of security. Moreover, a novel SWT algorithm is introduced to correctly recover information signals at the end of the scheme. The SWT based scheme can decompose the information signal into a set of intrinsic mode type (IMT) function components. Then, instantaneous frequency and instantaneous amplitude of each IMT component are calculated through Hilbert transform. Simulation results confirm that both the synchronization approach and the security communication scheme are effective. For multi-component signals with adjacent frequency, the accuracy of recovered signals by SWT based on our scheme is higher than that recovered by the other time-frequency denoising methods.

A switching control for finite-time synchronization of memristor-based BAM neural networks with stochastic disturbances

This paper deals with the finite-time stochastic synchronization for a class of memristorbased bidirectional associative memory neural networks (MBAMNNs) with time-varying delays and stochastic disturbances. Firstly, based on the physical property of memristor and the circuit of MBAMNNs, a MBAMNNs model with more reasonable switching conditions is established. Then, based on the theory of Filippov’s solution, by using Lyapunov–Krasovskii functionals and stochastic analysis technique, a sufficient condition is given to ensure the finite-time stochastic synchronization of MBAMNNs with a certain controller. Next, by a further discussion, an errordependent switching controller is given to shorten the stochastic settling time. Finally, numerical simulations are carried out to illustrate the effectiveness of theoretical results.

Finite-time stochastic synchronization of dynamic networks with nonlinear coupling strength via quantized intermittent control

This paper considers the finite-time synchronization of dynamic networks with nonlinear coupling strength and stochastic perturbations by using intermittent control. Since it is difficult to estimate the settling-time due to the uncertain intermittent intervals, a novel lemma is established. Then, two quantized intermittent controllers without chattering are designed, which can reduce the control cost and save channel resources. T-S fuzzy method is utilized to deal with the nonlinear coupling strength. By using Lyapunov direct method, sufficient conditions formulated by linear matrix inequalities (LMIs) are derived to ensure that the considered system can realize finite-time synchronization. Moreover, the control gains are designed. Two numerical simulations are given to show the merits of theoretical analysis.

Finite-Time Nonfragile Synchronization of Stochastic Complex Dynamical Networks with Semi-Markov Switching Outer Coupling

The problem of robust nonfragile synchronization is investigated in this paper for a class of complex dynamical networks subject to semi-Markov jumping outer coupling, time-varying coupling delay, randomly occurring gain variation, and stochastic noise over a desired finite-time interval. In particular, the network topology is assumed to follow a semi-Markov process such that it may switch from one to another at different instants. In this paper, the random gain variation is represented by a stochastic variable that is assumed to satisfy the Bernoulli distribution with white sequences. Based on these hypotheses and the Lyapunov-Krasovskii stability theory, a new finite-time stochastic synchronization criterion is established for the considered network in terms of linear matrix inequalities. Moreover, the control design parameters that guarantee the required criterion are computed by solving a set of linear matrix inequality constraints. An illustrative example is finally given to show the effectiveness and advantages of the developed analytical results.

Finite-time stochastic synchronization of time-delay neural networks with noise disturbance

The finite-time stochastic synchronization of time-delay neural networks with noise disturbance is investigated according to finite-time stability theory of stochastic differential equation. Via constructing suitable Lyapunov function and controllers, finite-time stochastic synchronization is realized and sufficient conditions are derived. By analyzing the synchronization progress, factors affecting the convergence speed are given and feasible suggestions are proposed to improve the convergence rate. Finally, numerical simulations are given to verify the theoretical results.

Finite-time stochastic synchronization of genetic regulatory networks

This paper is concerned with the finite-time synchronization for a class of stochastic genetic regulatory networks (GRNs). The purpose of the addressed problem is to design a controller that can synchronize the concentration of the mRNA and the protein of GRNs in finite time with probability. Based on the recent finite-time stability theorem of stochastic nonlinear systems, sufficient conditions are first established for ensuring the finite-time stochastic stability of synchronization error in probability. Then, the gain parameters of the controller are obtained by solving a linear matrix inequality and the robust finite-time synchronization is guaranteed for GRNs with uncertain parameters. Compared with the previous references, a continuous finite-time controller is designed to achieve the synchronization objective and a constructive method that may accelerate the convergence is discussed. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method.

Finite-time synchronization of chaotic systems with noise perturbation

In this paper, we investigate the finite-time stochastic synchronization problem of two chaotic systems with noise perturbation. We propose new adaptive controllers, with which we can synchronize two chaotic systems in finite time. Sufficient conditions for the finite-time stochastic synchronization are derived based on the finite-time stability theory of stochastic differential equations. Finally, some numerical examples are examined to demonstrate the effectiveness and feasibility of the theoretical results.

Finite-time synchronization of chaotic neural networks with mixed time-varying delays and stochastic disturbance

This paper treats of the finite-time stochastic synchronization problem of chaotic dynamic neural networks with mixed time-varying delays and stochastic disturbance. State feedback controller and adaptive controller are designed such that the response system can be finite-timely synchronized with corresponding drive system. Some novel and useful finite-time synchronization criteria are derived based on finite-time stability theory. A numerical example presents the effectiveness of our proposed methods.

Finite-Time Synchronization of Chaotic Complex Networks with Stochastic Disturbance

This paper is concerned with the problem of finite-time synchronization in complex networks with stochastic noise perturbations. By using a novel finite-time ℒ -operator differential inequality and other inequality techniques, some novel sufficient conditions are obtained to ensure finite-time stochastic synchronization for the complex networks concerned, where the coupling matrix need not be symmetric. The effects of control parameters on synchronization speed and time are also analyzed, and the synchronization time in this paper is shorter than that in the existing literature. The results here are also applicable to both directed and undirected weighted networks without any information of the coupling matrix. Finally, an example with numerical simulations is given to demonstrate the effectiveness of the proposed method.

Finite-time stochastic synchronization of complex networks

In this paper, we study the finite-time stochastic synchronization problem for complex networks with stochastic noise perturbations. By using finite-time stability theorem, inequality techniques, the properties of Weiner process and adding suitable controllers, sufficient conditions are obtained to ensure finite-time stochastic synchronization for the complex networks. The effects of control parameters on synchronization speed and time are also analyzed. The results of this paper are applicable to both directed and undirected weighted networks while do not need to know any information about eigenvalues of coupling matrix. Since finite-time synchronization means the optimality in convergence time and has better robustness and disturbance rejection properties, the results of this paper are important. A numerical example shows the effectiveness of our new results.