Xinsong Yang

Synchronization of Markovian Coupled Neural Networks With Nonidentical Node-Delays and Random Coupling Strengths

In this paper, a general model of coupled neural networks with Markovian jumping and random coupling strengths is introduced. In the process of evolution, the proposed model switches from one mode to another according to a Markovian chain, and all the modes have different constant time-delays. The coupling strengths are characterized by mutually independent random variables. When compared with most of existing dynamical network models which share common time-delay for all modes and have constant coupling strengths, our model is more practical because different chaotic neural network models can have different time-delays and coupling strength of complex networks may randomly vary around a constant due to environmental and artificial factors. By designing a novel Lyapunov functional and using some inequalities and the properties of random variables, we derive several new sufficient synchronization criteria formulated by linear matrix inequalities. The obtained criteria depend on mode-delays and mathematical expectations and variances of the random coupling strengths as well. Numerical examples are given to demonstrate the effectiveness of the theoretical results, meanwhile right-continuous Markovian chain is also presented.

p th moment exponential stochastic synchronization of coupled memristor-based neural networks with mixed delays via delayed impulsive control

This paper concerns the pth moment synchronization in an array of generally coupled memristor-based neural networks with time-varying discrete delays, unbounded distributed delays, as well as stochastic perturbations. Hybrid controllers are designed to cope with the uncertainties caused by the state-dependent parameters: (a) state feedback controllers combined with delayed impulsive controller; (b) adaptive controller combined with delayed impulsive controller. Based on an impulsive differential inequality, the properties of random variables, the framework of Filippov solution, and Lyapunov functional method, sufficient conditions are derived to guarantee that the considered coupled memristor-based neural networks can be pth moment globally exponentially synchronized onto an isolated node under both of the two classes of hybrid impulsive controllers. Finally, numerical simulations are given to show the effectiveness of the theoretical results.

Exponential Synchronization of Memristive Neural Networks With Delays: Interval Matrix Method

This paper considers the global exponential synchronization of drive-response memristive neural networks (MNNs) with heterogeneous time-varying delays. Because the parameters of MNNs are state-dependent, the MNNs may exhibit unexpected parameter mismatch when different initial conditions are chosen. Therefore, traditional robust control scheme cannot guarantee the synchronization of MNNs. Under the framework of Filippov solution, the drive and response MNNs are first transformed into systems with interval parameters. Then suitable controllers are designed to overcome the problem of mismatched parameters and synchronize the coupled MNNs. Based on some novel Lyapunov functionals and interval matrix inequalities, several sufficient conditions are derived to guarantee the exponential synchronization. Moreover, adaptive control is also investigated for the exponential synchronization. Numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

Vector variational-like inequality with pseudoinvexity

In this article, some properties of pseudoinvex functions are given and relations between vector variational-like inequalities and vector optimization problems are discussed under pseudoinvexity and invariant pseudomonotonicity conditions, respectively.

Synchronization of discrete-time neural networks with delays and Markov jump topologies based on tracker information

In this paper, synchronization in an array of discrete-time neural networks (DTNNs) with time-varying delays coupled by Markov jump topologies is considered. It is assumed that the switching information can be collected by a tracker with a certain probability and transmitted from the tracker to controller precisely. Then the controller selects suitable control gains based on the received switching information to synchronize the network. This new control scheme makes full use of received information and overcomes the shortcomings of mode-dependent and mode-independent control schemes. Moreover, the proposed control method includes both the mode-dependent and mode-independent control techniques as special cases. By using linear matrix inequality (LMI) method and designing new Lyapunov functionals, delay-dependent conditions are derived to guarantee that the DTNNs with Markov jump topologies to be asymptotically synchronized. Compared with existing results on Markov systems which are obtained by separately using mode-dependent and mode-independent methods, our result has great flexibility in practical applications. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results.

Finite-Time Synchronization of Complex-Valued Neural Networks with Mixed Delays and Uncertain Perturbations

This paper concerns the problem of finite-time synchronization for a class of complex-valued neural networks (CVNNs) with both time-varying and infinite-time distributed delays (mixed delays). Both the driving and response CVNNs are disturbed by external uncertain perturbations, which may be nonidentical. A simple state-feedback controller is designed such that the response CVNNs can be synchronized with the driving system in a settling time. By using inequality techniques and constructing some new Lyapunov–Krasovskii functionals, several sufficient conditions are derived to ensure the synchronization. It is discovered that the settling time cannot be estimated when the interested CVNNs exhibit infinite-time distributed delays, while it can be explicitly estimated for the CVNNs with bounded delays. The settling time is dependent on both the delays and the initial value of the error system. Finally, numerical simulations demonstrate the effectiveness of the theoretical results.

Finite-time synchronization for competitive neural networks with mixed delays and non-identical perturbations

This paper considers the drive-response synchronization in finite time of competitive neural networks (CNNs) with different time scales, time-varying and infinite-time distributed delays (mixed delays), as well as uncertain non-linear perturbations. The drive and response systems are disturbed by different uncertain non-linear perturbations. The effects of the non-identical uncertain non-linear perturbations are suppressed by designing some simple controllers. Moreover, by designing new Lyapunov-Krasovskii functionals, sufficient conditions are obtained to guarantee that the CNNs can be synchronized in a setting time without using existing finite-time stability theorem. Furthermore, the setting time is explicitly estimated for CNNs with bounded distributed delay and without delay. It is shown that the setting time is dependent on the time delays and the initial values of the coupled CNNs. Some results on synchronization of CNNs are essentially extended. Finally, numerical examples are provided to illustrate the effectiveness of the presented synchronization scheme.

Exponential synchronization of complex-valued complex networks with time-varying delays and stochastic perturbations via time-delayed impulsive control

Considering the fact that time delays are unavoidable in the control of practical systems, this paper considers globally exponential synchronization of complex-valued complex dynamical networks with multiple time-varying delays and stochastic perturbations by designing a time-delayed impulsive control scheme. By taking the advantage of Lyapunov method in complex field and utilizing an impulsive inequality with delays, several synchronization criteria are obtained through strict mathematical proofs. Our results are general which extend some existing ones concerning impulsive synchronization. A numerical example is given to illustrate the effectiveness of theoretical results.

Finite-Time Synchronization of Discontinuous Neural Networks With Delays and Mismatched Parameters

This paper investigates the problem of finite-time drive-response synchronization for a class of neural networks with discontinuous activations, time-varying discrete and infinite-time distributed delays, and mismatched parameters. In order to cope with the difficulties induced by discontinuous activations, time delays, as well as mismatched parameters simultaneously, new 1-norm-based analytical techniques are developed. Both state feedback and adaptive controllers with and without the sign function are designed. Based on differential inclusion theory and Lyapunov functional method, several sufficient conditions on the finite-time synchronization are obtained. Our results show that the controllers with a sign function can reduce the conservativeness of control gains and the controllers without a sign function can overcome the chattering phenomenon. Numerical examples are given to show the effectiveness of the theoretical analysis.

Finite-Time Synchronization of Coupled Markovian Discontinuous Neural Networks with Mixed Delays

This paper is concerned with finite-time synchronization in an array of coupled neural networks with discontinuous activation functions, Markovian jumping parameters, as well as discrete and infinite-time distributed delays (mixed delays) under the framework of Filippov solution. Based on novel Lyapunov–Krasovskii functionals and analytical techniques and M-matrix method, the difficulties caused by the uncertainties of Filippov solutions, time delays, as well as Markov chain are overcome. Several sufficient conditions are obtained to guarantee the synchronization in finite time. Different from existing results on finite-time synchronization of non-delayed systems, the settling time for time-delay systems is dependent not only on the values of the error state at time zero, but also on the histories of the error state, the time delays, and the initial value of Markov chain. Moreover, finite-time synchronization of the coupled neural networks with nonidentical uncertain perturbations is also considered. The obtained results are also applicable to continuous nonlinear systems, which essentially extend existing results which can only finite-timely synchronize or stabilize non-delayed systems. Finally, numerical examples are given demonstrate the effectiveness of the theoretical results.