Mode-dependent stochastic stability criteria of fuzzy Markovian jumping neural networks with mixed delays

This paper investigates the stochastic stability of fuzzy Markovian jumping neural networks with mixed delays in mean square. The mixed delays include time-varying delay and continuously distributed delay. By using the Lyapunov functional method, Jensen integral inequality, the generalized Jensen integral inequality, linear convex combination technique and the free-weight matrix method, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks in mean square. The proposed results, which do not require the differentiability of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.

The stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms

The global asymptotic stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms is investigated. Under some suitable assumptions and using Lyapunov-Krasovskii functional method, we apply the linear matrix inequality technique to propose some new sufficient conditions for the global asymptotic stability of the addressed model in the stochastic sense. The mixed time delays comprise both the time-varying and continuously distributed delays. The effectiveness of the theoretical result is illustrated by a numerical example.

Modeling of batch processes using explicitly time-dependent artificial neural networks

A neural network architecture incorporating time dependency explicitly, proposed recently, for modeling nonlinear nonstationary dynamic systems is further developed in this paper, and three alternate configurations are proposed to represent the dynamics of batch chemical processes. The first configuration consists of L subnets, each having M inputs representing the past samples of process inputs and output; each subnet has a hidden layer with polynomial activation function; the outputs of the hidden layer are combined and acted upon by an explicitly time-dependent modulation function. The outputs of all the subnets are summed to obtain the output prediction. In the second configuration, additional weights are incorporated to obtain a more generalized model. In the third configuration, the subnets are eliminated by incorporating an additional hidden layer consisting of L nodes. Backpropagation learning algorithm is formulated for each of the proposed neural network configuration to determine the weights, the polynomial coefficients, and the modulation function parameters. The modeling capability of the proposed neural network configuration is evaluated by employing it to represent the dynamics of a batch reactor in which a consecutive reaction takes place. The results show that all the three time-varying neural networks configurations are able to represent the batch reactor dynamics accurately, and it is found that the third configuration is exhibiting comparable or better performance over the other two configurations while requiring much smaller number of parameters. The modeling ability of the third configuration is further validated by applying to modeling a semibatch polymerization reactor challenge problem. This paper illustrates that the proposed approach can be applied to represent dynamics of any batch/semibatch process.

Lagrange stability of memristive neural networks with discrete and distributed delays

Memristive neuromorphic system is a good candidate for creating artificial brain. In this paper, a general class of memristive neural networks with discrete and distributed delays is introduced and studied. Some Lagrange stability criteria dependent on the network parameters are derived via nonsmooth analysis and control theory. In particular, several succinct criteria are provided to ascertain the Lagrange stability of memristive neural networks with and without delays. The proposed Lagrange stability criteria are the improvement and extension of the existing results in the literature. Three numerical examples are given to show the superiority of theoretical results.

Further results on robustness analysis of global exponential stability of recurrent neural networks with time delays and random disturbances

In this paper, further results on robustness analysis of global exponential stability of recurrent neural networks (RNNs) subjected to time delays and random disturbances are provided. Novel exponential stability criteria for the RNNs are derived, and upper bounds of the time delay and noise intensity are characterized by solving transcendental equations containing adjustable parameters. Through the selection of the adjustable parameters, the upper bounds are improved. It shows that our results generalize and improve the corresponding results of recent works. In addition, some numerical examples are given to show the effectiveness of the results we obtained.

Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled data

In this paper, the problem of sampled-data synchronization for Markovian jump neural networks with time-varying delay and variable samplings is considered. In the framework of the input delay approach and the linear matrix inequality technique, two delay-dependent criteria are derived to ensure the stochastic stability of the error systems, and thus, the master systems stochastically synchronize with the slave systems. The desired mode-independent controller is designed, which depends upon the maximum sampling interval. The effectiveness and potential of the obtained results is verified by two simulation examples.

Global exponential stability of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays

In this paper, a class of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays is investigated. The jumping parameters are modeled as a continuous-time finite-state Markov chain. At first, the existence of equilibrium point for the addressed neural networks is studied. By utilizing the Lyapunov stability theory, stochastic analysis theory and linear matrix inequality (LMI) technique, new delay-dependent stability criteria are presented in terms of linear matrix inequalities to guarantee the neural networks to be globally exponentially stable in the mean square. Numerical simulations are carried out to illustrate the main results.

Dynamics of random Boolean networks under fully asynchronous stochastic update based on linear representation

A novel algebraic approach is proposed to study dynamics of asynchronous random Boolean networks where a random number of nodes can be updated at each time step (ARBNs). In this article, the logical equations of ARBNs are converted into the discrete-time linear representation and dynamical behaviors of systems are investigated. We provide a general formula of network transition matrices of ARBNs as well as a necessary and sufficient algebraic criterion to determine whether a group of given states compose an attractor of length[Formula: see text] in ARBNs. Consequently, algorithms are achieved to find all of the attractors and basins in ARBNs. Examples are showed to demonstrate the feasibility of the proposed scheme.

On stabilization of stochastic Cohen-Grossberg neural networks with mode-dependent mixed time-delays and Markovian switching

The globally exponential stabilization problem is investigated for a general class of stochastic Cohen-Grossberg neural networks with both Markovian jumping parameters and mixed mode-dependent time-delays. The mixed time-delays consist of both discrete and distributed delays. This paper aims to design a memoryless state feedback controller such that the closed-loop system is stochastically exponentially stable in the mean square sense. By introducing a new Lyapunov-Krasovskii functional that accounts for the mode-dependent mixed delays, stochastic analysis is conducted in order to derive delay-dependent criteria for the exponential stabilization problem. Three numerical examples are carried out to demonstrate the feasibility of our delay-dependent stabilization criteria.

Robustness analysis for connection weight matrices of global exponential stability of stochastic recurrent neural networks

This paper analyzes the robustness of global exponential stability of stochastic recurrent neural networks (SRNNs) subject to parameter uncertainty in connection weight matrices. Given a globally exponentially stable stochastic recurrent neural network, the problem to be addressed here is how much parameter uncertainty in the connection weight matrices that the neural network can remain to be globally exponentially stable. We characterize the upper bounds of the parameter uncertainty for the recurrent neural network to sustain global exponential stability. A numerical example is provided to illustrate the theoretical result.

Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects

This paper focuses on the hybrid effects of parameter uncertainty, stochastic perturbation, and impulses on global stability of delayed neural networks. By using the Ito formula, Lyapunov function, and Halanay inequality, we established several mean-square stability criteria from which we can estimate the feasible bounds of impulses, provided that parameter uncertainty and stochastic perturbations are well-constrained. Moreover, the present method can also be applied to general differential systems with stochastic perturbation and impulses.

Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays

This paper discusses the issue of stability analysis for a class of impulsive stochastic bidirectional associative memory neural networks with both Markovian jump parameters and mixed time delays. The jumping parameters are modeled as a continuous-time discrete-state Markov chain. Based on a novel Lyapunov-Krasovskii functional, the generalized Itô's formula, mathematical induction, and stochastic analysis theory, a linear matrix inequality approach is developed to derive some novel sufficient conditions that guarantee the exponential stability in the mean square of the equilibrium point. At the same time, we also investigate the robustly exponential stability in the mean square of the corresponding system with unknown parameters. It should be mentioned that our stability results are delay-dependent, which depend on not only the upper bounds of time delays but also their lower bounds. Moreover, the derivatives of time delays are not necessarily zero or smaller than one since several free matrices are introduced in our results. Consequently, the results obtained in this paper are not only less conservative but also generalize and improve many earlier results. Finally, two numerical examples and their simulations are provided to show the effectiveness of the theoretical results.