Extended Dissipativity Analysis for Markovian Jump Neural Networks via Double-Integral-Based Delay-Product-Type Lyapunov Functional

A flexible membership-dependent functional method to stability and stabilization for T-S fuzzy systems with interval time-varying delay

In this paper, the stability and stabilization problems for T-S fuzzy delayed systems is studied. A flexible membership-dependent Lyapunov functional (FMDLF) is constructed to fully utilize the information of time-varying delay and fuzzy membership functions (FMFs). Different from some exiting ones, the upper and lower limits of the integral terms in the FMDLF are adjustable. By first introducing exponential gains in reciprocally convex inequality, an exponential-type reciprocally convex inequality (ETRCI) is developed to estimate the FMDLF, which generates some existing results. Based on the FMDLF and ETRCI, a novel stability criterion is obtained. By using a decoupling technique, the corresponding controller design problem is solved. Importantly, the dimensions of the solution space increase since the constraints on slack matrices in some previous studies are eliminated. The effectiveness of the proposed results can be demonstrated by some examples.

Pinning Spatiotemporal Sampled-Data Synchronization of Coupled Reaction-Diffusion Neural Networks Under Deception Attacks

In this article, we investigate the pinning spatiotemporal sampled-data (SD) synchronization of coupled reaction-diffusion neural networks (CRDNNs), which are directed networks with SD in time and space communications under random deception attacks. In order to handle with the random deception attacks, we establish a directed CRDNN model, which respects the impacts of variable sampling and random deception attacks within a unified framework. Through the designed pinning spatiotemporal SD controller, sufficient conditions are obtained by linear matrix inequalities (LMIs) that guarantee the mean square exponential stability of the synchronization error system (SES) derived by utilizing inequality techniques, the stochastic analysis technique, and Lyapunov-Krasovskii functional (LKF). Finally, a numerical example is utilized to support the presented pinning spatiotemporal SD synchronization method.

A Comprehensive Review of Continuous-/Discontinuous-Time Fractional-Order Multidimensional Neural Networks

The dynamical study of continuous-/discontinuous-time fractional-order neural networks (FONNs) has been thoroughly explored, and several publications have been made available. This study is designed to give an exhaustive review of the dynamical studies of multidimensional FONNs in continuous/discontinuous time, including Hopfield NNs (HNNs), Cohen-Grossberg NNs, and bidirectional associative memory NNs, and similar models are considered in real ( [Formula: see text]), complex ( [Formula: see text]), quaternion ( [Formula: see text]), and octonion ( [Formula: see text]) fields. Since, in practice, delays are unavoidable, theoretical findings from multidimensional FONNs with various types of delays are thoroughly evaluated. Some required and adequate stability and synchronization requirements are also mentioned for fractional-order NNs without delays.

Clustering Hidden Markov Models With Variational Bayesian Hierarchical EM

The hidden Markov model (HMM) is a broadly applied generative model for representing time-series data, and clustering HMMs attract increased interest from machine learning researchers. However, the number of clusters ( K ) and the number of hidden states ( S ) for cluster centers are still difficult to determine. In this article, we propose a novel HMM-based clustering algorithm, the variational Bayesian hierarchical EM algorithm, which clusters HMMs through their densities and priors and simultaneously learns posteriors for the novel HMM cluster centers that compactly represent the structure of each cluster. The numbers K and S are automatically determined in two ways. First, we place a prior on the pair (K,S) and approximate their posterior probabilities, from which the values with the maximum posterior are selected. Second, some clusters and states are pruned out implicitly when no data samples are assigned to them, thereby leading to automatic selection of the model complexity. Experiments on synthetic and real data demonstrate that our algorithm performs better than using model selection techniques with maximum likelihood estimation.

Delay-Variation-Dependent Criteria on Extended Dissipativity for Discrete-Time Neural Networks With Time-Varying Delay

This article is concerned with the extended dissipativity of discrete-time neural networks (NNs) with time-varying delay. First, the necessary and sufficient condition on matrix-valued polynomial inequalities reported recently is extended to a general case, where the variable of the polynomial does not need to start from zero. Second, a novel Lyapunov functional with a delay-dependent Lyapunov matrix is constructed by taking into consideration more information on nonlinear activation functions. By employing the Lyapunov functional method, a novel delay and its variation-dependent criterion are obtained to investigate the effects of the time-varying delay and its variation rate on several performances, such as H_∞ performance, passivity, and l₂-l_∞ performance, of a delayed discrete-time NN in a unified framework. Finally, a numerical example is given to show that the proposed criterion outperforms some existing ones.

Proportional-Integral State Estimator for Quaternion-Valued Neural Networks With Time-Varying Delays

This brief investigates the problem of state estimation of quaternion-valued neural networks (QVNNs) with time-varying delays. First, by extending the Jensen inequality to quaternion domain, an extended Jensen inequality with quaternion term is derived. Second, a class of proportional-integral state estimator (PISE) with exponential decay term is proposed. Then, by constructing a suitable Lyapunov-Krasovskii functional (LKF), some sufficient conditions are obtained to ensure the existence of the designed PISE and the gain matrices of the designed PISE can be directly computed. Simulations are given to illustrate the advantage of the proposed method.

Delayed Impulsive Control for Lag Synchronization of Delayed Neural Networks Involving Partial Unmeasurable States

In the framework of impulsive control, this article deals with the lag synchronization problem of neural networks involving partially unmeasurable states, where the time delay in impulses is fully addressed. Since the complexity of external environment and uncertainty of networks, which may lead to a result that the information of partial states is unmeasurable, the key problem for lag synchronization control is how to utilize the information of measurable states to design suitable impulsive control. By using linear matrix inequality (LMI) and transition matrix method coupled with dimension expansion technique, some sufficient conditions are derived to guarantee lag synchronization, where the requirement for information of all states is needless. Moreover, our proposed conditions not only allow the existence of unmeasurable states but also reduce the restrictions on the number of measurable states, which shows the generality of our results and wide-application in practice. Finally, two illustrative examples and their numerical simulations are presented to demonstrate the effectiveness of main results.

Competency of Neural Networks for the Numerical Treatment of Nonlinear Host-Vector-Predator Model

The aim of this work is to introduce a stochastic solver based on the Levenberg-Marquardt backpropagation neural networks (LMBNNs) for the nonlinear host-vector-predator model. The nonlinear host-vector-predator model is dependent upon five classes, susceptible/infected populations of host plant, susceptible/infected vectors population, and population of predator. The numerical performances through the LMBNN solver are observed for three different types of the nonlinear host-vector-predator model using the authentication, testing, sample data, and training. The proportions of these data are chosen as a larger part, i.e., 80% for training and 10% for validation and testing, respectively. The nonlinear host-vector-predator model is numerically treated through the LMBNNs, and comparative investigations have been performed using the reference solutions. The obtained results of the model are presented using the LMBNNs to reduce the mean square error (MSE). For the competence, exactness, consistency, and efficacy of the LMBNNs, the numerical results using the proportional measures through the MSE, error histograms (EHs), and regression/correlation are performed.