Exponential stability for markovian jumping stochastic BAM neural networks with mode-dependent probabilistic time-varying delays and impulse control

Abstract
In this article, an exponential stability analysis of Markovian jumping stochastic bidirectional associative memory (BAM) neural networks with mode-dependent probabilistic time-varying delays and impulsive control is investigated. By establishment of a stochastic variable with Bernoulli distribution, the information of probabilistic time-varying delay is considered and transformed into one with deterministic time-varying delay and stochastic parameters. By fully taking the inherent characteristic of such kind of stochastic BAM neural networks into account, a novel Lyapunov-Krasovskii functional is constructed with as many as possible positive definite matrices which depends on the system mode and a triple-integral term is introduced for deriving the delay-dependent stability conditions. Furthermore, mode-dependent mean square exponential stability criteria are derived by constructing a new Lyapunov-Krasovskii functional with modes in the integral terms and using some stochastic analysis techniques. The criteria are formulated in terms of a set of linear matrix inequalities, which can be checked efficiently by use of some standard numerical packages. Finally, numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results.

Development of a dynamic surface roughness monitoring system based on artificial neural networks (ANN) in milling operation

Dynamic surface roughness prediction during metal cutting operations plays an important role to enhance the productivity in manufacturing industries. Various machining parameters such as unwanted noises affect the surface roughness, whatever their effects have not been adequately quantified. In this study, a general dynamic surface roughness monitoring system in milling operations was developed. Based on the experimentally acquired data, the milling process of Al 7075 and St 52 parts was simulated. Cutting parameters (i.e., cutting speed, feed rate, and depth of cut), material type, coolant fluid, X and Z components of milling machine vibrations, and white noise were used as inputs. The original objective in the development of a dynamic monitoring system is to simulate wide ranges of machining conditions such as rough and finishing of several materials with and without cutting fluid. To achieve high accuracy of the resultant data, the full factorial design of experiment was used. To verify the accuracy of the proposed model, testing and recall/verification procedures have been carried out and results showed that the accuracy of 99.8 and 99.7 % were obtained for testing and recall processes.

Prediction interval-based control of nonlinear systems using neural networks

Prediction interval (PI) is a promising tool for quantifying uncertainties associated with point predictions. Despite its informativeness, the design and deployment of PI-based controller for complex systems is very rare. As a pioneering work, this paper proposes a framework for design and implementation of PI-based controller (PIC) for nonlinear systems. Neural network (NN)-based inverse model within internal model control structure is used to develop the PIC. Firstly, a PI-based model is developed to construct PIs for the system output. This model is then used as an online estimator for PIs. The PIs from this model are fed to the NN inverse model along with other traditional inputs to generate the control signal. The performance of the proposed PIC is examined for two case studies. This includes a nonlinear batch polymerization reactor and a numerical nonlinear plant. Simulation results demonstrated that the proposed PIC tracking performance is better than the traditional NN-based controller.

Dynamical analysis of neural networks with time-varying delays using the LMI approach

This study is concerned with the delay-range-dependent stability analysis for neural networks with time-varying delay and Markovian jumping parameters. The time-varying delay is assumed to lie in an interval of lower and upper bounds. The Markovian jumping parameters are introduced in delayed neural networks, which are modeled in a continuous-time along with finite-state Markov chain. Moreover, the sufficient condition is derived in terms of linear matrix inequalities based on appropriate Lyapunov-Krasovskii functionals and stochastic stability theory, which guarantees the globally asymptotic stable condition in the mean square. Finally, a numerical example is provided to validate the effectiveness of the proposed conditions.

New inequality-based approach to passivity analysis of neural networks with interval time-varying delay

This paper is concerned with the problem of passivity analysis of neural networks with an interval time-varying delay. Unlike existing results in the literature, the time-delay considered in this paper is subjected to interval time-varying without any restriction on the rate of change. Based on novel refined Jensen inequalities and by constructing an improved Lyapunov-Krasovskii functional (LKF), which fully utilizes information of the neuron activation functions, new delay-dependent conditions that ensure the passivity of the network are derived in terms of tractable linear matrix inequalities (LMIs) which can be effectively solved by various computational tools. The effectiveness and improvement over existing results of the proposed method in this paper are illustrated through numerical examples.

Passivity analysis of memristor-based complex-valued neural networks with time-varying delays

In this paper, the model of memristor-based complex-valued neural networks (MCVNNs) with time-varying delays is established and the problem of passivity analysis for MCVNNs is considered and extensively investigated. The analysis in this paper employs results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov. By employing the appropriate Lyapunov–Krasovskii functional, differential inclusion theory and linear matrix inequality (LMI) approach, some new sufficient conditions for the passivity of the given MCVNNs are obtained in terms of both complex-valued and real-value LMIs, which can be easily solved by using standard numerical algorithms. Numerical examples are provided to illustrate the effectiveness of our theoretical results.

Application of artificial neural networks in linear profile monitoring

In many quality control applications the quality of process or product is characterized and summarized by a relation (profile) between a response variable and one or more explanatory variables. Such profiles can be modeled using linear or nonlinear regression models. In this paper we use artificial neural networks to detect and classify the shifts in linear profiles. Three monitoring methods based on artificial neural networks are developed to monitor linear profiles. Their efficacies are assessed using average run length criterion. © 2010 Elsevier Ltd. All rights reserved.

Exponential stability of non-autonomous neural networks with heterogeneous time-varying delays and destabilizing impulses

In this paper, the problem of global exponential stability analysis of a class of non-autonomous neural networks with heterogeneous delays and time-varying impulses is considered. Based on the comparison principle, explicit conditions are derived in terms of testable matrix inequalities ensuring that the system is globally exponentially stableunder destabilizing impulsive effects. Numerical examples are given to demonstrate the effectiveness of the obtained results.

Exponential stabilization of non-autonomous delayed neural networks via Riccati equations

This paper concerns with the problem of exponential stabilization for a class of non-autonomous neural networks with mixed discrete and distributed time-varying delays. Two cases of discrete time-varying delay, namely (i) slowly time-varying; and (ii) fast time-varying, are considered. By constructing an appropriate Lyapunov-Krasovskii functional in case (i) and utilizing the Razumikhin technique in case (ii), we establish some new delay-dependent conditions for designing a memoryless state feedback controller which stabilizes the system with an exponential convergence of the resulting closed-loop system. The proposed conditions are derived through solutions of some types of Riccati differential equations. Applications to control a class of autonomous neural networks with mixed time-varying delays are also discussed in this paper. Some numerical examples are provided to illustrate the effectiveness of the obtained results.

On global dissipativity of nonautonomous neural networks with multiple proportional delays

This brief addresses the problem of global dissipativity analysis of nonautonomous neural networks with multiple proportional delays. By using a novel constructive approach based on some comparisontechniques for differential inequalities, new explicit delay-independentconditions are derived using M-matrix theory to ensure the existence ofgeneralized exponential attracting sets and the global dissipativity of thesystem. The method presented in this brief is also utilized to derive ageneralized exponential estimate for a class of Halanay-type inequalitieswith proportional delays. Finally, three numerical examples are given toillustrate the effectiveness and improvement of the obtained results.

Reachable sets bounding for generalized neural networks with interval time-varying delay and bounded disturbances

This paper deals with the problem of finding outer bound of forwards reachable sets and interbound of backwards reachable sets of generalized neural network systems with interval nondifferentiable time-varying delay and bounded disturbances. Based on constructing a suitable Lyapunov–Krasovskii functional and utilizing some improved Jensen integral-based inequalities, two sufficient conditions are derived for the existence of: (1) the smallest possible outer bound of forwards reachable sets and (2) the largest possible interbound of backwards reachable sets. These conditions are delay dependent and in the form of matrix inequalities, which therefore can be efficiently solved by using existing convex algorithms. Three numerical examples with simulation results are provided to demonstrate the effectiveness of our results.

On global exponential stability of positive neural networks with time-varying delay

This paper presents a new result on the existence, uniqueness and global exponential stability of a positive equilibrium of positiveneural networks in the presence of bounded time-varying delay. Based on some novel comparison techniques, a testable conditionis derived to ensure that all the state trajectories of the system converge exponentially to a unique positive equilibrium. Theeffectiveness of the obtained results is illustrated by a numerical example.

Neural choice by elimination via highway networks

We introduce Neural Choice by Elimination, a new framework that integrates deep neural networks into probabilistic sequential choice models for learning to rank. Given a set of items to chose from, the elimination strategy starts with the whole item set and iteratively eliminates the least worthy item in the remaining subset. We prove that the choice by elimination is equivalent to marginalizing out the random Gompertz latent utilities. Coupled with the choice model is the recently introduced Neural Highway Networks for approximating arbitrarily complex rank functions. We evaluate the proposed framework on a large-scale public dataset with over 425K items, drawn from the Yahoo! learning to rank challenge. It is demonstrated that the proposed method is competitive against state-of-the-art learning to rank methods.

Predicting worsted spinning performance with an artificial neural network model

For a given fiber spun to pre-determined yarn specifications, the spinning performance of the yarn usually varies from mill to mill. For this reason, it is necessary to develop an empirical model that can encompass all known processing variables that exist in different spinning mills, and then generalize this information and be able to accurately predict yarn quality for an individual mill. This paper reports a method for predicting worsted spinning performance with an artificial neural network (ANN) trained with backpropagation. The applicability of artificial neural networks for predicting spinning performance is first evaluated against a well established prediction and benchmarking tool (Sirolan YarnspecTM). The ANN is then subsequently trained with commercial mill data to assess the feasibility of the method as a mill-specific performance prediction tool. Incorporating mill-specific data results in an improved fit to the commercial mill data set, suggesting that the proposed method has the ability to predict the spinning performance of a specific mill accurately.

Predicting the pilling propensity of fabrics through artificial neural network modeling

Fabric pilling is affected by many interacting factors. This study uses artificial neural networks to model the multi-linear relationships between fiber, yarn and fabric properties and their effect on the pilling propensity of pure wool knitted fabrics. This tool shall enable the user to gauge the expected pilling performance of a fabric from a number of given inputs. It will also provide a means of improving current products by offering alternative material specification and/or selection. In addition to having the capability to predict pilling performance, the model will allow for clarification of major fiber, yarn and fabric attributes affecting fabric pilling.