Stability Analysis for Delayed Neural Networks via a Generalized Reciprocally Convex Inequality.

This article deals with the stability of neural networks (NNs) with time-varying delay. First, a generalized reciprocally convex inequality (RCI) is presented, providing a tight bound for reciprocally convex combinations. This inequality includes some existing ones as special case. Second, in order to cater for the use of the generalized RCI, a novel Lyapunov-Krasovskii functional (LKF) is constructed, which includes a generalized delay-product term. Third, based on the generalized RCI and the novel LKF, several stability criteria for the delayed NNs under study are put forward. Finally, two numerical examples are given to illustrate the effectiveness and advantages of the proposed stability criteria.

Event-Triggered Output Feedback Synchronization of Master-Slave Neural Networks Under Deception Attacks.

The problem of event-triggered synchronization of master-slave neural networks is investigated in this article. It is assumed that both communication channels from the sensor to controller and from controller to actuator are subject to stochastic deception attacks modeled by two independent Markov processes. Two discrete event-triggered mechanisms are introduced for both channels to reduce the number of data transmission through the communication channels. To comply with practical point of view, static output feedback is utilized. By employing the Lyapunov-Krasovskii functional method, some sufficient conditions on the synchronization of master-slave neural networks are derived in terms of linear matrix inequalities, which make it easy to design suitable output feedback controllers. Finally, a numerical example is presented to show the effectiveness of the proposed method.

Indoor occurrence and health risk of formaldehyde, toluene, xylene and total volatile organic compounds derived from an extensive monitoring campaign in Harbin, a megacity of China.

Human exposure to formaldehyde, toluene, xylene (FTX) and other volatile organic compounds (VOCs) are associated with negative health impact. To characterize the exposure and health effects of FTX and TVOC from indoor environments, we conducted an extensive monitoring campaign involving 1278 measurements of 472 indoor locations in Harbin, a megacity in China from May 2013 to March 2018. The results showed that household had the highest mean formaldehyde concentration (0.171 ± 0.084 mg m-3) among all types of indoor environments. Meanwhile, there was no significant differences in formaldehyde concentration of the living room, master bedroom, secondary bedroom and study room (p > 0.05), as well as toluene and xylene. The highest mean concentration of toluene, xylene and TVOC was measured in public bath center. Great difference was found between formaldehyde concentrations in 2013 and other years, except 2015. There were great positive nonlinear correlations between the indoor temperature and concentration of formaldehyde (p < 0.01), good negative nonlinear correlations between the finish time of decoration and concentration of formaldehyde (p < 0.01), good positive linear correlations between the relative humidity and concentration of formaldehyde (p < 0.01). A risk assessment methodology was utilized to evaluate the potential adverse health effects of the individual FTX compounds according to their carcinogenicities. The predicted carcinogenic risk of formaldehyde was greater than the threshold value 1E-06 at all environments. The non-carcinogenic risk of TX compounds in the population is negligible. For estimating human health risk exposure, sensitivity analysis showed that more attention should be given to the influential variables such as the level of pollutants.

Hierarchical Type Stability Criteria for Delayed Neural Networks via Canonical Bessel-Legendre Inequalities.

This paper is concerned with global asymptotic stability of delayed neural networks. Notice that a Bessel-Legendre inequality plays a key role in deriving less conservative stability criteria for delayed neural networks. However, this inequality is in the form of Legendre polynomials and the integral interval is fixed on . As a result, the application scope of the Bessel-Legendre inequality is limited. This paper aims to develop the Bessel-Legendre inequality method so that less conservative stability criteria are expected. First, by introducing a canonical orthogonal polynomial sequel, a canonical Bessel-Legendre inequality and its affine version are established, which are not explicitly in the form of Legendre polynomials. Moreover, the integral interval is shifted to a general one . Second, by introducing a proper augmented Lyapunov-Krasovskii functional, which is tailored for the canonical Bessel-Legendre inequality, some sufficient conditions on global asymptotic stability are formulated for neural networks with constant delays and neural networks with time-varying delays, respectively. These conditions are proven to have a hierarchical feature: the higher level of hierarchy, the less conservatism of the stability criterion. Finally, three numerical examples are given to illustrate the efficiency of the proposed stability criteria.

State Estimation for Static Neural Networks With Time-Varying Delays Based on an Improved Reciprocally Convex Inequality.

This brief is concerned with the problem of neural state estimation for static neural networks with time-varying delays. Notice that a Luenberger estimator can produce an estimation error irrespective of the neuron state trajectory. This brief provides a method for designing such an estimator for static neural networks with time-varying delays. First, in-depth analysis on a well-used reciprocally convex approach is made, leading to an improved reciprocally convex inequality. Second, the improved reciprocally convex inequality and some integral inequalities are employed to provide a tight upper bound on the time-derivative of some Lyapunov-Krasovskii functional. As a result, a novel bounded real lemma (BRL) for the resultant error system is derived. Third, the BRL is applied to present a method for designing suitable Luenberger estimators in terms of solutions of linear matrix inequalities with two tuning parameters. Finally, it is shown through a numerical example that the proposed method can derive less conservative results than some existing ones.

A Novel Finite-Sum Inequality-Based Method for Robust $H_\infty$ Control of Uncertain Discrete-Time Takagi-Sugeno Fuzzy Systems With Interval-Like Time-Varying Delays.

This paper is concerned with the problem of robust ${H}_{\infty}$ control of an uncertain discrete-time Takagi-Sugeno fuzzy system with an interval-like time-varying delay. A novel finite-sum inequality-based method is proposed to provide a tighter estimation on the forward difference of certain Lyapunov functional, leading to a less conservative result. First, an auxiliary vector function is used to establish two finite-sum inequalities, which can produce tighter bounds for the finite-sum terms appearing in the forward difference of the Lyapunov functional. Second, a matrix-based quadratic convex approach is employed to equivalently convert the original matrix inequality including a quadratic polynomial on the time-varying delay into two boundary matrix inequalities, which delivers a less conservative bounded real lemma (BRL) for the resultant closed-loop system. Third, based on the BRL, a novel sufficient condition on the existence of suitable robust ${H}_{\infty}$ fuzzy controllers is derived. Finally, two numerical examples and a computer-simulated truck-trailer system are provided to show the effectiveness of the obtained results.

Global Asymptotic Stability for Delayed Neural Networks Using an Integral Inequality Based on Nonorthogonal Polynomials.

This brief is concerned with global asymptotic stability of a neural network with a time-varying delay. First, by introducing an auxiliary vector with some nonorthogonal polynomials, a slack-matrix-based integral inequality is established, which includes some existing one as its special case. Second, a novel Lyapunov-Krasovskii functional is constructed to suit for the use of the obtained integral inequality. As a result, a less conservative stability criterion is derived, whose effectiveness is finally demonstrated through two well-used numerical examples.

Application of low-cost algal nitrogen source feeding in fuel ethanol production using high gravity sweet potato medium.

Protein-rich bloom algae biomass was employed as nitrogen source in fuel ethanol fermentation using high gravity sweet potato medium containing 210.0 g l(-1) glucose. In batch mode, the fermentation could not accomplish even in 120 h without any feeding of nitrogen source. While, the feeding of acid-hydrolyzed bloom algae powder (AHBAP) notably promoted fermentation process but untreated bloom algae powder (UBAP) was less effective than AHBAP. The fermentation times were reduced to 96, 72, and 72 h if 5.0, 10.0, and 20.0 g l(-1) AHBAP were added into medium, respectively, and the ethanol yields and productivities increased with increasing amount of feeding AHBAP. The continuous fermentations were performed in a three-stage reactor system. Final concentrations of ethanol up to 103.2 and 104.3 g l(-1) with 4.4 and 5.3 g l(-1) residual glucose were obtained using the previously mentioned medium feeding with 20.0 and 30.0 g l(-1) AHBAP, at dilution rate of 0.02 h(-1). Notably, only 78.5 g l(-1) ethanol and 41.6 g l(-1) residual glucose were obtained in the comparative test without any nitrogen source feeding. Amino acids analysis showed that approximately 67% of the protein in the algal biomass was hydrolyzed and released into the medium, serving as the available nitrogen nutrition for yeast growth and metabolism. Both batch and continuous fermentations showed similar fermentation parameters when 20.0 and 30.0 g l(-1) AHBAP were fed, indicating that the level of available nitrogen in the medium should be limited, and an algal nitrogen source feeding amount higher than 20.0 g l(-1) did not further improve the fermentation performance.