The problem of bounded-input bounded-output (BIBO) stabilization for discrete-time uncertain system with time delay is investigated. By constructing an augmented Lyapunov function, some sufficient conditions guaranteeing BIBO stabilization and robust BIBO stabilization are established. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Two numerical examples are provided to demonstrate the effectiveness of the derived results.
This paper concerns the problem of delay-dependent stability criteria for recurrent neural networks with time varying delays. By taking more information of states and activation functions as augmented vectors, a new class of the Lyapunov functional is proposed. Then, some less conservative stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.
We generalize the concept of well-posedness by perturbations for optimization problem to a class of variational-hemivariational inequalities. We establish some metric characterizations of the well-posedness by perturbations for the variational-hemivariational inequality and prove their equivalence between the well-posedness by perturbations for the variational-hemivariational inequality and the well-posedness by perturbations for the corresponding inclusion problem.2 Journal of Applied Mathematics by a family or a sequence of functionals. For this reason, another important concept of wellposedness for optimization problem, which is called the well-posedness by perturbations or extended well-posedness, has been introduced and studied by 3-6 . Also, many other notions of well-posedness have been introduced and studied for optimization problem. For details, we refer to 7 and the reference therein.The concept well-posedness also has been generalized to other related problems, especially to the variational inequality problem. Lucchetti and Patrone 8 first introduced the well-posedness for a variational inequality, which can be regarded as an extension of the Tykhonov well-posedness of optimization problem. Since then, many authors were devoted to generalizing the concept of well-posedness for the optimization problem to various variational inequalities. In 9 , Huang et al. introduced several types of generalized Levitin-Polyak well-posednesses for a variational inequality problem with abstract and functional constraint and gave some criteria, characterizations, and their relations for these types of well-posednesses. Recently, Fang et al. 10 generalized the concept of well-posedness by perturbations, introduced by Zelezzi for a minimization problem, to a generalized mixed variational inequality problem in Banach space. They established some metric characterizations of well-posedness by perturbations and discussed its links with well-posedness by perturbations of corresponding inclusion problem and the well-posedness by perturbations of corresponding fixed point problem. Also they derived some conditions under which the well-posedness by perturbations of the mixed variational inequality is equivalent to the existence and uniqueness of its solution. For further more results on the well-posedness of variational inequalities, we refer to 8-15 and the references therein.When the corresponding energy functions are not convex, the mathematical model describing many important phenomena arising in mechanics and engineering is no longer variational inequality but a new type of inequality problem that is called hemivariational inequality, which was first introduced by Panagiotopoulos 16 as a generalization of variational inequality. A more generalized variational formulation which is called variationalhemivariational inequality is presented to model the problems subject to constraints because the setting of hemivariational inequalities cannot incorporate the indicator function of a convex closed subset. Due to the fact that the ...
Text classification is the critical content of machine learning, and it is widely applied in information filtering, sentimental analysis, and text review. It is very important to improve the accuracy of classification results, and this is also the main research purpose of researchers in this field in recent years. Feature selection plays an important role in text classification, which has the functions of eliminating irrelevant features, reducing dimensionality, and improving classification accuracy. So, this paper studies the CHI feature selection algorithm, and the main work and innovations are as follows: firstly, this paper analyzed the CHI algorithm’s flaws, determined that the introduction of new parameters will be the improvement direction of the CHI algorithm, and thus proposed a new algorithm based on variance and coefficient of variation. Secondly, experiment to verify the effectiveness of the new algorithm. In terms of language, the experiment in this paper includes two text classification systems, which were Chinese and English. In terms of classifiers, two classifier algorithms were used, which included the KNN classifier and the Naive Bayes classifier. In terms of data types, two distribution types of data were used: balanced datasets and unbalanced datasets. Finally, experiment and result analysis. This paper has conducted 3 comparative experiments and analyzed the results of each experiment. The experimental results obtained are all significantly improved compared to the results before the improvement.
The robust stability of uncertain discrete-time recurrent neural networks with time-varying delay is investigated. By decomposing some connection weight matrices, new Lyapunov-Krasovskii functionals are constructed, and serial new improved stability criteria are derived. These criteria are formulated in the forms of linear matrix inequalities LMIs . Compared with some previous results, the new results are less conservative. Three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed method.
In the existing research on time-series event prediction (TSEP) methods, most of the work is focused on improving the algorithm for classifying subsequence sets (sets composed of multiple adjacent subsequences). However, these prediction methods ignore the timing dependence between the subsequence sets, nor do they capture the mutual transition relationship between events, the prediction effect on a small sample data set is very poor. Meanwhile, the sequence labeling problem is one of the common problems in natural language processing and image segmentation. To solve this problem, this paper proposed a new framework for time-series event prediction, which transforms the event prediction problem into a labeling problem, to better capture the timing relationship between the subsequence sets. Specifically, the framework used a sequence clustering algorithm for the first time to identify representative patterns in the time series, then represented the set of subsequences as a weighted combination of patterns, and used the eXtreme gradient boosting algorithm (XGBoost) for feature selection. After that, the selected pattern feature was used as the input of the long-term short-term memory model (LSTM) to obtain the preliminary prediction value. Furthermore, the fully-linked conditional random field (CRF) was used to smooth and refine the preliminary prediction value to obtain the final prediction result. Finally, the experimental results of event prediction on five real data sets show that the CX-LC method has a certain improvement in prediction accuracy compared with the other six models.
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