It is revealed that the dynamic stability of 2-D recursive continuous-discrete systems with interval parameters involves the problem of robust Hurwitz-Schur stability of bivariate polynomials family. It is proved that...It is revealed that the dynamic stability of 2-D recursive continuous-discrete systems with interval parameters involves the problem of robust Hurwitz-Schur stability of bivariate polynomials family. It is proved that the Hurwitz-Schur stability of the denominator polynomials of the systems is necessary and sufficient for the asymptotic stability of the 2-D hybrid systems. The 2-D hybrid transformation, i. e. 2-D Laplace-Z transformation, has been proposed to solve the stability analysis of the 2-D continuous-discrete systems, to get the 2-D hybrid transfer functions of the systems. The edge test for the Hurwitz-Schur stability of interval bivariate polynomials is introduced. The Hurwitz-Schur stability of the interval family of 2-D polynomials can be guaranteed by the stability of its finite edge polynomials of the family. An algorithm about the stability test of edge polynomials is given.展开更多
This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on th...This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.展开更多
In this paper,a class of unconstrained discrete minimax problems is described,in which the objective functions are in C 1.The paper deals with this problem by means of taking the place of maximum entropy function...In this paper,a class of unconstrained discrete minimax problems is described,in which the objective functions are in C 1.The paper deals with this problem by means of taking the place of maximum entropy function with adjustable entropy function.By constructing an interval extension of adjustable entropy function an d some region deletion test rules,a new interval algorithm is presented.The rele vant properties are proven.The minimax value and the localization of the minimax points of the problem can be obtained by this method. This method can overcome the flow problem in the maximum entropy algorithm.Both theoretical and numerica l results show that the method is reliable and efficient.展开更多
An interval algorlthm for inequality coustrained discrete minimax problems is described, in which the constrained and objective functions are C1 functions. First, based on the penalty function methods, we trans form t...An interval algorlthm for inequality coustrained discrete minimax problems is described, in which the constrained and objective functions are C1 functions. First, based on the penalty function methods, we trans form this problem to unconstrained optimization. Second, the interval extensions of the penalty functions and the test rules of region deletion are discussed. At last, we design an interval algorithm with the bisection rule of Moore. The algorithm provides bounds on both the minimax value and the localization of the minimax points of the problem. Numerical results show that algorithm is reliable and efficiency.展开更多
Let X denote a discrete distribution as Poisson, binomial or negative binomial variable. The score confidence interval for the mean of X is obtained based on inverting the hypothesis test and the central limit theorem...Let X denote a discrete distribution as Poisson, binomial or negative binomial variable. The score confidence interval for the mean of X is obtained based on inverting the hypothesis test and the central limit theorem is discussed and recommended widely. But it has sharp downward spikes for small means. This paper proposes to move the score interval left a little (about 0.04 unit), called by moved score confidence interval. Numerical computation and Edgeworth expansion show that the moved score interval is analogous to the score interval completely and behaves better for moderate means;for small means the moved interval raises the infimum of the coverage probability and improves the sharp spikes significantly. Especially, it has unified explicit formulations to compute easily.展开更多
In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-str...In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-strength interference( SSI) model based on classical probabilistic approach can not be used to evaluate reliabilities of components. To solve this issue, the traditional universal generating function( UGF) is introduced and then it is extended to represent the discrete interval-valued random variable.Based on the extended UGF,an improved discrete interval-valued SSI model is proposed, which has higher calculation precision compared with the existing methods. Finally,an illustrative case is given to demonstrate the validity of the proposed model.展开更多
The problem of passivity analysis for a class of discrete-time stochastic neural networks (DSNNs) with time-varying interval delay was investigated. The delay-dependent sufficient criteria were derived in terms of lin...The problem of passivity analysis for a class of discrete-time stochastic neural networks (DSNNs) with time-varying interval delay was investigated. The delay-dependent sufficient criteria were derived in terms of linear matrix inequalities (LMIs). The results are shown to be generalization of some previous results and are less conservative than the existing works. Meanwhile, the computational complexity of the obtained stability conditions is reduced because less variables are involved. A numerical example is given to show the effectiveness and the benefits of the proposed method.展开更多
Fusing the structure feature of interval concept lattice and the actual needs of rough control rules,we have constructed the decision interval concept lattice,further more,we also have built a rules mining model of ro...Fusing the structure feature of interval concept lattice and the actual needs of rough control rules,we have constructed the decision interval concept lattice,further more,we also have built a rules mining model of rough control based on decision interval concept lattice,in order to achieve the optimality between rough control mining cost and control efficiency.Firstly,we have preprocessed the collected original data,so that we can transform it into Boolean formal context form,and then we have constructed the decision interval concept lattice in rough control;secondly,we have established the control rules mining algorithm based on decision interval concept lattice.By analyzing and judging redundant rules,we have formed the rough control association rule base in end.Analysis shows that under the premise of improving the reliability of rules,we have achieved the rough control optimization goal between cost and efficiency.Finally,the model of reservoir scheduling has verified its feasibility and efficiency.展开更多
基金This project was supported by National Natural Science Foundation of China (69971002).
文摘It is revealed that the dynamic stability of 2-D recursive continuous-discrete systems with interval parameters involves the problem of robust Hurwitz-Schur stability of bivariate polynomials family. It is proved that the Hurwitz-Schur stability of the denominator polynomials of the systems is necessary and sufficient for the asymptotic stability of the 2-D hybrid systems. The 2-D hybrid transformation, i. e. 2-D Laplace-Z transformation, has been proposed to solve the stability analysis of the 2-D continuous-discrete systems, to get the 2-D hybrid transfer functions of the systems. The edge test for the Hurwitz-Schur stability of interval bivariate polynomials is introduced. The Hurwitz-Schur stability of the interval family of 2-D polynomials can be guaranteed by the stability of its finite edge polynomials of the family. An algorithm about the stability test of edge polynomials is given.
基金supported by the National Natural Science Foundation of China(7090104171171113)the Aeronautical Science Foundation of China(2014ZG52077)
文摘This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.
基金Supported by the National Natural Science Foundation of China(50 1 740 51 )
文摘In this paper,a class of unconstrained discrete minimax problems is described,in which the objective functions are in C 1.The paper deals with this problem by means of taking the place of maximum entropy function with adjustable entropy function.By constructing an interval extension of adjustable entropy function an d some region deletion test rules,a new interval algorithm is presented.The rele vant properties are proven.The minimax value and the localization of the minimax points of the problem can be obtained by this method. This method can overcome the flow problem in the maximum entropy algorithm.Both theoretical and numerica l results show that the method is reliable and efficient.
文摘An interval algorlthm for inequality coustrained discrete minimax problems is described, in which the constrained and objective functions are C1 functions. First, based on the penalty function methods, we trans form this problem to unconstrained optimization. Second, the interval extensions of the penalty functions and the test rules of region deletion are discussed. At last, we design an interval algorithm with the bisection rule of Moore. The algorithm provides bounds on both the minimax value and the localization of the minimax points of the problem. Numerical results show that algorithm is reliable and efficiency.
文摘Let X denote a discrete distribution as Poisson, binomial or negative binomial variable. The score confidence interval for the mean of X is obtained based on inverting the hypothesis test and the central limit theorem is discussed and recommended widely. But it has sharp downward spikes for small means. This paper proposes to move the score interval left a little (about 0.04 unit), called by moved score confidence interval. Numerical computation and Edgeworth expansion show that the moved score interval is analogous to the score interval completely and behaves better for moderate means;for small means the moved interval raises the infimum of the coverage probability and improves the sharp spikes significantly. Especially, it has unified explicit formulations to compute easily.
基金National Natural Science Foundation of China(No.51265025)
文摘In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-strength interference( SSI) model based on classical probabilistic approach can not be used to evaluate reliabilities of components. To solve this issue, the traditional universal generating function( UGF) is introduced and then it is extended to represent the discrete interval-valued random variable.Based on the extended UGF,an improved discrete interval-valued SSI model is proposed, which has higher calculation precision compared with the existing methods. Finally,an illustrative case is given to demonstrate the validity of the proposed model.
基金Projects(60874030,60835001,60574006)supported by the National Natural Science Foundation of ChinaProjects(07KJB510125,08KJD510008)supported by the Natural Science Foundation of Jiangsu Higher Education Institutions of ChinaProject supported by the Qing Lan Program,Jiangsu Province,China
文摘The problem of passivity analysis for a class of discrete-time stochastic neural networks (DSNNs) with time-varying interval delay was investigated. The delay-dependent sufficient criteria were derived in terms of linear matrix inequalities (LMIs). The results are shown to be generalization of some previous results and are less conservative than the existing works. Meanwhile, the computational complexity of the obtained stability conditions is reduced because less variables are involved. A numerical example is given to show the effectiveness and the benefits of the proposed method.
文摘Fusing the structure feature of interval concept lattice and the actual needs of rough control rules,we have constructed the decision interval concept lattice,further more,we also have built a rules mining model of rough control based on decision interval concept lattice,in order to achieve the optimality between rough control mining cost and control efficiency.Firstly,we have preprocessed the collected original data,so that we can transform it into Boolean formal context form,and then we have constructed the decision interval concept lattice in rough control;secondly,we have established the control rules mining algorithm based on decision interval concept lattice.By analyzing and judging redundant rules,we have formed the rough control association rule base in end.Analysis shows that under the premise of improving the reliability of rules,we have achieved the rough control optimization goal between cost and efficiency.Finally,the model of reservoir scheduling has verified its feasibility and efficiency.
