The descriptor Markovian jump systems( DMJSs)with partially unknown transition probabilities( PUTPs) are studied by means of variable structure control. First,by virtue of the strictly linear matrix inequality( LMI) t...The descriptor Markovian jump systems( DMJSs)with partially unknown transition probabilities( PUTPs) are studied by means of variable structure control. First,by virtue of the strictly linear matrix inequality( LMI) technique,a sufficient condition is presented, under which the DMJSs subject to PUTPs are stochastically admissible. Secondly,a novel sliding surface function based on the system state and input is constructed for DMJSs subject to PUTPs; and a dynamic sliding mode controller is synthesized, which guarantees that state trajectories will reach the pre-specified sliding surface in finite time despite uncertainties and disturbances. The results indicate that by checking the feasibility of a series of LMIs,the stochastic admissibility of the overall closed loop system is determined. Finally,the validity of the theoretical results is illustrated with the example of the direct-current motor. Furthermore,compared with the existing literature,the state convergence rate,buffeting reduction and overshoot reduction are obviously optimized.展开更多
Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studie...Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation ofpiecewise linear regression models. The method used to estimate the parameters ofpicewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC （Marcov Chain Monte Carlo） algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters ofpicewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.展开更多
This paper analyzes the detection means of the feeding coal in the jigging process, and puts forward a fuzzy control system of the variable construction in order to control the feeding coal. The fuzzy control system c...This paper analyzes the detection means of the feeding coal in the jigging process, and puts forward a fuzzy control system of the variable construction in order to control the feeding coal. The fuzzy control system consists of three parts: bang-bang control, keep control and fuzzy control.展开更多
In order to characterizc large fluctuations of the financial markets and optimize financial portfolio, a new dynamic asset control strategy was proposed in this work. Firstly, a random process item with variable jump ...In order to characterizc large fluctuations of the financial markets and optimize financial portfolio, a new dynamic asset control strategy was proposed in this work. Firstly, a random process item with variable jump intensity was introduced to the existing discrete microstructure model to denote large price fluctuations. The nonparametric method of LEE was used for detecting jumps. Further, the extended Kalman filter and the maximum likelihood method were applied to discrete microstructure modeling and the estimation of two market potential variables： market excess demand and liquidity. At last, based on the estimated variables, an assets allocation strategy using evolutionary algorithm was designed to control the weight of each asset dynamically. Case studies on IBM Stock show that jumps with variable intensity are detected successfully, and the assets allocation strategy may effectively keep the total assets growth or prevent assets loss at the stochastic financial market.展开更多
This paper presents the notions of exact observability and exact detectability for Markov jump linear stochastic systems of Ito type with multiplieative noise （for short, MJLSS）. Stochastic Popov-Belevith-Hautus （...This paper presents the notions of exact observability and exact detectability for Markov jump linear stochastic systems of Ito type with multiplieative noise （for short, MJLSS）. Stochastic Popov-Belevith-Hautus （PBH） Criterions for exact observability and exact detectability are respectively obtained. As an application, stochastic H2/H∞ control for such MJLSS is discussed under exact detectability.展开更多
The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical system...The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical systems to do qualitative analysis,all possible phase portraits in the parametric space for the traveling wave systems are obtained.It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied.The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.展开更多
This paper mainly studies observability and detectability for continuous-time stochastic Markov jump systems.Two concepts called W-observability and W-detectability for such systems are introduced,which are shown to c...This paper mainly studies observability and detectability for continuous-time stochastic Markov jump systems.Two concepts called W-observability and W-detectability for such systems are introduced,which are shown to coincide with various notions of observability and detectability reported recently in literature,such as exact observability,exact detectability and detectability.Besides,by introducing an accumulated energy function,some efficient criteria and interesting properties for both W-observability and W-detectability are obtained.展开更多
Jockusch, Li and Yang showed that the Lown and Low1 r.e. degrees are not elementarily equivalent for n>1. We answer a question they raise by using the results of Nies, Shore and Slaman to show that the Lown and Low...Jockusch, Li and Yang showed that the Lown and Low1 r.e. degrees are not elementarily equivalent for n>1. We answer a question they raise by using the results of Nies, Shore and Slaman to show that the Lown and Lowm r.e. degrees are not elementarily equivalent for n > m > 1.展开更多
A general exchange pair approach is developed to identify the limiting distribution for any sequence of random variables, by calculating the conditional mean and the conditional second moments. The error of approximat...A general exchange pair approach is developed to identify the limiting distribution for any sequence of random variables, by calculating the conditional mean and the conditional second moments. The error of approximation is also studied. In particular, a Berry-Esseen type bound of O(n^(-3/4)) is obtained for the Curie-Weiss model at the critical temperature.展开更多
基金The National Natural Science Foundation of China(No.61573199)
文摘The descriptor Markovian jump systems( DMJSs)with partially unknown transition probabilities( PUTPs) are studied by means of variable structure control. First,by virtue of the strictly linear matrix inequality( LMI) technique,a sufficient condition is presented, under which the DMJSs subject to PUTPs are stochastically admissible. Secondly,a novel sliding surface function based on the system state and input is constructed for DMJSs subject to PUTPs; and a dynamic sliding mode controller is synthesized, which guarantees that state trajectories will reach the pre-specified sliding surface in finite time despite uncertainties and disturbances. The results indicate that by checking the feasibility of a series of LMIs,the stochastic admissibility of the overall closed loop system is determined. Finally,the validity of the theoretical results is illustrated with the example of the direct-current motor. Furthermore,compared with the existing literature,the state convergence rate,buffeting reduction and overshoot reduction are obviously optimized.
文摘Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation ofpiecewise linear regression models. The method used to estimate the parameters ofpicewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC （Marcov Chain Monte Carlo） algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters ofpicewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.
文摘This paper analyzes the detection means of the feeding coal in the jigging process, and puts forward a fuzzy control system of the variable construction in order to control the feeding coal. The fuzzy control system consists of three parts: bang-bang control, keep control and fuzzy control.
基金Projects(71271215,71221061) supported by the National Natural Science Foundation of ChinaProject(2011DFA10440) supported by the International Science&Technology Cooperation Program of ChinaProject(CX2012B067) supported by Hunan Provincial Innovation Foundation for Postgraduate,China
文摘In order to characterizc large fluctuations of the financial markets and optimize financial portfolio, a new dynamic asset control strategy was proposed in this work. Firstly, a random process item with variable jump intensity was introduced to the existing discrete microstructure model to denote large price fluctuations. The nonparametric method of LEE was used for detecting jumps. Further, the extended Kalman filter and the maximum likelihood method were applied to discrete microstructure modeling and the estimation of two market potential variables： market excess demand and liquidity. At last, based on the estimated variables, an assets allocation strategy using evolutionary algorithm was designed to control the weight of each asset dynamically. Case studies on IBM Stock show that jumps with variable intensity are detected successfully, and the assets allocation strategy may effectively keep the total assets growth or prevent assets loss at the stochastic financial market.
基金supported by National Natural Science Foundation of China under Grant Nos 60774020, 60736028,and 60821091
文摘This paper presents the notions of exact observability and exact detectability for Markov jump linear stochastic systems of Ito type with multiplieative noise （for short, MJLSS）. Stochastic Popov-Belevith-Hautus （PBH） Criterions for exact observability and exact detectability are respectively obtained. As an application, stochastic H2/H∞ control for such MJLSS is discussed under exact detectability.
基金National Natural Science Foundation of China(No.19731003,No.19961003)Yunnan Provincial Natural Science Foundation of China(No.1999A0018M,No.2000A0002M)
文摘The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical systems to do qualitative analysis,all possible phase portraits in the parametric space for the traveling wave systems are obtained.It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied.The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.
基金supported by the Natural Science Foundation of China under Grant No.61174078the Research Fund for the Taishan Scholar Project of Shandong Province of China+1 种基金the SDUST Research Fund under Grant No.2011KYTD105the State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources under Grant No.LAPS13018
文摘This paper mainly studies observability and detectability for continuous-time stochastic Markov jump systems.Two concepts called W-observability and W-detectability for such systems are introduced,which are shown to coincide with various notions of observability and detectability reported recently in literature,such as exact observability,exact detectability and detectability.Besides,by introducing an accumulated energy function,some efficient criteria and interesting properties for both W-observability and W-detectability are obtained.
文摘Jockusch, Li and Yang showed that the Lown and Low1 r.e. degrees are not elementarily equivalent for n>1. We answer a question they raise by using the results of Nies, Shore and Slaman to show that the Lown and Lowm r.e. degrees are not elementarily equivalent for n > m > 1.
基金supported by Hong Kong Research Grants Council General Research Fund (Grant Nos. 403513 and 14302515)
文摘A general exchange pair approach is developed to identify the limiting distribution for any sequence of random variables, by calculating the conditional mean and the conditional second moments. The error of approximation is also studied. In particular, a Berry-Esseen type bound of O(n^(-3/4)) is obtained for the Curie-Weiss model at the critical temperature.
