Necessary and sufficient conditions for the exact controllability and exact observability of a descriptor infinite dimensional system are obtained in the sense of distributional solution.These general results are used...Necessary and sufficient conditions for the exact controllability and exact observability of a descriptor infinite dimensional system are obtained in the sense of distributional solution.These general results are used to examine the exact controllability and exact observability of the Dzektser equation in the theory of seepage and the exact controllability of wave equation.展开更多
In this paper,the authors define the strong (weak) exact boundary controllability and the strong (weak) exact boundary observability for first order quasilinear hyperbolic systems,and study their properties and the re...In this paper,the authors define the strong (weak) exact boundary controllability and the strong (weak) exact boundary observability for first order quasilinear hyperbolic systems,and study their properties and the relationship between them.展开更多
Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the authors apply a unified constructive method to establish the local exact boundary(null) controllability and the local bound...Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the authors apply a unified constructive method to establish the local exact boundary(null) controllability and the local boundary(weak) observability for a coupled system of 1-D quasilinear wave equations with various types of boundary conditions.展开更多
Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the local exact boundary observability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive ...Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the local exact boundary observability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive method.展开更多
The author establishes the exact boundary observability of unsteady supercritical flows in a tree-like network of open canals with general topology. An implicit duality between the exact boundary controllability and t...The author establishes the exact boundary observability of unsteady supercritical flows in a tree-like network of open canals with general topology. An implicit duality between the exact boundary controllability and the exact boundary observability is also given for unsteady supercritical flows.展开更多
The spatial prediction of a continuous response variable when spatially exhaustive predictor variables are available within the region under study has become ubiquitous in many geoscience fields.The response variable ...The spatial prediction of a continuous response variable when spatially exhaustive predictor variables are available within the region under study has become ubiquitous in many geoscience fields.The response variable is often subject to detection limits due to limitations of the measuring instrument or the sampling protocol used.Consequently,the response variable's observations are censored(left-censored,right-censored,or intervalcensored).Machine learning methods dedicated to the spatial prediction of uncensored response variables can not explicitly account for the response variable's censored observations.In such cases,they are routinely applied through ad hoc approaches such as ignoring the response variable's censored observations or replacing them with arbitrary values.Therefore,the response variable's spatial prediction may be inaccurate and sensitive to the assumptions and approximations involved in those arbitrary choices.This paper introduces a random forest-based machine learning method for spatially predicting a censored response variable,in which the response variable's censored observations are explicitly taken into account.The basic idea consists of building an ensemble of regression tree predictors by training the classical regression random forest on the subset of data containing only the response variable's uncensored observations.Then,the principal component analysis applied to this ensemble allows translating the response variable's observations(uncensored and censored)into a linear equalities and inequalities system.This system of linear equalities and inequalities is solved through randomized quadratic programming,which allows obtaining an ensemble of reconstructed regression tree predictors that exactly honor the response variable's observations(uncensored and censored).The response variable's spatial prediction is then obtained by averaging this latter ensemble.The effectiveness of the proposed machine learning method is illustrated on simulated data for which ground truth is available and showcased on real-world data,including geochemical data.The results suggest that the proposed machine learning technique allows greater utilization of the response variable's censored observations than ad hoc methods.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
In this paper the authors first present the definition and some properties of weak solutions to 1-D first order linear hyperbolic systems. Then they show that the constructive method with modular structure originally ...In this paper the authors first present the definition and some properties of weak solutions to 1-D first order linear hyperbolic systems. Then they show that the constructive method with modular structure originally given in the framework of classical solutions is still very powerful and effective in the framework of weak solutions to prove the exact boundary(null) controllability and the exact boundary observability for first order hyperbolic systems.展开更多
基金This work was supported by the National Natural Science Foundation of China(11926402,61973338).
文摘Necessary and sufficient conditions for the exact controllability and exact observability of a descriptor infinite dimensional system are obtained in the sense of distributional solution.These general results are used to examine the exact controllability and exact observability of the Dzektser equation in the theory of seepage and the exact controllability of wave equation.
基金supported by the Basic Research Program of China(No. 2007CB814800)
文摘In this paper,the authors define the strong (weak) exact boundary controllability and the strong (weak) exact boundary observability for first order quasilinear hyperbolic systems,and study their properties and the relationship between them.
文摘Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the authors apply a unified constructive method to establish the local exact boundary(null) controllability and the local boundary(weak) observability for a coupled system of 1-D quasilinear wave equations with various types of boundary conditions.
基金supported by the National Natural Science Foundation of China(No.11526050)
文摘Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the local exact boundary observability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive method.
文摘The author establishes the exact boundary observability of unsteady supercritical flows in a tree-like network of open canals with general topology. An implicit duality between the exact boundary controllability and the exact boundary observability is also given for unsteady supercritical flows.
文摘The spatial prediction of a continuous response variable when spatially exhaustive predictor variables are available within the region under study has become ubiquitous in many geoscience fields.The response variable is often subject to detection limits due to limitations of the measuring instrument or the sampling protocol used.Consequently,the response variable's observations are censored(left-censored,right-censored,or intervalcensored).Machine learning methods dedicated to the spatial prediction of uncensored response variables can not explicitly account for the response variable's censored observations.In such cases,they are routinely applied through ad hoc approaches such as ignoring the response variable's censored observations or replacing them with arbitrary values.Therefore,the response variable's spatial prediction may be inaccurate and sensitive to the assumptions and approximations involved in those arbitrary choices.This paper introduces a random forest-based machine learning method for spatially predicting a censored response variable,in which the response variable's censored observations are explicitly taken into account.The basic idea consists of building an ensemble of regression tree predictors by training the classical regression random forest on the subset of data containing only the response variable's uncensored observations.Then,the principal component analysis applied to this ensemble allows translating the response variable's observations(uncensored and censored)into a linear equalities and inequalities system.This system of linear equalities and inequalities is solved through randomized quadratic programming,which allows obtaining an ensemble of reconstructed regression tree predictors that exactly honor the response variable's observations(uncensored and censored).The response variable's spatial prediction is then obtained by averaging this latter ensemble.The effectiveness of the proposed machine learning method is illustrated on simulated data for which ground truth is available and showcased on real-world data,including geochemical data.The results suggest that the proposed machine learning technique allows greater utilization of the response variable's censored observations than ad hoc methods.
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supported by the National Natural Science Foundation of China(Nos.11831011,11901082)the Natural Science Foundation of Jiangsu Province(No.BK20190323)the Fundamental Research Funds for the Central Universities of China。
文摘In this paper the authors first present the definition and some properties of weak solutions to 1-D first order linear hyperbolic systems. Then they show that the constructive method with modular structure originally given in the framework of classical solutions is still very powerful and effective in the framework of weak solutions to prove the exact boundary(null) controllability and the exact boundary observability for first order hyperbolic systems.
