In order to visualize singularity of SGCMGs in gimbal angle space,a novel continuous bounded singularity parameter--Singularity Radius,whose sign can distinctly determine singularity type,is proposed.Then a rapid sing...In order to visualize singularity of SGCMGs in gimbal angle space,a novel continuous bounded singularity parameter--Singularity Radius,whose sign can distinctly determine singularity type,is proposed.Then a rapid singularity-escape steering law is proposed basing on gradient of Singularity Radius and residual base vector to drive the SGCMG system to neighboring singular boundary,and quickly escape elliptic singularities.Finally,simulation results on Pyramid-type and skew-type configuration demonstrate the effectiveness and rapidness of the proposed steering law.展开更多
In this paper,the method of differential inequalities has been applied to study theboundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and t...In this paper,the method of differential inequalities has been applied to study theboundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and the remainders have been estimated.展开更多
A method for simultaneous determination of mixed model parameters,which have different physical dimensions or different responses to data,is presented.Mixed parameter estimation from observed data within a single mode...A method for simultaneous determination of mixed model parameters,which have different physical dimensions or different responses to data,is presented.Mixed parameter estimation from observed data within a single model space shows instabilities and trade-offs of the solutions. We separate the model space into N-subspaces based on their physical properties or computational convenience and solve the N-subspaces systems by damped least-squares and singular-value decomposition. Since the condition number of each subsystem is smaller than that of the single global system,the approach can greatly increase the stability of the inversion. We also introduce different damping factors into the subsystems to reduce the tradeoffs between the different parameters. The damping factors depend on the conditioning of the subsystems and may be adequately chosen in a range from 0.1 % to 10 % of the largest singular value. We illustrate the method with an example of simultaneous determination of source history,source geometry,and hypocentral location from regional seismograms,although it is applicable to any geophysical inversion.展开更多
This paper focuses on synthesizing a mixed robust H_2/H_∞ linear parameter varying（LPV） controller for the longitudinal motion of an air-breathing hypersonic vehicle via a high order singular value decomposition（H...This paper focuses on synthesizing a mixed robust H_2/H_∞ linear parameter varying（LPV） controller for the longitudinal motion of an air-breathing hypersonic vehicle via a high order singular value decomposition（HOSVD） approach.The design of hypersonic flight control systems is highly challenging due to the enormous complexity of the vehicle dynamics and the presence of significant uncertainties.Motivated by recent results on both LPV control and tensor-product（TP） model transformation approach,the velocity and altitude tracking control problems for the air-breathing hypersonic vehicle is reduced to that of a state feedback stabilizing controller design for a polytopic LPV system with guaranteed performances.The controller implementation is converted into a convex optimization problem with parameterdependent linear matrix inequalities（LMIs） constraints,which is intuitively tractable using LMI control toolbox.Finally,numerical simulation results demonstrate the effectiveness of the proposed approach.展开更多
A singularity free cosmological model is obtained in a homogeneous and isotropic background with a specific form of the Hubble parameter in the presence of an interacting dark energy represented by a time-varying cosm...A singularity free cosmological model is obtained in a homogeneous and isotropic background with a specific form of the Hubble parameter in the presence of an interacting dark energy represented by a time-varying cosmological constant in general relativity. Different cases that arose have been extensively studied for different values of the curvature parameter. Some interesting results have been found with this form of the Hubble parameter to meet the possible negative value of the decelera- tion parameter （- 1/3≤ q 〈 0） as the current observations reveal. For some particular values of these parameters, the model reduces to Berman＇s model.展开更多
Exponential stability of the first order singular distributed parameter systems is discussedin the light of degenerate semi-group methods,which is described by the abstract developing equationin Hilbert space.The nece...Exponential stability of the first order singular distributed parameter systems is discussedin the light of degenerate semi-group methods,which is described by the abstract developing equationin Hilbert space.The necessary and sufficient conditions concerning the exponential stability of thefirst order singular distributed parameter systems are given.展开更多
Exact controllability of singular distributed parameter control system is discussed via functional analysis and the theory of generalized operator semi-group in Hilbert space, Necessary and sufficient conditions conce...Exact controllability of singular distributed parameter control system is discussed via functional analysis and the theory of generalized operator semi-group in Hilbert space, Necessary and sufficient conditions concerning the exact controllability are given. Relations between exact controllability and stability of singular distributed parameter system are specified.展开更多
Necessary and sufficient conditions for the exact controllability and approximate controllability of a singular distributed parameter system are obtained.These general results are used to examine the exact controllabi...Necessary and sufficient conditions for the exact controllability and approximate controllability of a singular distributed parameter system are obtained.These general results are used to examine the exact controllability and approximate controllability of the Dzektser equation in the theory of seepage.展开更多
Feedback stabilization for a class of second order singular distributed parameter system with multi- inputs is discussed via functional analysis and operator theory in Hilbert space, the solutions of the problem and t...Feedback stabilization for a class of second order singular distributed parameter system with multi- inputs is discussed via functional analysis and operator theory in Hilbert space, the solutions of the problem and the constructive expressions of the solutions are given by the generalized inverse of bounded linear operator. This research is theoretically important for studying the stability of the singular distributed parameter system.展开更多
State feedback and pole assignment of the second order coupled singular distributed parameter systems are discussed via functional analysis and operator theory in Hilbert space, in which infinite many poles are change...State feedback and pole assignment of the second order coupled singular distributed parameter systems are discussed via functional analysis and operator theory in Hilbert space, in which infinite many poles are changed. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse of bounded linear operator. This research is theoretically important for studying the pole assignment and stabilization of the singular distributed parameter systems.展开更多
基金funded under the National Natural Science Foundation of China(No.61873312)。
文摘In order to visualize singularity of SGCMGs in gimbal angle space,a novel continuous bounded singularity parameter--Singularity Radius,whose sign can distinctly determine singularity type,is proposed.Then a rapid singularity-escape steering law is proposed basing on gradient of Singularity Radius and residual base vector to drive the SGCMG system to neighboring singular boundary,and quickly escape elliptic singularities.Finally,simulation results on Pyramid-type and skew-type configuration demonstrate the effectiveness and rapidness of the proposed steering law.
基金Project Supported by the Science Fund of the Chinese Academy of Sciences
文摘In this paper,the method of differential inequalities has been applied to study theboundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and the remainders have been estimated.
基金supported by Innovation Project of Chinese Academy of Sciences
文摘A method for simultaneous determination of mixed model parameters,which have different physical dimensions or different responses to data,is presented.Mixed parameter estimation from observed data within a single model space shows instabilities and trade-offs of the solutions. We separate the model space into N-subspaces based on their physical properties or computational convenience and solve the N-subspaces systems by damped least-squares and singular-value decomposition. Since the condition number of each subsystem is smaller than that of the single global system,the approach can greatly increase the stability of the inversion. We also introduce different damping factors into the subsystems to reduce the tradeoffs between the different parameters. The damping factors depend on the conditioning of the subsystems and may be adequately chosen in a range from 0.1 % to 10 % of the largest singular value. We illustrate the method with an example of simultaneous determination of source history,source geometry,and hypocentral location from regional seismograms,although it is applicable to any geophysical inversion.
基金supported by the National Natural Science Foundation of China(6120300761304239+1 种基金61503392)the Natural Science Foundation of Shaanxi Province(2015JQ6213)
文摘This paper focuses on synthesizing a mixed robust H_2/H_∞ linear parameter varying（LPV） controller for the longitudinal motion of an air-breathing hypersonic vehicle via a high order singular value decomposition（HOSVD） approach.The design of hypersonic flight control systems is highly challenging due to the enormous complexity of the vehicle dynamics and the presence of significant uncertainties.Motivated by recent results on both LPV control and tensor-product（TP） model transformation approach,the velocity and altitude tracking control problems for the air-breathing hypersonic vehicle is reduced to that of a state feedback stabilizing controller design for a polytopic LPV system with guaranteed performances.The controller implementation is converted into a convex optimization problem with parameterdependent linear matrix inequalities（LMIs） constraints,which is intuitively tractable using LMI control toolbox.Finally,numerical simulation results demonstrate the effectiveness of the proposed approach.
基金Department of Atomic Energy (DAE),Government of India for financial support through the post-doctoral fellowship of the National board of Higher Mathematics (NBHM)
文摘A singularity free cosmological model is obtained in a homogeneous and isotropic background with a specific form of the Hubble parameter in the presence of an interacting dark energy represented by a time-varying cosmological constant in general relativity. Different cases that arose have been extensively studied for different values of the curvature parameter. Some interesting results have been found with this form of the Hubble parameter to meet the possible negative value of the decelera- tion parameter （- 1/3≤ q 〈 0） as the current observations reveal. For some particular values of these parameters, the model reduces to Berman＇s model.
基金This research is supported by the National Natural Science Foundation of China under Grant No.60674018.
文摘Exponential stability of the first order singular distributed parameter systems is discussedin the light of degenerate semi-group methods,which is described by the abstract developing equationin Hilbert space.The necessary and sufficient conditions concerning the exponential stability of thefirst order singular distributed parameter systems are given.
基金Supported by the National Natural Science Foundation of China (Grant No. 60674018)
文摘Exact controllability of singular distributed parameter control system is discussed via functional analysis and the theory of generalized operator semi-group in Hilbert space, Necessary and sufficient conditions concerning the exact controllability are given. Relations between exact controllability and stability of singular distributed parameter system are specified.
基金supported by the National Natural Science Foundation of China under Grant Nos.61174081and 61273135。
文摘Necessary and sufficient conditions for the exact controllability and approximate controllability of a singular distributed parameter system are obtained.These general results are used to examine the exact controllability and approximate controllability of the Dzektser equation in the theory of seepage.
基金Supported by the National Natural Science Foundation of China(No.60674018)the Natural Sciences Research Foundation of the Education Department of Jiangsu Province in China(No.08KJD510003)
文摘Feedback stabilization for a class of second order singular distributed parameter system with multi- inputs is discussed via functional analysis and operator theory in Hilbert space, the solutions of the problem and the constructive expressions of the solutions are given by the generalized inverse of bounded linear operator. This research is theoretically important for studying the stability of the singular distributed parameter system.
基金supported by the National Nature Science Foundation of China under Grant No.60674018
文摘State feedback and pole assignment of the second order coupled singular distributed parameter systems are discussed via functional analysis and operator theory in Hilbert space, in which infinite many poles are changed. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse of bounded linear operator. This research is theoretically important for studying the pole assignment and stabilization of the singular distributed parameter systems.
