A discrete observer-based repetitive control(RC) design method for a linear system with uncertainties was presented based on two-dimensional(2D) system theory. Firstly, a 2D discrete model was established to describe ...A discrete observer-based repetitive control(RC) design method for a linear system with uncertainties was presented based on two-dimensional(2D) system theory. Firstly, a 2D discrete model was established to describe both the control behavior within a repetition period and the learning process taking place between periods. Next, by converting the designing problem of repetitive controller into one of the feedback gains of reconstructed variables, the stable condition was obtained through linear matrix inequality(LMI) and also the gain coefficient of repetitive system. Numerical simulation shows an exceptional feasibility of this proposal with remarkable robustness and tracking speed.展开更多
In this paper spectral Galerkin approximation of optimal control problem governed by fractional elliptic equation is investigated.To deal with the nonlocality of fractional Laplacian operator the Caffarelli-Silvestre ...In this paper spectral Galerkin approximation of optimal control problem governed by fractional elliptic equation is investigated.To deal with the nonlocality of fractional Laplacian operator the Caffarelli-Silvestre extension is utilized.The first order optimality condition of the extended optimal control problem is derived.A spectral Galerkin discrete scheme for the extended problem based on weighted Laguerre polynomials is developed.A priori error estimates for the spectral Galerkin discrete scheme is proved.Numerical experiments are presented to show the effectiveness of our methods and to verify the theoretical findings.展开更多
Linear multistep methods and one-leg methods are applied to a class of index-2 nonlinear differential-algebraic equations with a variable delay.The corresponding convergence results are obtained and successfully confi...Linear multistep methods and one-leg methods are applied to a class of index-2 nonlinear differential-algebraic equations with a variable delay.The corresponding convergence results are obtained and successfully confirmed by some numerical examples.The results obtained in this work extend the corresponding ones in literature.展开更多
The iterative solution of the sequence of linear systems arising from threetemperature(3-T)energy equations is an essential component in the numerical simulation of radiative hydrodynamic(RHD)problem.However,due to th...The iterative solution of the sequence of linear systems arising from threetemperature(3-T)energy equations is an essential component in the numerical simulation of radiative hydrodynamic(RHD)problem.However,due to the complicated application features of the RHD problems,solving 3-T linear systems with classical preconditioned iterative techniques is challenging.To address this difficulty,a physicalvariable based coarsening two-level(PCTL)preconditioner has been proposed by dividing the fully coupled system into four individual easier-to-solve subsystems.Despite its nearly optimal complexity and robustness,the PCTL algorithm suffers from poor efficiency because of the overhead associatedwith the construction of setup phase and the solution of subsystems.Furthermore,the PCTL algorithm employs a fixed strategy for solving the sequence of 3-T linear systems,which completely ignores the dynamically and slowly changing features of these linear systems.To address these problems and to efficiently solve the sequence of 3-T linear systems,we propose an adaptive two-level preconditioner based on the PCTL algorithm,referred to as αSetup-PCTL.The adaptive strategies of the αSetup-PCTL algorithm are inspired by those of αSetup-AMG algorithm,which is an adaptive-setup-based AMG solver for sequence of sparse linear systems.The proposed αSetup-PCTL algorithm could adaptively employ the appropriate strategies for each linear system,and thus increase the overall efficiency.Numerical results demonstrate that,for 36 linear systems,the αSetup-PCTL algorithm achieves an average speedup of 2.2,and a maximum speedup of 4.2 when compared to the PCTL algorithm.展开更多
.The geometric multigrid method(GMG)is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations.GMG utilizes a hierarchy of grids or discretizati....The geometric multigrid method(GMG)is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations.GMG utilizes a hierarchy of grids or discretizations and reduces the error at a number of frequencies simultaneously.Graphics processing units(GPUs)have recently burst onto the scientific computing scene as a technology that has yielded substantial performance and energy-efficiency improvements.A central challenge in implementing GMG on GPUs,though,is that computational work on coarse levels cannot fully utilize the capacity of a GPU.In this work,we perform numerical studies of GMG on CPU–GPU heterogeneous computers.Furthermore,we compare our implementation with an efficient CPU implementation of GMG and with the most popular fast Poisson solver,Fast Fourier Transform,in the cuFFT library developed by NVIDIA.展开更多
This paper is concerned with the problem of the full-order observer design for a class of fractional-order Lipschitz nonlinear systems. By introducing a continuous frequency distributed equivalent model and using an i...This paper is concerned with the problem of the full-order observer design for a class of fractional-order Lipschitz nonlinear systems. By introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach, the sufficient condition for asymptotic stability of the full-order observer error dynamic system is presented. The stability condition is obtained in terms of LMI, which is less conservative than the existing one. A numerical example demonstrates the validity of this approach.展开更多
The Hagedorn wavepacket method is an important numerical method for solving the semiclassical time-dependent Schrödinger equation.In this paper,a new semi-discretization in space is obtained by wavepacket operato...The Hagedorn wavepacket method is an important numerical method for solving the semiclassical time-dependent Schrödinger equation.In this paper,a new semi-discretization in space is obtained by wavepacket operator.In a sense,such semi-discretization is equivalent to the Hagedorn wavepacket method,but this discretization is more intuitive to show the advantages of wavepacket methods.Moreover,we apply the multi-time-step method and the Magnus-expansion to obtain the improved algorithms in time-stepping computation.The improved algorithms are of the Gauss–Hermite spec-tral accuracy to approximate the analytical solution of the semiclassical Schrödinger equation.And for the given accuracy,the larger time stepsize can be used for the higher oscillation in the semiclassical Schrödinger equation.The superiority is shown by the error estimation and numerical experiments.展开更多
The generating function methods have been applied successfully to generalized Hamiltonian systems with constant or invertible Poisson-structure matrices.In this paper,we extend these results and present the generating...The generating function methods have been applied successfully to generalized Hamiltonian systems with constant or invertible Poisson-structure matrices.In this paper,we extend these results and present the generating function methods preserving the Poisson structures for generalized Hamiltonian systems with general variable Poisson-structure matrices.In particular,some obtained Poisson schemes are applied efficiently to some dynamical systems which can be written into generalized Hamiltonian systems(such as generalized Lotka-Volterra systems,Robbins equations and so on).展开更多
We consider computing the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation with M-matrix.It is well known that such equations can be efficiently solved via the structure-preserving doubling ...We consider computing the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation with M-matrix.It is well known that such equations can be efficiently solved via the structure-preserving doubling algorithm(SDA)with the shift-and-shrink transformation or the generalized Cayley transformation.In this paper,we propose a more generalized transformation of which the shift-and-shrink transformation and the generalized Cayley transformation could be viewed as two special cases.Meanwhile,the doubling algorithm based on the proposed generalized transformation is presented and shown to be well-defined.Moreover,the convergence result and the comparison theorem on convergent rate are established.Preliminary numerical experiments show that the doubling algorithm with the generalized transformation is efficient to derive the minimal nonnegative solution of nonsymmetric algebraic Riccati equation with M-matrix.展开更多
基金Project(61104072) supported by the National Natural Science Foundation of China
文摘A discrete observer-based repetitive control(RC) design method for a linear system with uncertainties was presented based on two-dimensional(2D) system theory. Firstly, a 2D discrete model was established to describe both the control behavior within a repetition period and the learning process taking place between periods. Next, by converting the designing problem of repetitive controller into one of the feedback gains of reconstructed variables, the stable condition was obtained through linear matrix inequality(LMI) and also the gain coefficient of repetitive system. Numerical simulation shows an exceptional feasibility of this proposal with remarkable robustness and tracking speed.
基金supported by the National Natural Science Foundation of China Project(Nos.12071402,11931003,12261131501,and 11971276)the Project of Scientific Research Fund of the Hunan Provincial Science and Technology Department(No.2022RC3022).
文摘In this paper spectral Galerkin approximation of optimal control problem governed by fractional elliptic equation is investigated.To deal with the nonlocality of fractional Laplacian operator the Caffarelli-Silvestre extension is utilized.The first order optimality condition of the extended optimal control problem is derived.A spectral Galerkin discrete scheme for the extended problem based on weighted Laguerre polynomials is developed.A priori error estimates for the spectral Galerkin discrete scheme is proved.Numerical experiments are presented to show the effectiveness of our methods and to verify the theoretical findings.
基金This work is supported by NSF of China(10971175)Specialized Research Fund for the Doctoral Program of Higher Education of China(20094301110001)+2 种基金Program for Changjiang Scholars and Innovative Research Team in University of China(IRT1179)NSF of Hunan Province(10JJ7001)the Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province,and Fund Project of Hunan Province Education Office(11C1220).
文摘Linear multistep methods and one-leg methods are applied to a class of index-2 nonlinear differential-algebraic equations with a variable delay.The corresponding convergence results are obtained and successfully confirmed by some numerical examples.The results obtained in this work extend the corresponding ones in literature.
基金financially supported by the National Natural Science Foundation of China(62032023 and 11971414)Hunan National Applied Mathematics Center(2020ZYT003)the Research Foundation of Education Bureau of Hunan(21B0162).
文摘The iterative solution of the sequence of linear systems arising from threetemperature(3-T)energy equations is an essential component in the numerical simulation of radiative hydrodynamic(RHD)problem.However,due to the complicated application features of the RHD problems,solving 3-T linear systems with classical preconditioned iterative techniques is challenging.To address this difficulty,a physicalvariable based coarsening two-level(PCTL)preconditioner has been proposed by dividing the fully coupled system into four individual easier-to-solve subsystems.Despite its nearly optimal complexity and robustness,the PCTL algorithm suffers from poor efficiency because of the overhead associatedwith the construction of setup phase and the solution of subsystems.Furthermore,the PCTL algorithm employs a fixed strategy for solving the sequence of 3-T linear systems,which completely ignores the dynamically and slowly changing features of these linear systems.To address these problems and to efficiently solve the sequence of 3-T linear systems,we propose an adaptive two-level preconditioner based on the PCTL algorithm,referred to as αSetup-PCTL.The adaptive strategies of the αSetup-PCTL algorithm are inspired by those of αSetup-AMG algorithm,which is an adaptive-setup-based AMG solver for sequence of sparse linear systems.The proposed αSetup-PCTL algorithm could adaptively employ the appropriate strategies for each linear system,and thus increase the overall efficiency.Numerical results demonstrate that,for 36 linear systems,the αSetup-PCTL algorithm achieves an average speedup of 2.2,and a maximum speedup of 4.2 when compared to the PCTL algorithm.
基金the assistance provided by Mr.Xiaoqiang Yue and Mr.Zheng Li from Xiangtan University in regard in our numerical experiments.Feng is partially supported by the NSFC Grant 11201398Program for Changjiang Scholars and Innovative Research Team in University of China Grant IRT1179+4 种基金Specialized research Fund for the Doctoral Program of Higher Education of China Grant 20124301110003Shu is partially supported by NSFC Grant 91130002 and 11171281the Scientific Research Fund of the Hunan Provincial Education Department of China Grant 12A138Xu is partially supported by NSFC Grant 91130011 and NSF DMS-1217142.Zhang is partially supported by the Dean Startup Fund,Academy of Mathematics and System Sciences,and by NSFC Grant 91130011.
文摘.The geometric multigrid method(GMG)is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations.GMG utilizes a hierarchy of grids or discretizations and reduces the error at a number of frequencies simultaneously.Graphics processing units(GPUs)have recently burst onto the scientific computing scene as a technology that has yielded substantial performance and energy-efficiency improvements.A central challenge in implementing GMG on GPUs,though,is that computational work on coarse levels cannot fully utilize the capacity of a GPU.In this work,we perform numerical studies of GMG on CPU–GPU heterogeneous computers.Furthermore,we compare our implementation with an efficient CPU implementation of GMG and with the most popular fast Poisson solver,Fast Fourier Transform,in the cuFFT library developed by NVIDIA.
基金supported by National Natural Science Foundation of China(Nos.61104072,61104210 and 61174211)Construct Program of the Key Discipline in Hunan Province
文摘This paper is concerned with the problem of the full-order observer design for a class of fractional-order Lipschitz nonlinear systems. By introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach, the sufficient condition for asymptotic stability of the full-order observer error dynamic system is presented. The stability condition is obtained in terms of LMI, which is less conservative than the existing one. A numerical example demonstrates the validity of this approach.
基金supported by projects NSF of China(11271311)Program for Changjiang Scholars and Innovative Research Team in University of China(IRT1179)Hunan Province Innovation Foundation for Postgraduate(CX2011B245).
文摘The Hagedorn wavepacket method is an important numerical method for solving the semiclassical time-dependent Schrödinger equation.In this paper,a new semi-discretization in space is obtained by wavepacket operator.In a sense,such semi-discretization is equivalent to the Hagedorn wavepacket method,but this discretization is more intuitive to show the advantages of wavepacket methods.Moreover,we apply the multi-time-step method and the Magnus-expansion to obtain the improved algorithms in time-stepping computation.The improved algorithms are of the Gauss–Hermite spec-tral accuracy to approximate the analytical solution of the semiclassical Schrödinger equation.And for the given accuracy,the larger time stepsize can be used for the higher oscillation in the semiclassical Schrödinger equation.The superiority is shown by the error estimation and numerical experiments.
基金projects NSF of China(11271311)Program for Changjiang Scholars and Innovative Research Team in University of China(IRT1179)the Aid Program for Science and Technology,Innovative Research Team in Higher Educational Institutions of Hunan Province of China,and Hunan Province Innovation Foundation for Postgraduate(CX2011B245).
文摘The generating function methods have been applied successfully to generalized Hamiltonian systems with constant or invertible Poisson-structure matrices.In this paper,we extend these results and present the generating function methods preserving the Poisson structures for generalized Hamiltonian systems with general variable Poisson-structure matrices.In particular,some obtained Poisson schemes are applied efficiently to some dynamical systems which can be written into generalized Hamiltonian systems(such as generalized Lotka-Volterra systems,Robbins equations and so on).
基金The work of B.Tang was supported partly by Hunan Provincial Innovation Foundation for Postgraduate(No.CX2016B249)Hunan Provincial Natural Science Foundation of China(No.2018JJ3019)+1 种基金The work of N.Dong was supported partly by the Hunan Provincial Natural Science Foundation of China(Nos.14JJ2114,2017JJ2071)the Excellent Youth Foundation and General Foundation of Hunan Educational Department(Nos.17B071,17C0466).
文摘We consider computing the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation with M-matrix.It is well known that such equations can be efficiently solved via the structure-preserving doubling algorithm(SDA)with the shift-and-shrink transformation or the generalized Cayley transformation.In this paper,we propose a more generalized transformation of which the shift-and-shrink transformation and the generalized Cayley transformation could be viewed as two special cases.Meanwhile,the doubling algorithm based on the proposed generalized transformation is presented and shown to be well-defined.Moreover,the convergence result and the comparison theorem on convergent rate are established.Preliminary numerical experiments show that the doubling algorithm with the generalized transformation is efficient to derive the minimal nonnegative solution of nonsymmetric algebraic Riccati equation with M-matrix.