The objective of this research is the presentation of a neural network capable of solving complete nonlinear algebraic systems of n equations with n unknowns. The proposed neural solver uses the classical back propaga...The objective of this research is the presentation of a neural network capable of solving complete nonlinear algebraic systems of n equations with n unknowns. The proposed neural solver uses the classical back propagation algorithm with the identity function as the output function, and supports the feature of the adaptive learning rate for the neurons of the second hidden layer. The paper presents the fundamental theory associated with this approach as well as a set of experimental results that evaluate the performance and accuracy of the proposed method against other methods found in the literature.展开更多
The Klein-Cordon equation arises in many scientific areas of quantum mechanics and quantum field theory. In this paper a novel method based on spectral method and Jacobian free Newton method composed by generalized mi...The Klein-Cordon equation arises in many scientific areas of quantum mechanics and quantum field theory. In this paper a novel method based on spectral method and Jacobian free Newton method composed by generalized minimum residual （JFNGMRes） method with adaptive preconditioner will be introduced to solve nonlinear Klein-Gordon equation. In this work the nonlinear Klein-Gordon equation has been converted to a nonlinear system of algebraic equations using collocation method based on Bessel functions without any linearization, discretization and getting help of any other methods. Finally, by using JFNGMRes, solution of the nonlinear algebraic system will be achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the Klein-Gordon equation and compare our results with other methods.展开更多
The stabilization and H∞ control of nonlinear differential algebraic systems （NDAS） are investigated using the Hamiltonian function method. Firstly, we put forward a novel dissipative Hamiltonian realization （DHR...The stabilization and H∞ control of nonlinear differential algebraic systems （NDAS） are investigated using the Hamiltonian function method. Firstly, we put forward a novel dissipative Hamiltonian realization （DHR） structure and give the condition to complete the Hamiltonian realization. Then, based on the DHR, we present a criterion for the stability analysis of NDAS and construct a stabilization controller for NDAS in absence of disturbances. Finally, for NDAS in presence of disturbances, the L2 gain is analyzed via generalized Hamilton-Jacobi inequality and an H∞ control strategy is constructed. The proposed stabilization and robust controller can effectively take advantage of the structural characteristics of NDAS and is simple in form.展开更多
Using an energy-based Hamiltonian function method,this paper investigates the robust excitation control of multi-machine multi-load power systems described by a set of uncertain differential algebraic equations.First,...Using an energy-based Hamiltonian function method,this paper investigates the robust excitation control of multi-machine multi-load power systems described by a set of uncertain differential algebraic equations.First,we complete the dissipative Hamiltonian realization of the power system and adjust its operating point by the means of pre-feedback control.Then,based on the obtained Hamiltonian realization,we discuss the robust excitation control of the power system and put forward an H1 excitation control strategy.Simulation results demonstrate the effectiveness of the control scheme.展开更多
Pyramidal elements are often used to connect tetrahedral and hexahedral elements in the finite element method.In this paper we derive three new higher order numerical cubature formulae for pyramidal elements.
文摘The objective of this research is the presentation of a neural network capable of solving complete nonlinear algebraic systems of n equations with n unknowns. The proposed neural solver uses the classical back propagation algorithm with the identity function as the output function, and supports the feature of the adaptive learning rate for the neurons of the second hidden layer. The paper presents the fundamental theory associated with this approach as well as a set of experimental results that evaluate the performance and accuracy of the proposed method against other methods found in the literature.
文摘The Klein-Cordon equation arises in many scientific areas of quantum mechanics and quantum field theory. In this paper a novel method based on spectral method and Jacobian free Newton method composed by generalized minimum residual （JFNGMRes） method with adaptive preconditioner will be introduced to solve nonlinear Klein-Gordon equation. In this work the nonlinear Klein-Gordon equation has been converted to a nonlinear system of algebraic equations using collocation method based on Bessel functions without any linearization, discretization and getting help of any other methods. Finally, by using JFNGMRes, solution of the nonlinear algebraic system will be achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the Klein-Gordon equation and compare our results with other methods.
基金the National Natural Science Foundation of China （Grant Nos. 69774011 and 60433050）.
文摘The stabilization and H∞ control of nonlinear differential algebraic systems （NDAS） are investigated using the Hamiltonian function method. Firstly, we put forward a novel dissipative Hamiltonian realization （DHR） structure and give the condition to complete the Hamiltonian realization. Then, based on the DHR, we present a criterion for the stability analysis of NDAS and construct a stabilization controller for NDAS in absence of disturbances. Finally, for NDAS in presence of disturbances, the L2 gain is analyzed via generalized Hamilton-Jacobi inequality and an H∞ control strategy is constructed. The proposed stabilization and robust controller can effectively take advantage of the structural characteristics of NDAS and is simple in form.
基金supported by the National Natural Science Foundation of China(Grant No.60974005)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20094101120008)the Nature Science Foundation of Henan Province(No.092300410201).
文摘Using an energy-based Hamiltonian function method,this paper investigates the robust excitation control of multi-machine multi-load power systems described by a set of uncertain differential algebraic equations.First,we complete the dissipative Hamiltonian realization of the power system and adjust its operating point by the means of pre-feedback control.Then,based on the obtained Hamiltonian realization,we discuss the robust excitation control of the power system and put forward an H1 excitation control strategy.Simulation results demonstrate the effectiveness of the control scheme.
基金This paper was supported by The National Natural Science Foundation of China(No.10771063)Key Laboratory ofHigh performance Computation and Stochastic Information Processing,Hunan Province and Ministry of Education,Institutional Research Plan No.AV0Z 10190503,Anhui Agricultural University(yj2012-03)Grant No.IAA 100190803 of the Academy of Sciences of the Czech Republic and The Natural Sciences and Engineering Research Council of Canada.The authors are indebted to Pavel Krızek and Kevin B.Davies for their help in preparation of Figs.1 and 2,and Jan Brandts for fruitful discussions.
文摘Pyramidal elements are often used to connect tetrahedral and hexahedral elements in the finite element method.In this paper we derive three new higher order numerical cubature formulae for pyramidal elements.
