The nature of infinite-dimensional Hamiltonian systems are studied for the purpose of further study on some generalized Hamiltonian systems equipped with a given Poisson bracket. From both theoretical and practical vi...The nature of infinite-dimensional Hamiltonian systems are studied for the purpose of further study on some generalized Hamiltonian systems equipped with a given Poisson bracket. From both theoretical and practical viewpoints, we summarize a general method of constructing symplectic-like difference schemes of these kinds of systems. This study provides a new algorithm for the application of the symplectic geometry method in numerical solutions of general evolution equations.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
This paper investigates the relationship between state feedback and Hamiltonian realization. First, it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian real...This paper investigates the relationship between state feedback and Hamiltonian realization. First, it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian realization. Necessary and sufficient conditions are obtained for it to have a Hamiltonian realization with natural output. Then some conditions for an affine nonlinear system to have a Hamiltonian realization are given. For generalized outputs, the conditions of the feedback, keeping Hamiltonian, are discussed. Finally, the admissible feedback controls for generalized Hamiltonian systems are considered.展开更多
基金Acknowledgments. This work was supported by the China National Key Development Planning Project for Ba-sic Research (Abbreviation: 973 Project Grant No. G1999032801), the Chinese Academy of Sciences Key Innovation Direction Project (Grant No. KZCX2208)
文摘The nature of infinite-dimensional Hamiltonian systems are studied for the purpose of further study on some generalized Hamiltonian systems equipped with a given Poisson bracket. From both theoretical and practical viewpoints, we summarize a general method of constructing symplectic-like difference schemes of these kinds of systems. This study provides a new algorithm for the application of the symplectic geometry method in numerical solutions of general evolution equations.
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This research is supported partly by the National Natural Science Foundation of China(No.G59837270)and National 973 Project(No.G
文摘This paper investigates the relationship between state feedback and Hamiltonian realization. First, it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian realization. Necessary and sufficient conditions are obtained for it to have a Hamiltonian realization with natural output. Then some conditions for an affine nonlinear system to have a Hamiltonian realization are given. For generalized outputs, the conditions of the feedback, keeping Hamiltonian, are discussed. Finally, the admissible feedback controls for generalized Hamiltonian systems are considered.
