The main purpose of this paper is to provide a systematic geometric frame for generalized controlled Hamiltonian systems. The pseudo-Poisson manifold and the ω-manifold are proposed as the statespace of the generaliz...The main purpose of this paper is to provide a systematic geometric frame for generalized controlled Hamiltonian systems. The pseudo-Poisson manifold and the ω-manifold are proposed as the statespace of the generalized controlled Hamiltonian systems. A Lie group, calledN-group, and its Lie algebra, calledN-algebra, are introduced for the structure analysis of the systems. Some properties, including spectrum, structure-preservation, etc. are investigated. As an example the theoretical results are applied to power systems. The stabilization of excitation systems is investigated.展开更多
考虑电力系统的非线性特性,基于H am ilton能量函数理论,设计了一种新的非线性稳定控制器。阐述了广义哈密顿系统理论及H am ilton能量函数理论,然后针对包含静止无功补偿器的单机无穷大系统建立非线性数学模型,并应用哈密顿系统理论对...考虑电力系统的非线性特性,基于H am ilton能量函数理论,设计了一种新的非线性稳定控制器。阐述了广义哈密顿系统理论及H am ilton能量函数理论,然后针对包含静止无功补偿器的单机无穷大系统建立非线性数学模型,并应用哈密顿系统理论对其进行实现,再从能量的观点出发,利用能量函数法设计系统稳定控制器。单机无穷大系统数字仿真结果验证了该控制律的有效性。展开更多
This paper deals with observer design for generalized Hamiltonian systems and its applications. First, by using the systems' structural properties, a new observer design method called Augment Plus Feedback is prov...This paper deals with observer design for generalized Hamiltonian systems and its applications. First, by using the systems' structural properties, a new observer design method called Augment Plus Feedback is provided and two kinds of observers are obtained: non-adaptive and adaptive ones. Then, based on the obtained observer, H∞ control design is investigated for generalized Hamiltonian systems, and an observer-based control design is proposed. Finally, as an application to power systems, an observer and an observer-based H∞ control law are designed for single-machine infinite-bus systems. Simulations show that both the observer and controller obtained in this paper work very well.展开更多
In this paper we prove the persistence of hyperbolic invariant tori in generalized Hamiltonian systems, which may admit a distinct number of action and angle variables. The systems under consideration can be odd dimen...In this paper we prove the persistence of hyperbolic invariant tori in generalized Hamiltonian systems, which may admit a distinct number of action and angle variables. The systems under consideration can be odd dimensional in tangent direction. Our results generalize the well-known results of Graft and Zehnder in standard Hamiltonians. In our case the unperturbed Hamiltonian systems may be degenerate. We also consider the persistence problem of hyperbolic tori on submanifolds.展开更多
Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated. The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach. Based o...Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated. The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach. Based on Lya-punov＇s stability theory, linear and nonlinear feedback control of adaptive H∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an Hoe-norm constraint. Adaptive H∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems. Numerical simulations are also given to identify the effectiveness of the theoretical analysis.展开更多
It this paper we obtain existence and bifurcation theorems for homoclinic orbits in three-dimeensional,time dependent and independent,perturbations of generalized Hamiltonian differential equations defined on three-d...It this paper we obtain existence and bifurcation theorems for homoclinic orbits in three-dimeensional,time dependent and independent,perturbations of generalized Hamiltonian differential equations defined on three-dimensional Poisson manifolds.Thed we apply them to a truncated spectral model of the quasi-geostrophic flow on a cyclic β-plane.展开更多
The form invariance and the Lie symmetry of the generalized Hamiltonian system are studied. Firstly, de?nitions and criteria of the form invariance and the Lie symmetry of the system are given. Next, the r...The form invariance and the Lie symmetry of the generalized Hamiltonian system are studied. Firstly, de?nitions and criteria of the form invariance and the Lie symmetry of the system are given. Next, the relation between the form invariance and the Lie symmetry is studied. Finally, two examples are given to illustrate the application of the results.展开更多
In this paper, we develop a global perturbation technique for the study of periodic orbits in three-dimensional, time dependent and independent, perturbations of generalized Hamiltonian differential equations defined ...In this paper, we develop a global perturbation technique for the study of periodic orbits in three-dimensional, time dependent and independent, perturbations of generalized Hamiltonian differential equations defined on three-dimensional Poisson manifolds. We give existence, stability and bifurcation theorems and illustrate our results with a truncated spectral model of the forced, dissipative quasi-geostrophic flow on a cyclic beta-plane.展开更多
In this paper we mainly concern the persistence of invariant tori in generalized Hamiltonian systems. Here the generalized Hamiltonian systems refer to the systems which may admit a distinct number of action and angle...In this paper we mainly concern the persistence of invariant tori in generalized Hamiltonian systems. Here the generalized Hamiltonian systems refer to the systems which may admit a distinct number of action and angle variables. In particular, system under consideration can be odd dimensional. Under the Riissmann type non-degenerate condition, we proved that the majority of the lower-dimension invariant tori of the integrable systems in generalized Hamiltonian system are persistent under small perturbation. The surviving lower-dimensional tori might be elliptic, hyperbolic, or of mixed type.展开更多
文摘The main purpose of this paper is to provide a systematic geometric frame for generalized controlled Hamiltonian systems. The pseudo-Poisson manifold and the ω-manifold are proposed as the statespace of the generalized controlled Hamiltonian systems. A Lie group, calledN-group, and its Lie algebra, calledN-algebra, are introduced for the structure analysis of the systems. Some properties, including spectrum, structure-preservation, etc. are investigated. As an example the theoretical results are applied to power systems. The stabilization of excitation systems is investigated.
文摘考虑电力系统的非线性特性,基于H am ilton能量函数理论,设计了一种新的非线性稳定控制器。阐述了广义哈密顿系统理论及H am ilton能量函数理论,然后针对包含静止无功补偿器的单机无穷大系统建立非线性数学模型,并应用哈密顿系统理论对其进行实现,再从能量的观点出发,利用能量函数法设计系统稳定控制器。单机无穷大系统数字仿真结果验证了该控制律的有效性。
基金This work was supported by the National Natural Science Foundation of China(Grant No.G60474001)RFDP of China(Grant No,G20040422059).
文摘This paper deals with observer design for generalized Hamiltonian systems and its applications. First, by using the systems' structural properties, a new observer design method called Augment Plus Feedback is provided and two kinds of observers are obtained: non-adaptive and adaptive ones. Then, based on the obtained observer, H∞ control design is investigated for generalized Hamiltonian systems, and an observer-based control design is proposed. Finally, as an application to power systems, an observer and an observer-based H∞ control law are designed for single-machine infinite-bus systems. Simulations show that both the observer and controller obtained in this paper work very well.
文摘In this paper we prove the persistence of hyperbolic invariant tori in generalized Hamiltonian systems, which may admit a distinct number of action and angle variables. The systems under consideration can be odd dimensional in tangent direction. Our results generalize the well-known results of Graft and Zehnder in standard Hamiltonians. In our case the unperturbed Hamiltonian systems may be degenerate. We also consider the persistence problem of hyperbolic tori on submanifolds.
文摘Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated. The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach. Based on Lya-punov＇s stability theory, linear and nonlinear feedback control of adaptive H∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an Hoe-norm constraint. Adaptive H∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems. Numerical simulations are also given to identify the effectiveness of the theoretical analysis.
文摘It this paper we obtain existence and bifurcation theorems for homoclinic orbits in three-dimeensional,time dependent and independent,perturbations of generalized Hamiltonian differential equations defined on three-dimensional Poisson manifolds.Thed we apply them to a truncated spectral model of the quasi-geostrophic flow on a cyclic β-plane.
基金Project supported by the National Natural Science Foundation of China (Nos.19972010 and 10272021).
文摘The form invariance and the Lie symmetry of the generalized Hamiltonian system are studied. Firstly, de?nitions and criteria of the form invariance and the Lie symmetry of the system are given. Next, the relation between the form invariance and the Lie symmetry is studied. Finally, two examples are given to illustrate the application of the results.
文摘In this paper, we develop a global perturbation technique for the study of periodic orbits in three-dimensional, time dependent and independent, perturbations of generalized Hamiltonian differential equations defined on three-dimensional Poisson manifolds. We give existence, stability and bifurcation theorems and illustrate our results with a truncated spectral model of the forced, dissipative quasi-geostrophic flow on a cyclic beta-plane.
基金Partially supported by the Talent Foundation (522-7901-01140418) of Northwest A & FUniversity.
文摘In this paper we mainly concern the persistence of invariant tori in generalized Hamiltonian systems. Here the generalized Hamiltonian systems refer to the systems which may admit a distinct number of action and angle variables. In particular, system under consideration can be odd dimensional. Under the Riissmann type non-degenerate condition, we proved that the majority of the lower-dimension invariant tori of the integrable systems in generalized Hamiltonian system are persistent under small perturbation. The surviving lower-dimensional tori might be elliptic, hyperbolic, or of mixed type.
