In this paper, we propose a new definition of symplectic multistep methods. This definition differs from the old ones in that it is given via the one step method defined directly on M which is corresponding to the m s...In this paper, we propose a new definition of symplectic multistep methods. This definition differs from the old ones in that it is given via the one step method defined directly on M which is corresponding to the m step scheme defined on M while the old definitions are given out by defining a corresponding one step method on M × M ×…× M = Mm with a set of new variables. The new definition gives out a steptransition operator g: M → M. Under our new definition, the Leap-frog method is symplectic only for linear Hamiltonian systems. The transition operator g will be constructed via continued fractions and rational approximations.展开更多
This paper discusses the harmonic problems in control systems from two aspects:Oneis the harmonic control among different subsystems,and the other is the harmonic control amongmultiple inputs.Some intrinsic problems i...This paper discusses the harmonic problems in control systems from two aspects:Oneis the harmonic control among different subsystems,and the other is the harmonic control amongmultiple inputs.Some intrinsic problems in such systems are discussed.It is pointed out that somesubsystems must be unstable to stabilize the whole interconnected system by an example.Especiallyfor discrete-time multi-input systems,a necessary and sufficient condition is presented for the strictdecrease of the quadratic optimal performance index with the control input extensions.This showsan essential difference between single-input and multi-input control systems.Finally,some futureresearch directions are discussed in harmonic control of interconnected systems,allocation of multi-control inputs,fault-tolerant control,and fault-diagnosis.展开更多
文摘In this paper, we propose a new definition of symplectic multistep methods. This definition differs from the old ones in that it is given via the one step method defined directly on M which is corresponding to the m step scheme defined on M while the old definitions are given out by defining a corresponding one step method on M × M ×…× M = Mm with a set of new variables. The new definition gives out a steptransition operator g: M → M. Under our new definition, the Leap-frog method is symplectic only for linear Hamiltonian systems. The transition operator g will be constructed via continued fractions and rational approximations.
基金supported by National Natural Science Foundation of China under Grant Nos. 90916003 and 60674093the Key Projects of Educational Ministry under Grant No. 107110
文摘This paper discusses the harmonic problems in control systems from two aspects:Oneis the harmonic control among different subsystems,and the other is the harmonic control amongmultiple inputs.Some intrinsic problems in such systems are discussed.It is pointed out that somesubsystems must be unstable to stabilize the whole interconnected system by an example.Especiallyfor discrete-time multi-input systems,a necessary and sufficient condition is presented for the strictdecrease of the quadratic optimal performance index with the control input extensions.This showsan essential difference between single-input and multi-input control systems.Finally,some futureresearch directions are discussed in harmonic control of interconnected systems,allocation of multi-control inputs,fault-tolerant control,and fault-diagnosis.
