In this paper, the singular perturbation of initial value problem for nonlinear second order vector differential equationsis discussed, where r>0 is an arbitrary constant, e>0 is a small parameter, x, f,a and Un...In this paper, the singular perturbation of initial value problem for nonlinear second order vector differential equationsis discussed, where r>0 is an arbitrary constant, e>0 is a small parameter, x, f,a and Under suitable assumptions, by using the method of many-parameter expansion and the technique of diagonalization, the existence oj the solution of perturbation problem is proved and its uniformly valid asymptotic expansion of higher order is derived.展开更多
In this paper existence, uniqueness and asymptotic estimations of solutions of the boundary value problems on infinite interval for the second order nonlinear equation depending singularly on a small parameterare exam...In this paper existence, uniqueness and asymptotic estimations of solutions of the boundary value problems on infinite interval for the second order nonlinear equation depending singularly on a small parameterare examined, where are constants, and i=0,1.展开更多
In this paper, by the technique and the method of diagonalization, the boundary value problem for second order singularly perturbed nonlinear system as follows is dealt with: epsilon y '=f(t, y, y', epsilon), ...In this paper, by the technique and the method of diagonalization, the boundary value problem for second order singularly perturbed nonlinear system as follows is dealt with: epsilon y '=f(t, y, y', epsilon), y(0, epsilon)=a(epsilon), y(1,epsilon)=b(epsilon) The existance of the solution and its asymptotic properties are discussed when the eigenvalues of Jacobi matrix f(y') has K negative real parts and N-K positve real parts.展开更多
In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniform...In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniformly convergent second order scheme.展开更多
This paper, will seek the optimal control and corresponding trajectories of the singularly perturbed nonlinear state regulator problem. Under appropriate hypotheses. it will be possible to complete an asymptotic solut...This paper, will seek the optimal control and corresponding trajectories of the singularly perturbed nonlinear state regulator problem. Under appropriate hypotheses. it will be possible to complete an asymptotic solution which is uniformly valid when e→0.展开更多
In this paper we study the singular perturbation of boundary value problem for second order nonlinear system by the method and the technique of diagonalization. Under the appropriate assumptions we prove the existenc...In this paper we study the singular perturbation of boundary value problem for second order nonlinear system by the method and the technique of diagonalization. Under the appropriate assumptions we prove the existence of solution and give its asymptotic estimation as ε→0+展开更多
In this paper we consider the existence of infinitely many positive solutions for second order nonlinear eigenvalue problem with singular coefficient function. By the use of Krasnosel'skii fixed point theorem of c...In this paper we consider the existence of infinitely many positive solutions for second order nonlinear eigenvalue problem with singular coefficient function. By the use of Krasnosel'skii fixed point theorem of cone expansion-compression type we give several sufficient conditions.展开更多
We investigate the existence, uniqueness and asymptotic estimates of solutions for a class of second order quasi-linear singularly perturbed boundary value problem on the infinite interval when its reduced problem has...We investigate the existence, uniqueness and asymptotic estimates of solutions for a class of second order quasi-linear singularly perturbed boundary value problem on the infinite interval when its reduced problem has weakly discontinuous solutions. In this paper, a class of quasi-linear turning point problem on the finite interval is discussed.展开更多
This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed(SP)system using approximate feedback linearization(AFL)method.The essence of AFL method lies in the feed...This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed(SP)system using approximate feedback linearization(AFL)method.The essence of AFL method lies in the feedback linearization only of a certain part of the original nonlinear system.According to AFL approach,we suggest to solve feedback linearization problems for continuous nonlinear SP system by reducing it to two feedback linearization problems for slow and fast subsystems separately.The resulting AFL control is constructed in the form of asymptotic composition(composite control).Standard procedure for the composite control design consists of the following steps:1)system decomposition,2)solution of control problem for fast subsystem,3)solution of control problem for slow subsystem,4)construction of the resulting control in the form of the composition of slow and fast controls.The main difficulty during system decomposition is associated with dynamics separation condition for nonlinear SP system.To overcome this,we propose to change the sequence of the design procedure:1)solving the control problem for fast state variables part,2)system decomposition,3)solving the control problem for slow state variables part,4)construction of the resulting composite control.By this way,fast feedback linearizing control is chosen so that the dynamics separation condition would be met and the fast subsystem would be stabilizable.The application of the proposed approach is illustrated through several examples.展开更多
Consider the following vector boundary value problem with boundary perturbation where μ（】0） and ε are real small parameters, x, f, b and y, g, a are respectively r-dimensional and m-dimensional vector functions a...Consider the following vector boundary value problem with boundary perturbation where μ（】0） and ε are real small parameters, x, f, b and y, g, a are respectively r-dimensional and m-dimensional vector functions and a<sub>i</sub>, b<sub>i</sub>（i=1, 2）are matrices of appropriate orders. We assume that a<sub>2</sub>（0, 0）, b<sub>2</sub>（0, 0）are nonsingular and ψ（ε）, ψ（ε）展开更多
在永磁直线同步电机(permanent-magnet linear synchr-onous motor,PMLSM)伺服系统中,模型的阶次高,且速度和电流等变量间存在的耦合严重影响速度跟踪的快速性和精度。采用基于奇异摄动理论的对角化方法将永磁直线同步电机伺服系统分解...在永磁直线同步电机(permanent-magnet linear synchr-onous motor,PMLSM)伺服系统中,模型的阶次高,且速度和电流等变量间存在的耦合严重影响速度跟踪的快速性和精度。采用基于奇异摄动理论的对角化方法将永磁直线同步电机伺服系统分解成慢变和快变子系统。为了保证系统的鲁棒性,利用2阶滑模控制的次优算法分别独立设计慢变和快变子系统的控制律,再将2个控制律合成得到永磁直线同步电机的复合控制律。仿真结果表明,所提出的策略具有良好的速度跟踪性能,同时对负载扰动和参数变化具有很强的鲁棒性。展开更多
文摘In this paper, the singular perturbation of initial value problem for nonlinear second order vector differential equationsis discussed, where r>0 is an arbitrary constant, e>0 is a small parameter, x, f,a and Under suitable assumptions, by using the method of many-parameter expansion and the technique of diagonalization, the existence oj the solution of perturbation problem is proved and its uniformly valid asymptotic expansion of higher order is derived.
文摘In this paper existence, uniqueness and asymptotic estimations of solutions of the boundary value problems on infinite interval for the second order nonlinear equation depending singularly on a small parameterare examined, where are constants, and i=0,1.
文摘In this paper, by the technique and the method of diagonalization, the boundary value problem for second order singularly perturbed nonlinear system as follows is dealt with: epsilon y '=f(t, y, y', epsilon), y(0, epsilon)=a(epsilon), y(1,epsilon)=b(epsilon) The existance of the solution and its asymptotic properties are discussed when the eigenvalues of Jacobi matrix f(y') has K negative real parts and N-K positve real parts.
文摘In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniformly convergent second order scheme.
基金Project supported by the National Natural Science Foundation of Chinathe Natural Science Foundation of Fujian Province
文摘This paper, will seek the optimal control and corresponding trajectories of the singularly perturbed nonlinear state regulator problem. Under appropriate hypotheses. it will be possible to complete an asymptotic solution which is uniformly valid when e→0.
文摘In this paper we study the singular perturbation of boundary value problem for second order nonlinear system by the method and the technique of diagonalization. Under the appropriate assumptions we prove the existence of solution and give its asymptotic estimation as ε→0+
文摘In this paper we consider the existence of infinitely many positive solutions for second order nonlinear eigenvalue problem with singular coefficient function. By the use of Krasnosel'skii fixed point theorem of cone expansion-compression type we give several sufficient conditions.
文摘We investigate the existence, uniqueness and asymptotic estimates of solutions for a class of second order quasi-linear singularly perturbed boundary value problem on the infinite interval when its reduced problem has weakly discontinuous solutions. In this paper, a class of quasi-linear turning point problem on the finite interval is discussed.
基金supported by Russian Foundation for Basic Research(No.15-08-06859a)and by the Ministry of Education and Science of the Russian Federation in the framework of the basic part of the state order(No.2.8629.2017).
文摘This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed(SP)system using approximate feedback linearization(AFL)method.The essence of AFL method lies in the feedback linearization only of a certain part of the original nonlinear system.According to AFL approach,we suggest to solve feedback linearization problems for continuous nonlinear SP system by reducing it to two feedback linearization problems for slow and fast subsystems separately.The resulting AFL control is constructed in the form of asymptotic composition(composite control).Standard procedure for the composite control design consists of the following steps:1)system decomposition,2)solution of control problem for fast subsystem,3)solution of control problem for slow subsystem,4)construction of the resulting control in the form of the composition of slow and fast controls.The main difficulty during system decomposition is associated with dynamics separation condition for nonlinear SP system.To overcome this,we propose to change the sequence of the design procedure:1)solving the control problem for fast state variables part,2)system decomposition,3)solving the control problem for slow state variables part,4)construction of the resulting composite control.By this way,fast feedback linearizing control is chosen so that the dynamics separation condition would be met and the fast subsystem would be stabilizable.The application of the proposed approach is illustrated through several examples.
文摘Consider the following vector boundary value problem with boundary perturbation where μ（】0） and ε are real small parameters, x, f, b and y, g, a are respectively r-dimensional and m-dimensional vector functions and a<sub>i</sub>, b<sub>i</sub>（i=1, 2）are matrices of appropriate orders. We assume that a<sub>2</sub>（0, 0）, b<sub>2</sub>（0, 0）are nonsingular and ψ（ε）, ψ（ε）
文摘在永磁直线同步电机(permanent-magnet linear synchr-onous motor,PMLSM)伺服系统中,模型的阶次高,且速度和电流等变量间存在的耦合严重影响速度跟踪的快速性和精度。采用基于奇异摄动理论的对角化方法将永磁直线同步电机伺服系统分解成慢变和快变子系统。为了保证系统的鲁棒性,利用2阶滑模控制的次优算法分别独立设计慢变和快变子系统的控制律,再将2个控制律合成得到永磁直线同步电机的复合控制律。仿真结果表明,所提出的策略具有良好的速度跟踪性能,同时对负载扰动和参数变化具有很强的鲁棒性。
