Output regulation of nonlinear singularly perturbed systems based on T-S fuzzy model

Based on the T-S model, the output regulation of nonlinear singularly perturbed systems via state feedback is discussed. It is shown that, under standard assumptions, this problean is solvable if and only if certain linear matrix equations are solvable. Once these equations are solvable, the state feedback regulator can easily be constructed.

BOUNDARY VALUE PROBLEM FOR A SINGULARLY PERTURBED NONLINEAR SYSTEM

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.

A Class of Singularly Perturbed Problems for Nonlinear Two-Species Competitive Reaction-Diffusion System

A class of nonlinear two-species competitive singularly perturbed initial-boundary-value problems for reaction-diffusion systems are studied. Under suitable assumptions, by using the stretched variable, the formal asymptotic expansion for the problems is constructed. The uniform validity of the solution for initial-boundary-value problems is obtained by using the theory of differential inequalities.

THE NONLINEAR SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS WITH TIME DELAY

A class of nonlinear for singularly perturbed problems for reaction diffusion equations with time delays are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied.

Singular perturbation of a second-order three-point boundary value problem for nonlinear systems

This paper deals with the existence of solutions to a singularly perturbed second-order three-point boundary value problem for nonlinear differential systems. The authors construct an appropriate generalized lower- and upper-solution pair, a concept defined in this paper, and employ the Nagumo conditions and algebraic boundary layer functions to ensure the existence of solutions of the problem. The uniformly valid asymptotic estimate of the solutions is given as well. The differential systems have nonlinear dependence on all order derivatives of the unknown.

Output regulation of nonaffine nonlinear systems using singular perturbation theory

A control synthesis method for output regulation based on singular perturbation theory combined with inverting design is considered for a class of nonaffine nonlinear systems. The resulting control signal is defined as a solution to ＂fast＂ dynamics which inverts a series error model, whose state is exponentially stable. It is shown that, under sufficient conditions being consistent with the assumptions of singular perturbation theory, this problem is solvable with （ε） tracking error if and only if a set of first-order nonlinear partial differential equations are solvable. The control law can be easily constructed and the simulations show the feasibility and effectiveness of the controller.

SINGULAR PERTURBATION OF INITIAL VALUE PROBLEM FOR A NONLINEAR SECOND ORDER SYSTEMS

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.

SINGULAR PERTURBATION OF GENERAL BOUNDARY VALUE PROBLEM FOR NONLINEAR DIFFERENTIAL EQUATION SYSTEM

In this paper, the singular perturbation of nonlinear differential equation system with nonlinear boundary conditions is discussed. Under suitable assumptions, with the asymptotic method of Lyusternik-Vishik([1]) and fixed point theory, the existence of the solution of the perturbation problem is proved and its uniformly valid asymptotic expansion of higher order is derived.

Interval Type-2 Fuzzy Passive Filtering for Nonlinear Singularly Perturbed PDT-Switched Systems and Its Application

The problem of designing a passive filter for nonlinear switched singularly perturbed systems with parameter uncertainties is explored in this paper.Firstly,the multiple-time-scale phenomenon is settled effectively by introducing a singular perturbation parameter in the plant.Secondly,the interval type-2 fuzzy set theory is employed where parameter uncertainties are expressed in membership functions rather than the system matrices.It is worth noting that interval type-2 fuzzy sets of the devised filter are different from the plant,which makes the design of the filter more flexible.Thirdly,the persistent dwell-time switching rule,as a kind of time-dependent switching rules,is used to manage the switchings among nonlinear singularly perturbed subsystems,and this rule is more general than dwell-time and average dwell-time switching rules.Next,sufficient conditions are provided for guaranteeing that the filtering error system is globally uniformly exponentially stable with a passive performance.Furthermore,on the basis of the linear matrix inequalities,the explicit expression of the designed filter can be obtained.Finally,a tunnel diode electronic circuit is rendered as an example to confirm the correctness and the validity of the developed filter.

THE SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM OF NONLINEAR INTEGRO-DIFFERENTIAL SYSTEM

In this paper, using the differential inequality and singularly perturbed theory, the singularly perturbed boundary value problems for nonlinear integro-differential system has been studied. Under some appropriate assumptions, the existence of solution has been proved and the uniform validness of the asymptotic expansions for arbitrary nth-order have been obtained simply and conveniently.

SINGULAR PERTURBATION OF TWO─POINT BOUNDARY VALUE PROBLEM FOR NONLINEAR SYSTEM

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+

SINGULAR PERTURBATION OF ROBIN BOUNDARY VALUE PROBLEM FOR THIRD ORDER NONLINEAR SYSTEM WITH BOUNDARY PERTURBATION

In this paper we study the singular perturbation of Robin boundary value problem for third order nonlinear system with bounary perturbation. Under the appropriate assumptions, using the fixed-point theorem we obtain the existence of the pertUrbed solution and give its asymptotic expansion, which is uniformly valid for the arbitrary order.

ASYMPTOTIC SOLUTION OF ACTIVATOR INHIBITOR SYSTEMS FOR NONLINEAR REACTION DIFFUSION EQUATIONS

为使活跃之物禁止者系统的非线性的反应散开方程被考虑的 A。第一，第二，在合适的条件下面，原来的问题的外部解决方案用多重规模的变量被获得；力量系列的膨胀理论答案的正式 asymptotic 扩大被构造，；最后，使用微分不平等的理论一致有效性；答案的 asymptotic 行为被学习。

一种非线性多时间尺度系统模型降阶方法

基于奇异摄动理论和非线性系统稳定域边界二次近似方法,推导出非线性多时间尺度系统忽略快动态降阶时,降阶前后系统稳定性的一般规律。通过将原系统稳定裕度指标在奇异摄动参数处进行高阶泰勒级数展开,给出定量预测降阶系统稳定裕度指标的表达式。在此基础上,提出一种非线性多时间尺度系统模型降阶方法,该降阶方法能保证降阶前后系统的稳定性一致。运用该降阶方法,对某交直流电力系统的数学模型进行了忽略快动态降阶研究。降阶前后系统的时域仿真结果证明所提出降阶方法是有效的,能为交直流电力系统的动态特性分析提供简化模型。

基于LMI的小时滞饱和系统稳定域估计方方法法

基于Pade近似变换,将小时滞饱和系统的稳定域估计转化为估计奇异摄动饱和系统的稳定域问题.证明了此奇异摄动饱和系统的稳定域具有可解耦性,并在此基础上建立LMI优化模型并提出小时滞饱和系统稳定域估计的降阶方法.算例仿真验证了方法的正确性和有效性.

交流电动机锁相调速系统的非线性特性(英文)

基于一种新的鉴相器模型 ,并鉴于交流调速系统中存在双时标特性 ,应用奇异摄动理论中的时标分解原理 ,对交流锁相调速系统进行了降阶处理 .在简化模型的基础上分析了系统的非线性特性 ,并推导出了系统的稳定条件和捕捉带 .

一类非线性奇摄动捕食-被捕食反应扩散系统

研究了一类具有非线性捕食—被捕食反应扩散系统奇摄动问题．在适当的条件下,利用微分不等式理论讨论了问题解的渐近性态．

一类输入饱和非仿射非线性系统的非线性动态逆控制

输入饱和是实际系统中经常遇到的问题,很多已有的控制方法要求被控系统具有仿射结构.本文针对一类具有输入饱和的非仿射纯反馈非线性系统提出了一种基于奇异值摄动理论的非线性动态逆控制方法.首先构建一个快变子系统,在慢时间尺度下将非仿射非线性系统转换为具有仿射结构的线性系统,从而应用已有的控制算法实现控制目的.为了消除输入饱和带来的影响,建立一个中间子系统对理想控制量与输入饱和限制下控制量的差进行估计和补偿.所提出的控制方法不依赖于被控系统固有的时标分离特性,并能证明闭环系统指数跟踪参考轨迹.该方法具有良好的扩展性,可以根据实际需求与多种控制算法相结合.与动态面控制器和传统近似动态逆控制器的对比仿真结果验证了本文控制方法的有效性.

飞行轨迹指令综合跟踪控制器设计

运用多重尺度奇异摄动理论，结合动态逆解耦理论和动态平衡点邻区域优化线性化系统的优化解耦控制律理论，研究了战术任务综合飞行管理系统的综合飞行轨迹指令跟踪控制器系统化设计方法。对Ｆ－１５飞机，设计了综合飞行轨迹跟踪控制器。数字仿真结果表明，设计的跟踪控制器能够控制飞机精确跟踪不同时标集的飞行指令。

一种估计奇异摄动饱和系统稳定域的方法

针对奇异摄动饱和系统,提出了一种估计其稳定域的降阶方法。结合饱和函数的特殊性质,证明了此类系统的稳定域可分解为伴随系统的不变集与一个足够大球体的笛卡尔积,将原系统稳定域估计问题转化为低阶伴随系统稳定域的估计问题,利用线性矩阵不等式(Linear matrix inequality,LMI)优化方法估计伴随系统的稳定域以减少保守性。本方法不仅可以克服奇异摄动饱和系统的奇异性,还可以一定程度克服系统的"维数灾"等问题.