非局部半线性积微分系统的可控制性(英文)

本文运用半群理论和Schauder不动点定理,在Banach空间研究了一类非局部半线性积微分系统的可控制性.最后,举例说明了所得结果.

具有不变直线的非Hamilton系统的极限环分支

本文研究扰动可积微分系统x·=-y(y+1)2+εf(x,y),[AKy·]=x(y+1)2+εg(x,y),式中:0<|ε|1;f(x,y)=∑ni+j=0a i,j x iy j;g(x,y)=∑ni+j=0b i,j x iy j。应用一阶平均法证明该系统恰好存在n个极限环。

受控系统带积分项的最优控制问题的控制参数化方法

针对一类受控微分系统带积分项的最优控制问题,提出了一种控制参数化计算方法.将时间区间分成许多的小区间,在每一个小区间内,控制向量用一个逐段连续的常函数来逼近,最优控制问题相应地用一系列最优参数选择问题来逼近,而每个逼近问题可用有效的最优化方法求解.证明了算法的一系列收敛性结果,表明设计的算法是收敛的和有效的.

二次可积非Hamilton系统的极限环分支

研究了如下扰动二次可积微分系统其中 x=-y（x＋1）＋εf（x,y）,y=x（x＋1）＋εg（x,y）,其中0〈｜ε｜〈〈1，f（x,y）和g（x,y）是关于x，y的n次多项式．应用Abelian积分法得到该系统至多存在几个极限环，且这个上界是可达的．

Analysis of the effect on control systems of order variation for fractional-orderPI~λD~μcontrollers

This paper is concerned with fractional-order PI~λD~μcontrollers. The definitions and properties of fractional calculus are introduced. The mathematical descriptions of a fractional-order controller and fractional-order control systems are outlined. The effects on control systems of order variation for fractional-order PI~λD~μ controllers are investigated by qualitative analysis and simulation. The conclusions and simulation examples are given. The results show the fractional-order PI~λD~μ controller is not sensitive to variation of its order.

Observer-based Iterative and Repetitive Learning Control for a Class of Nonlinear Systems

In this paper, both output-feedback iterative learning control(ILC) and repetitive learning control(RLC) schemes are proposed for trajectory tracking of nonlinear systems with state-dependent time-varying uncertainties. An iterative learning controller, together with a state observer and a fully-saturated learning mechanism, through Lyapunov-like synthesis, is designed to deal with time-varying parametric uncertainties. The estimations for outputs, instead of system outputs themselves, are applied to form the error equation, which helps to establish convergence of the system outputs to the desired ones. This method is then extended to repetitive learning controller design. The boundedness of all the signals in the closed-loop is guaranteed and asymptotic convergence of both the state estimation error and the tracking error is established in both cases of ILC and RLC. Numerical results are presented to verify the effectiveness of the proposed methods.

Constraints and Soliton Solutions for KdV Hierarchy and AKNS Hierarchy

It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator. We generalize the result to a special form of Lax pair,from which a method to constrain the integrable system to a lower-dimensional or fewer variable integrable system is proposed.A direct result is that the n-soliton solutions of the KdV hierarchy can be completely depicted by a series of ordinary differential equations(ODEs),which may be gotten by a simple but unfamiliar Lax pair.Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies.The key is a special form of Lax pair for the AKNS hierarchy.It is proved that under the constraints all equations of the AKNS hierarchy are linearizable.

Vector Product and an Integrable Dynamical System

We study an autonomous system of first order ordinary differential equations based on the vector product. We show that the system is completely integrable by constructing the first integrals.The connection with Nambu mechanics is established.The extension to higher dimensions is also discussed.

Application of PID Controller Based on BP Neural Network in Export Steam’s Temperature Control System

By combining the Back-Propagation （BP） neural network with conventional proportional Integral Derivative （PID） controller, a new temperature control strategy of the export steam in supercritical electric power plant is put forward. This scheme can effectively overcome the large time delay, inertia of the export steam and the influencee of object in varying operational parameters. Thus excellent control quality is obtaitud. The present paper describes the development and application of neural network based controller to control the temperature of the boiler＇s export steam. Through simulation in various situations, it validates that the control quality of this control system is apparently superior to the conventional PID control system.

External stability of fractional-order control systems

The external stability of fractional-order continuous linear control systems described by both fractional-order state space representation and fractional-order transfer function is mainly investigated in this paper. In terms of Lyapunov’s stability theory and the stability analysis of the integer-order linear control systems, the definitions of external stability for fractional-order control systems are presented. By using the theorems of the Mittag-Leffler function in two parameters, the necessary and sufficient conditions of external stability are directly derived. The illustrative examples and simulation results are also given.

CAUCHY PROBLEM FOR A NONLINEAR SINGULAR INTEGRAL－DIFFERENTIAL EVOLUTION SYSTEM

We study the Cauchy problem for a nonlinear evolution system with singularintegral differential terms.By means of some a priori estimates of the solution and theLeray-Schauder's fixed point theorem, we prove the existence and the uniqueness theoremsof the generalized global solution of the mentioned problem.

The Scope of the Structural Completeness in the Class of all Over-Systems of the Classical Functional Calculus with Identity

This paper is the continuation of the paper [13]. Namely, in [13], the scope of the structural completeness in the class of all over-systems of the classical predicate calculus, has been established. In this paper we establish the scope of the structural completeness in the class of all over-systems of the classical functional calculus with identity.

Digital Control Design for the Boiler Drum BDT921

A boiler drum BDT921 that is installed in the Control Laboratory, Department of Mechatronics and Robotics Engineering, Faculty of Electric and Electronic Engineering, Universiti Tun Hussein Onn Malaysia （UTHM） is being used as a model plant to achieve the digital control system since its analog. Implementing a digital system to boiler quite a though work. This paper covers analysis from the experiment done to match with digital design that will be implemented to the real system. The digital control design will come up with the mathematical model and will be analyzed with MATLAB and SIMULINK software named as ＂Discrete Analysis ofBDT921 Simulation＂. A proportional integral and derivative （PID） controller is being chosen as the control element in discrete form as the real system is using the same control element. The output responses behave as the second order system with a bit difference in rise times and peak times compared with data obtained from experiment. With regarding to the analysis done, the digital control can be implemented and for further viewing, to be controlled digitally with computer in the control room.

New minimal surfaces in the hyperbolic space

We obtain new complete minimal surfaces in the hyperbolic space H3, by using Ribaucour transformations. Starting with the family of spherical catenoids in H^3 found by Mori(1981), we obtain 2-and 3-parameter families of new minimal surfaces in the hyperbolic space, by solving a non trivial integro-differential system. Special choices of the parameters provide minimal surfaces whose parametrizations are defined on connected regions of R^2 minus a disjoint union of Jordan curves. Any connected region bounded by such a Jordan curve, generates a complete minimal surface, whose boundary at infinity of H^3 is a closed curve. The geometric properties of the surfaces regarding the ends, completeness and symmetries are discussed.

FOUR STEP SCHEME FOR GENERAL MARKOVIAN FORWARD-BACKWARD SDES

This paper studies a class of forward-backward stochastic differential equations (FBSDE)in a general Markovian framework.The forward SDE represents a large class of strong Markov semimartingales,and the backward generator requires only mild regularity assumptions.The authors showthat the Four Step Scheme introduced by Ma,et al.(1994) is still effective in this case.Namely,the authors show that the adapted solution of the FBSDE exists and is unique over any prescribedtime duration;and the backward components can be determined explicitly by the forward componentvia the classical solution to a system of parabolic integro-partial differential equations.An importantconsequence the authors would like to draw from this fact is that,contrary to the general belief,in aMarkovian set-up the martingale representation theorem is no longer the reason for the well-posednessof the FBSDE,but rather a consequence of the existence of the solution of the decoupling integralpartialdifferential equation.Finally,the authors briefly discuss the possibility of reducing the regularityrequirements of the coefficients by using a scheme proposed by F.Delarue (2002) to the current case.

Integrable discretization of soliton equations via bilinear method and Backlund transformation

We present a systematic procedure to derive discrete analogues of integrable PDEs via Hirota’s bilinear method.This approach is mainly based on the compatibility between an integrable system and its B¨acklund transformation.We apply this procedure to several equations,including the extended Korteweg-deVries(Kd V)equation,the extended Kadomtsev-Petviashvili(KP)equation,the extended Boussinesq equation,the extended Sawada-Kotera(SK)equation and the extended Ito equation,and obtain their associated semidiscrete analogues.In the continuum limit,these differential-difference systems converge to their corresponding smooth equations.For these new integrable systems,their B¨acklund transformations and Lax pairs are derived.

EVANS FUNCTIONS AND ASYMPTOTIC STABILITY OF TRAVELING WAVE SOLUTIONS

This paper studies the asymptotic stability of traveling we solutions of nonlinear systems of integral-differential equations. It has been established that linear stability of traveling waves is equivalent to nonlinear stability and some "nice structure" of the spectrum of an associated operator implies the linear stability. By using the method of variation of parameter, the author defines some complex analytic function, called the Evans function. The zeros of the Evans function corresponds to the eigenvalues of the associated linear operator. By calculating the zeros of the Evans function, the asymptotic stability of the travling wave solutions is established.