FEEDBACK CONTROL OF A CLASS OF FLEXIBLE SYSTEMS WITH COUPLED BENDING AND TORSIONAL VIBRATIONS

In this paper, a class of flexible systems of beams with coupled bending andtorsional vibrations, which has important applications in the dynamics of aircraft is dis-cussed. The existence and uniqueness of the solution for this class of systems are proved,where the spectral analysis method and the unconditional base theory are used, and asufficient condition for the asymptotic stability of the closed-loop system is obtained bymeans of the (D) class operators theory.     

ASYMPTOTIC SIMILARITY OF INFINITE-DIMENSIONAL LINEAR SYSTEMS AND APPLICATIONS TO STABILITY

1.IntroductionInfinite-dimensionallinearsystemstheory,itiseasytoverifythatthespectrumandtheexponentialgroWthboundarepreservedunderasimilaritytransformation.ThispropertyisaIsosatisfiedfortheinfinite-dimensionalcaseifthesimilarityoperatorisboundedandbound-edlyinvertible.Inthisnote,weilltroduceageneralizationoftheconceptofsimilaritycalledasymptoticsimila-rityforindnite-dimensionallinearsystems.Inthefinite-dimensionalcase1similarityandasymptoticsimilarityareequivalellt.Weshowthatthisasymptoticsi…     

OPTIMAL CONTROL OF A CLASS OF DISTRIBUTED PARAMETER DELAY SYSTEMS

1.IntroductionManyphysicalsystems,suchajsthemodynamics,electrodynamics,populationbiology,aregovernedbydifferentialequations,integrodifferentialequationsormoregenerallyfunctionaldifferentialevolutionequationsonBanachspace.Associatedoptimalcontrolprobl...     

THE RANKINGS OF CONTROL SYSTEMS AND APPLICATIONS

The notion of ranking was initiated into control theory by Glad a few yearsago. In this paper we mainly discuss one kind of rankings and study its invarianceproperties. This kind of rankings is closely related to the structure algorithm. The relationsbetween invariants of this kind of rankings and the invariants given by other studies, e.g.the invertibility indices of a system and so on, are examined. As applications of rankings,we deal with some well-known problems in "ranking technique". In this paper we mainlyintroduce a new method rather than solve new problems.     

OPTIMAL CONTROL OF GROWTH RATE FOR A CLASS OF POPULATION SYSTEMS

In this paper,we discuss the optimal control of growth rate for a class of population systems governed by nonlinear degenerate parabolic equations.Given an ap-propriate cost functional,we prove the existence of the optimal growth rate and give some necessary conditions for optimal growth rate.     

SYNTHESIS AND ANALYSIS OF A FEEDBACK CONTROL SYSTEM

In this paper, supposing that the received signals at the input are of the formv(t)=s_1[t, x_1(t)]s_2[t, x_2(t)]+n(t) where s_i are FM signals (i=1, 2), a novel cross-coupledphase-locked loop (CCPLL(M)) and its mathematical model are obtained. The globalqualitativestructural analysis of the mathematical model of the first-order loop, the acqui-sition region and synchronization region of the first-order loop, and the synchronizationregion of the second-order loop are obtained.     

THE POLE ASSIGNMENT OF LINEAR SYSTEMS

In this paper the pole assignment problem of a time invariant linear control system issolved by using the Wu Elimination Method.In general,the questions are classified into(i)the poleassignment by using state feedback,(ii)the pole assignment by using output feedback,(iii)the poleassignment via dynamic compensator.The key point of all these problems is to solve a certaincorresponding system of polynomial equations.Based on algebraic geometry,the Wu methodprovides a mechanical algorithm for solving the system of polynomial equations.Therefore,a unifieddefinite algorithm for solving all these problems is given in this paper.During the procedure ofelimination,the unknowns are automatically separated into parameters and apparent variables.Thus,the freedom of the corresponding feedback can be defined as the number of parameters.Meanwhile,the explicit expressions of the apparent variables depending on the parameters areobtained.     

OUTPUT REGULATION PROBLEM FOR A CLASS OF SISO INFINITE DIMENSIONAL SYSTEMS VIA A FINITE DIMENSIONAL DYNAMIC CONTROL

This paper deals with the output regulation problem for a class of SISO infinite dimensional systems with an uncertain exosystem. For these systems, a concept of relative degree is firstly introduced and used to construct a transformation which leads to the canonical form of output feedback systems. Then, based on this canonical form, by means of an internal model and a recursive adaptive control, the authors obtain an adaptive regulator which solves the problem. It should be pointed out that the proposed regulator is finite dimensional while it is usually infinite dimensional in existing literatures.     

INFORMATION AND COMPLEXITY IN CONTROL SYSTEMS: A TUTORIAL

1 IntroductionPhysical systems differ greatly in their sizes, structtires, compositions and operations. Consequently, quatiflcation and comparison of system complexities at physical levels are far beyondthe domain of control systems and information science. Systems theory studies physical systems from a generic and information poillt of view: Systems are regarded as plats that processsignals and information, regardless the underlying physical realizations. This paper will explore complealty i…     

EXISTENCE AND ANALYTICAL APPROXIMATIONS OF LIMIT CYCLES IN A THREE-DIMENSIONAL NONLINEAR AUTONOMOUS FEEDBACK CONTROL SYSTEM

This paper is concerned with the existence and the analytical approximations of limit cycles in a three-dimensional nonlinear autonomous feedback control system. Based on three-dimensional Hopf bifurcation theorem, the existence of limit cycles is first proved. Then the homotopy analysis method （HAM） is applied to obtain the analytical approximations of the limit cycle and its frequency. In deriving the higher-order approximations, the authors utilized the idea of a perturbation procedure proposed for limit cycles＇ approximation in van der Pol equation. By comparing with the numerical integration solutions, it is shown that the accuracy of the analytical results obtained in this paper is very high, even when the amplitude of the limit cycle is large.     

EXACT CONTROLLABILITY OF A CLASS OF DISTRIBUTED PARAMETER SYSTEMS

The exact controllability of a class of distributed parameter systems governedby Petrowsky equations is considered.On the basis of the Hilbert Uniqueness Methodproposed by J.L.Lions,it is found that the Petrowsky systems with Dirichlet boundarycontrol are exactly controllable.     

ON SUFFICIENT AND NECESSARY OF EXISTENCE FOR A CLASS OF SINGULAR OPTIMAL STOCHASTIC CONTROL

We study a class of discounted models of singular stochastic control. In this kind of models, not only the structure of cost function has been extended to some general type, but also the state can be represented as the solution of a class of stochastic differential equations with nonlinear drift and diffusion term. By the various methods of stochastic analysis, we derive the sufllcient and necessary conditions of the existence of optimal control.     

A FEW RESULTS ON ARNOLDI''''S METHOD AND IOM FOR LARGE NON-HERMITIAN LINEAR SYSTEMS

1.IntroductionArnoldi'smethod[1'2]anditsincomplete0rth0g0nalizati0nversion(IOM)["']areextensivelyusedforsolvinglargenon-Hermitianlinearsystems.Itiswellknownthattheformerisanorthogonalprojectionmethod,whilethelatterisanobliqueprojecti0nmethod.Wereferto[2,4]and[3]forconvergenceanalyses0fthesetwomethods,respectively.RecelltlyBrown[5],Chronopoul0sI6landSaadl2,7]andmanyothershavederivedupdatingrecursionsoftheresidualnormsandaPprokimatesolutionsobtainedbyArnoldi'smethod.TheaPproachestheyuseeith…     

ADMISSIBILITY OF LINEAR ESTIMATORS OF REGRESSION COEFFICIENTS IN THE CLASS OF ALL ESTIMATORS UNDER THE MATRIX LOSS FUNCTION

For the general fixed effects linear model:Y=Xτ+ε,ε～N(0,V)(or N(0,σ~2V)),V≥0,we obtain the necessary and sufficient condition for LY+α to be admissible for Sτ in the class of allestimators under matrix loss function(d-Sτ)(d-Sτ)′;for the general random effects linear model:Y=Xβ+ε,(?)where (?)=XV_(11)X′+XV_(12)+V_(21)X′+V_(22)≥0,we also obtain the necessary and sufficient condition for LY+α to be admissible for Sα+Qβin the class of all estimators under matrix loss function(d-Sα-Qβ)(d-Sα-Qβ)′.     

EXISTENCE OF THE VALUE FOR A DIFFERENTIAL GAME WITH SWITCHING STRATEGIES IN A BANACH SPACE

A two-player zero-sum differential game in some Banach space is studied.Positiveswitching costs are associated with each player.By regularizing the game and combining thenotion of viscosity solutions for Isaacs-Bellman equation,we obtain the existence of the Elliot-Kalton value of the game under suitable conditions.     

因素空间理论与知识表示的数学框架——概念的反馈外延与因素的重合性

本文是文献（１，２）的继续，该文及后续的论文的将系统地研究因素空间理论及其在知识表示中的应用，首先引入反馈外延这一表示概念的新工具，它为表达概念提供了直接的操作方法，然后设计了反馈外延的包络，它是对概念外延的一种逼近，最后讨论了关于概念的重合性重合性测度的公理化定义。     

THE SPECTRAL COMPLETION OF A CLASS OF OPERATOR PARTIAL MATRICES

1. IntroductionLet Hi be complex Banach spaces, i = 1, 2,'' 5 n, and B(Hi, Hi) (B(Hi) if i = j) denotethe Banach space of all bounded linear operators from Hi to Hi. Let H ~ ffi:=IHi; thenA E B(H) may .be denoted by (Ail)... with Ail e B(Hj,Hi). Given a subset J C {(i,j)li,j = 1, 2,'',n} and Ail E B(Hj,Hi) for (i,i) e J, we get a partially specified n x n matriX(Xij)... with Xij ~ Ail if (i,i) e J and Xby (Ail)J If Q = (oil) E B(H) such that oil ~ Aijwhenever (i,i) e J, the…     

一类动态消费系统建模复杂性的先验分析方法

本文基于线性系统的度量复杂性理论，通过描述消费过程的一个机理模型，研究了一类消费系统的建模复杂性问题．利用系统量度复杂性理论中的Ｋｏｌｍｏｇｏｒｏｖｎ－宽度和辨识ｎ－宽度等概念，给出一类经济计量模型的建模误差及辨识误差与观测信息多少之间的关系，并证明了此类经济计量模型关于模型阶数和观测信息多少具有一定的鲁棒性．     

EXISTENCE OF SOLUTIONS FOR A CLASS OF SYSTEMS GOVERNED BY NONLINEAR DIFFERENTIAL INCLUSIONS

ＥＸＩＳＴＥＮＣＥＯＦＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＳＹＳＴＥＭＳＧＯＶＥＲＮＥＤＢＹＮＯＮＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＩＮＣＬＵＳＩＯＮＳ￥ＸＩＡＮＧＸｉａｏｌｉｎｇ；ＷＡＮＧＹｕａｎｄｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔ...     

COHERENT, REGULAR AND SIMPLE SYSTEMS IN ZERO DECOMPOSITIONS OF PARTIAL DIFFERENTIAL SYSTEMS

1.IntroductionWeareconcernedwithalgebraicdifferentialpolynomials(abbreviatedas'd-pcis)inafinitenumberofdifferentialindeterminatesoveradifferentialfieldofcharacteristic0.Givenafinitesetofsuchd-pcis,wewouldliketostudyd-Zero(),thedifferentialalgebraicsetdefinedbyPoverauniversaldifferentialfield.Wemayaskwhetherd-Zero()isempty,whetherad-pcivanishesond-Zero()(differentialradicalidealmembershipproblem),whatthedimensionofd-Zero()is,howtodecomposed-Zero()intoirreduciblealgebraicdifferentialsets,andso…