A CLASS OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR NONLINEAR DIFFERENTIAL SYSTEMS

Considerthesingularlyperturbednonlinearproblemfory=(y1,…,yn)oftheformwhereεisasmallpositiveparameter,f=(f1,…,fn),g=(g1,…gn),fi(x,y')≡fi(x,y'1,…,y'n),gi(x,y')≡gi(x,y'1,…,y'n),A=(A1,…,An),B=(B1,…,Bn).ManyauthorssuchasHowes[1],O'DonnelllZ],Lin[3],Mo[4--7]andothershavediscussedthisproblemundervarioussituationsusingthemethodofdifferentialinequalities.Thispaperconcernsaclassofboundaryvalueproblemsfornonlineardifferentialsystemsusingtheiterationmethodandthetheoryofdifferentialinequaliti…     

FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS, LINEAR QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO SUM DIFFERENTIAL GAMES

In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.     

ON A CLASS OF ANISOTROPIC DIFFUSION EQUATIONS

ＯＮＡＣＬＡＳＳＯＦＡＮＩＳＯＴＲＯＰＩＣＤＩＦＦＵＳＩＯＮＥＱＵＡＴＩＯＮＳＯＮＡＣＬＡＳＳＯＦＡＮＩＳＯＴＲＯＰＩＣＤＩＦＦＵＳＩＯＮＥＱＵＡＴＩＯＮＳ￥ＧＡＯＨａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｄａｎＵｎｉｖｅｒｓｉｔ...     

A NECESSARY AND SUFFICIENT CONDITION FOR A POINT TO BE A GLOBAL MAXIMIZER OF A CONSTRAINED OPTIMIZATION

It is difficult to judge whether a given point is a global maximizer of an unconstrained optimization problem. This paper deals with this problem by considering global information via integral and gives a necessary and sufficient condition judging whether a given point is a global maximizer of an unconstrained optimization problem. An algorithm is offered under such a condition and finally two test problems are verified via the offered algorithm.     

POSITIVE SOLUTIONS FOR DIRICHLET PROBLEMS OF SINGULAR SEMILINEAR ELLIPTIC EQUATIONS

ＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＦＯＲＤＩＲＩＣＨＬＥＴＰＲＯＢＬＥＭＳＯＦＳＩＮＧＵＬＡＲＳＥＭＩＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳ￥ＣＵＩＳｈａｎｇｂｉｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＬａｎｚｈｏｕＵｎｉｖｅｒｓ...     

OPTIMAL CONTROL OF A CLASS OF DISTRIBUTED PARAMETER DELAY SYSTEMS

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

A REMARK ON PERIODIC SOLUTIONS OF SINGULAR HAMILTONIAN SYSTEMS WITH SUBLINEAR TERMS

In this paper,we prove the existence of multiple periodic solutionsfor a class of singular Hamiltonian systems with sublinear terms via variationalmethods.     

STABILITY AND FEEDBACK CONTROL OF A CLASS OF SECOND-ORDER LINEAR SYSTEMS IN BANACH SPACE

In this paper. we are concerned with the stability and control problem for aclass of second-order linear systems in Banach space. First. a criterion for the exponentialstability of a first-order linear system is presented. Then. the exponential stability as wellas some properties of a class of second-order linear systems is proved. At last. the feedbackcontrol of this class of systems is investigated.     

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.     

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.     

BOUND ON SOLUTIONS TO THE GENERAL SYSTEM OF VOLTERRA－TYPE LINEAR INTEGRAL INEQUALITIES IN SEVERAL VARIABLES AND ITS APPLICATIONS TO INTEGRO－PARTIAL DIFFERENTIAL EQUATIONS

ＢＯＵＮＤＯＮＳＯＬＵＴＩＯＮＳＴＯＴＨＥＧＥＮＥＲＡＬＳＹＳＴＥＭＯＦＶＯＬＴＥＲＲＡ－ＴＹＰＥＬＩＮＥＡＲＩＮＴＥＧＲＡＬＩＮＥＱＵＡＬＩＴＩＥＳＩＮＳＥＶＥＲＡＬＶＡＲＩＡＢＬＥＳＡＮＤＩＴＳＡＰＰＬＩＣＡＴＩＯＮＳＴＯＩＮＴＥＧＲＯ－ＰＡＲＴ...     

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.     

APPROXIMATE OPTIMAL BIRTH CONTROL OF POTULATION SYSTEMS

We consider optimal birth control for the McKendrick equation of population dyna-mics.It consists of optimizing a system described by a first order partial differential equationwith nonlo-cal bilinear boundary control.Approximate minimum principles are obtained usingEkeland's vari ational principle.     

THREE-POINT BOUNDARY VALUE PROBLEMSFOR A CLASS OF THREE ORDER DIFFERENTIAL INCLUSIONS

1.IntroductionandLemmasThree-pointboundaryvalueproblems(BVPforshort)forthreeorderdifferentialequationsareveryusefulincertainpracticalworkandattractcloseattentionextensively,see[l--41.Recently,in[11,GuptaandLakshmikanthamstudiedthefollowingthree-pointBVP:U'(x)=f(x,ulU',U)--e(x),(l)u(0)=u(n)=u(1)~0,(2)wheref:[0,1]xR3-RdoesnothavetobecontinuousandnE(0,1).ThemainresultisthefollowingTheoremLetfsatisfyCarntheodory'sc.nditions[1]andthefollowingconditions:i)3a,b,cER,or(x)ELI[0,1],suchthatfo…     

THE OPTIMAL CONTROL OF AGE－DEPENDENT POPULATION DYNAMICS BASED ON PARITY PROGRESSION

ＴＨＥＯＰＴＩＭＡＬＣＯＮＴＲＯＬＯＦＡＧＥ－ＤＥＰＥＮＤＥＮＴＰＯＰＵＬＡＴＩＯＮＤＹＮＡＭＩＣＳＢＡＳＥＤＯＮＰＡＲＩＴＹＰＲＯＧＲＥＳＳＩＯＮ￥ＧＵＯＢａｏｚｈｕ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＢｅｉｊｉｎｇＩｎ...     

STOCHASTIC ADAPTIVE SWITCHING CONTROL BASED ON MULTIPLE MODELS

1 IntroductionIn an uncertain and complex environment, the approach of "optimal" switching is often usedfor making decisions through predicting and comparing the effects of multiple schemes. In thearea of control, the mu1tipIe model approach, which has been used to improve estimations andcontrol accuracies, can be traced back at least to 1960s--1970s(see, e.g., [1l--[3l). Some practicalapplications have also been reported[4,']. In adaptive control, switching cootroller based onmultiple models…     

EXISTENCE AND ALGORITHM OF SOLUTIONS FOR GENERALIZED STRONGLY MIXED IMPLICIT QUASI-VARIATIONAL INEQUALITIES

The purpose of this paper is to introduce and study a new class of generalized strongly mixed implicit quasi-variational inequalities in Hilbert spaces, which includes the known class of generalized mixed implicit quasi-variational inequalities as a special case. By applying the auxiliary variational principle technique, the existence of solutions for this class of quasi-variational inequalities is proved. Moreover, a new iterative algorithm for computing approximate solutions is constructed and the convergence criteria for this iterative algorithm are also established.     

ON A CLASS OF WEIGHT HIERARCHIES OFTERNARY LINEAR CODES OF DIMENSION 4

The possible weight hierarchies of ternary codes of dimension 4 satisfying thealmost chain condition are completely determined in this paper.     

REDUCED FORM OF YANG-MILLS EQUATION OF SU(2) ON R~(3,1)

1.NotationsLetR3,1betheMinkowskifour-dimensionalspacewithcoordinatesx=(x')x',x',x').ThemetricdsZ=Zgijdx'dxjofR3'1isgivenbygll=gab=gb3=l,g'=--1,andgij~0fori/j.Letgi(2)betheLiealgebraofgroupSU(2).Theanti-Hermitianrepresentationsofabasisofgi(2)aretakenasfollows:inwhichi=n.Theconnectionisa1-forminwhichThereare12unknownfunctionsA,Thecurvaturetensorsaregivenbyinwhichoj=0/oxj,j=l,2,3,4.TheYang-MillsequationofSU(2)onR3)1is(see[1])TheYang-Millsequationconsistsof12equationsYMjk=0,j~1,2,3,4,k~…