1991年, 第4卷, 第3期　刊出日期：1991-08-15

  

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  ON THE CONSTRUCTION OF GROEBNER BASIS OF A POLYNOMIAL IDEAL BASED ON RIQUIER-JANET THEORY

  Wu Wenjun

  Journal of Systems Science and Complexity. 1991, 4(3): 193-207.

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  As a consequence of a previons study of algebraic differential geometry(see [WU1]) there may be associated to certain special kinds of differential ideals some well-behaved basis enjoying some well-behaved properties. If the differential ideals are further specialized so that they correspond to ordinary polynomial ideals then such a well-behaved basis will become the usual Groebner basis of the polynomial ideals while the latter is not known for differential ideals.
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  SOME NEW MULTIPLE SERIES INVERSIONS AND THEIR APPLICATIONS

  Chu Wenchang

  Journal of Systems Science and Complexity. 1991, 4(3): 208-214.

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  By means of difference calculus, a pair of reciprocal formulae for multi-indexed seque-nces is established which may be regarded as the multifold extension of Gould-Hsu inversions Some applications to expansion formulae and the solution for the linear system are presented.
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  A UNIFIED APPROACH TO THE METHOD OF GRADIENT PROJECTION WITH ARBITRARY INITIAL POINT

  Lai Yanlian;Wei Zengxin

  Journal of Systems Science and Complexity. 1991, 4(3): 215-224.

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  In this paper, we present a family of gradient projection method with arbitrary initial point. The formula of search direction in the method is unitary. The convergent conditions of the method are given.When the initial point is feasible, the family of the method contains several known algorithms. When the initial point is infeasible, the method is exactly that given in [6]. Finally, we give a new method which has global convergence property.
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  FINITE ELEMENT ERROR EXPANSIONS FOR THE EIGENVALUE APPROXIMATION TO THE MULTIGROUP DIFFUSION EQUATIONS

  Ding Yanheng;Lin Qun

  Journal of Systems Science and Complexity. 1991, 4(3): 225-235.

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  Asymptotic expansions for the finite element approximation to the eigenvalues of the mult-igroup diffusion equations on Ω(?)R~n(n=2,3)of reactor theory are given, firstly for a piecewise uniform triangulation, then for nonuniform quadrilateral meshes, and finally for nonuniform hexahedral meshes. The effect of certain classes of numerical integrations is studied. As applications of the expansions, several extrapolation formulas and a posteriori error estimates are obtained.
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  LOCAL MAXIMUM PRINCIPLE FOR SINGULAR DISCRETE-TIME LINEAR SYSTEMS

  Wang Enping

  Journal of Systems Science and Complexity. 1991, 4(3): 236-243.

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  In this paper a local maximum principle for the singular discrete-time linear system Mx(k)=φx(k-1)+Bu(k-1)is investigated. By using this local maximum principle we can discussthe linear-quadratic optimal regulator problem and the minimum energy problem for singular discrete-time linear systems.
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  SOME PROBLEMS OF LYAPUNOV METHOD IN LINEAR CONTINUOUS-TIME SYSTEM

  Huang Lin;C.V;Hollot ;Xu Zhongling

  Journal of Systems Science and Complexity. 1991, 4(3): 244-253.

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  In this paper, some problems of Lyapunov method in linear continuous-time system are discussed. In part 1, some motivations are given. In part 2, in order to get a good estimate ofthe decaying time in the system, the concept of appropriate Lyapunov function is introduced andthe condition of the system is given to guarantee the existence of the appropriate Lyapunov function An application of the appropriate Lyapunov function is introduced to give the bound of time varying perturbation for the stable system. In part 3, some extensions of the Lyapunov asymptotical stabilitytheorem are given, where the condition of the total derivative of the Lyapunov function along thetrajectory of the system can be reduced from negative definiteness to semi-negative definiteness andcommon quadratic forms with some reasonable conditions, the example shows the extensions are interesting.
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  OPTIMAL ADAPTIVE CONTROL WITH CONSTRAINT FOR ARMAX MODEL

  Tang Qianyu;Chen Hanfu

  Journal of Systems Science and Complexity. 1991, 4(3): 254-263.

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  For the ARMAX system with unknown coefficients the optimal adaptive control isdesigned so that the following requirements are met simultaneously: 1)the transfer function from a reference signal to the system output in the closed loop equals a prescribed rational function; 2)under the constraint mentioned in 1) a quadratic loss function is minimized; 3)the parameter estimate is strongly consistent.
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  APPROXIMATING DISTRIBUTIONS IN DISCRETE DMRL AND NBUE CLASSES

  Cheng Kan;Ma Bencheng

  Journal of Systems Science and Complexity. 1991, 4(3): 264-274.

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  In this paper we discuss the problem of approximating distributions in certain discrete life classes. Let X be a random variable (r.v.)taking nonnegative integers, EX=μ. Suppose Y is a geometric r.v. taking nonnegative integers and with the same mean μ. Denote B_2=(?), α=1-(B_2)/(μ~2), Δ(X,Y)=(?)|P(X≥k)-P(Y≥k)|. The main results are: 1)If X∈(D) DMRL (discrete decreasing mean residual life), then Δ(X,Y)≤max(α,1-e~(-2α)). 2) If X∈(D) NBUE (discrete new better than use in expectation) then Δ(X,Y)≤max(α,1-e~(-(2α)~(1/2)).
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  STOCHASTIC SYSTEM IDENTIFICATION VIA ADAPTIVE SPECTRAL FACTORIZATION

  Guo Lei;John B.Moore

  Journal of Systems Science and Complexity. 1991, 4(3): 275-288.

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  We consider in this paper the problem of recursive identification for stochastic systems when the noise model does not satisfy the positive real condition associated with convergence of standard algorithms.To avoid the positive real condition, adaptive spectral factorization techniquesare exploited on the basis of a class of non-standard time-varying recursive Riccati equations. The asymptotic properties of the Riccati equations are studied as a crucial step to the convergence results of the paper.