2010年, 第23卷, 第3期　刊出日期：2010-06-25

  

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  Journal of Systems Science and Complexity. 2010, 23(3): 413-413. https://doi.org/10.1007/s11424-010-0000-0

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  ASYMPTOTIC LIMITS AND STABILIZATION FOR THE 1D NONLINEARMINDLIN-TIMOSHENKO SYSTEM

  F. D. ARARUNA;P. BRAZ E SILVA;E. ZUAZUA

  Journal of Systems Science and Complexity. 2010, 23(3): 414-430. https://doi.org/10.1007/s11424-010-0137-8

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  This paper shows how the so called von K\'{a}rm\'{a}n model can be obtained as a singular limit of a modified Mindlin-Timoshenko system when the modulus of elasticity in shear $k$ tends to infinity, provided a regularizing term through a fourth order dispersive operator is added. Introducing damping mechanisms, the
  authors also show that the energy of solutions for this modified Mindlin-Timoshenko system decays exponentially, uniformly with respect to the parameter $k$. As $k\rightarrow\infty$, the authors obtain the damped von K\'{a}rm\'{a}n model with associated energy exponentially decaying to zero as well.
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  BOUNDARY CONTROL OF TWO PDE'S SEPARATED BY INTERFACE CONDITIONS

  Orazio ARENA;Walter LITTMAN

  Journal of Systems Science and Complexity. 2010, 23(3): 431-437. https://doi.org/10.1007/s11424-010-0138-7

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  This paper discusses the null boundary controllability of two PDE's, modeling a composite solid with different physical properties in each layer. Interface conditions are imposed.
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  AN APPROXIMATION SCHEME FOR BLACK-SCHOLES EQUATIONS WITHDELAYS

  Mou-Hsiung CHANG;Tao PANG;Moustapha PEMY

  Journal of Systems Science and Complexity. 2010, 23(3): 438-455. https://doi.org/10.1007/s11424-010-0139-6

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  This paper addresses a finite difference approximation for an infinite dimensional Black-Scholes equation obtained by Chang and Youree (2007). The equation arises from a consideration of an European option pricing problem in a market in which stock prices and the riskless asset prices have hereditary structures. Under a
  general condition on the payoff function of the option, it is shown that the pricing function is the unique viscosity solution of the infinite dimensional Black-Scholes equation. In addition, a finite difference approximation of the viscosity solution is provided and the convergence results are proved.
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  AN AUGMENTED BV SETTING FOR FEEDBACK SWITCHING CONTROL

  Falk M. HANTE;G\"unter LEUGERING;Thomas I. SEIDMAN

  Journal of Systems Science and Complexity. 2010, 23(3): 456-466. https://doi.org/10.1007/s11424-010-0140-0

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  This paper considers dynamical systems under feedback with control actions limited to switching. The authors wish to understand the closed-loop systems as approximating multi-scale problems in which the implementation of switching merely acts on a fast scale. Such hybrid dynamical systems are extensively studied in the literature, but not much so far for feedback with partial state observation. This becomes in particular relevant when the dynamical systems are governed by partial differential equations. The authors introduce an augmented BV setting which permits recognition of certain fast scale effects and give a corresponding well-posedness result for observations with such minimal regularity. As an application for this setting, the authors show existence of solutions for systems of semilinear hyperbolic equations under such feedback with pointwise observations.
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  INTERIOR PENALTY BILINEAR IFE DISCONTINUOUS GALERKIN METHODSFOR ELLIPTIC EQUATIONS WITH DISCONTINUOUS COEFFICIENT

  Xiaoming HE;Tao LIN;Yanping LIN

  Journal of Systems Science and Complexity. 2010, 23(3): 467-483.

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  This paper applies bilinear immersed finite elements (IFEs) in the interior penalty discontinuous Galerkin (DG) methods for solving a second order elliptic equation with discontinuous coefficient. A discontinuous bilinear IFE space is constructed and
  applied to both the symmetric and nonsymmetric interior penalty DG formulations. The new methods can solve an interface problem on a Cartesian mesh independent of the interface with local refinement at any locations needed even if the interface has a nontrivial geometry. Numerical examples are provided to show features of
  these methods.
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  INTEREST RATE RISK PREMIUM AND EQUITY VALUATION

  Zhuang KANG;Srdjan D. STOJANOVIC

  Journal of Systems Science and Complexity. 2010, 23(3): 484-498. https://doi.org/10.1007/s11424-010-0142-y

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  The authors employ the recent stochastic-control-based approach to financial mathematics to solve a problem of determination of the risk premium for a stochastic interest rate model, and the corresponding problem of equity valuation. The risk premium is determined explicitly, by means of solving a corresponding partial differential equation (PDE), in two forms: one, time-dependent, corresponding to a finite time contract expiration, and the simpler version corresponding to perpetual contracts. As stocks are perpetual contracts, when solving the problem of equity valuation, the latter form of the risk premium is used. By means of solving the general pricing PDE, an efficient equity valuation method was developed that is a combination of some sophisticated explicit formulas, and a numerical procedure.
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  NONHOMOGENEOUS BOUNDARY VALUE PROBLEMS FOR THE KORTEWEG-DEVRIES EQUATION ON A BOUNDED DOMAIN

  Eugene F. KRAMER;Bingyu ZHANG

  Journal of Systems Science and Complexity. 2010, 23(3): 499-526. https://doi.org/10.1007/s11424-010-0143-x

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  This paper studies an initial-boundary-value problem (IBVP) of the Korteweg-de Vries equation posed on a finite interval with general nonhomogeneous boundary conditions. Using the strong Kato smoothing property of the associated linear problem, the IBVP is shown to be locally well-posed in the space $H^s (0,1)$ for any $s\geq0$ via the contraction mapping principle.
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  RECENT PROGRESS ON CONTROLLABILITY/OBSERVABILITY FOR SYSTEMSGOVERNED BY PARTIAL DIFFERENTIAL EQUATIONS

  Hongheng LI;Qi L\"U;Xu ZHANG

  Journal of Systems Science and Complexity. 2010, 23(3): 527-545. https://doi.org/10.1007/s11424-010-0144-9

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  The main purpose of this paper is to overview some recent methods and results on controllability/observability problems for systems governed by partial differential equations. First, the authors review the theory for linear partial differential equations, including the iteration method for the null controllability of the
  time-invariant heat equation and the Rellich-type multiplier method for the exact controllability of the time-invariant wave equation, and especially a unified controllability/observability theory for parabolic and hyperbolic equations based on a global Carleman estimate. Then, the authors present sharp global controllability
  results for both semi-linear parabolic and hyperbolic equations, based on linearization approach, sharp observability estimates for the corresponding linearized systems and the fixed point argument. Finally, the authors survey the local null controllability result for a class of quasilinear parabolic equations based on the global Carleman estimate, and the local exact controllability result for
  general hyperbolic equations based on a new unbounded perturbation technique.
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  FOUR STEP SCHEME FOR GENERAL MARKOVIAN FORWARD-BACKWARD SDES

  Jin MA;Jiongmin YONG;Yanhong ZHAO

  Journal of Systems Science and Complexity. 2010, 23(3): 546-571. https://doi.org/10.1007/s11424-010-0145-8

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  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 semi-martingales, and the backward generator requires only mild regularity assumptions. The authors show that 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 prescribed time duration; and the backward
  components can be determined explicitly by the forward component via
  the classical solution to a system of parabolic integro-partial
  differential equations. An important consequence the authors would like to draw from this fact is that, contrary to the general belief, in a Markovian set-up
  the martingale representation theorem is no longer the reason for the well-posedness of the FBSDE, but rather a consequence of the existence of the solution of the decoupling integral-partial differential equation. Finally, the authors briefly discuss the possibility of reducing the regularity requirements of the coefficients by using a scheme proposed by F. Delarue (2002) to the current case.
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  STOCK LOAN VALUATION UNDER A REGIME-SWITCHING MODEL WITHMEAN-REVERTING AND FINITE MATURITY

  David PRAGER; Qing ZHANG

  Journal of Systems Science and Complexity. 2010, 23(3): 572-583. https://doi.org/10.1007/s11424-010-0146-7

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  Stock loans are business contracts between borrowers and lenders in which the borrower uses shares of stock as collateral for the loan. Since the value of the collateral is subject to wide and frequent price swings, valuing such a transaction behaves more like an option pricing problem than a debt valuation problem. This paper will list, prove, and analyze formulas for stock loan valuation with finite horizon under various stock models, including classical geometric Brownian motion, mean-reverting, and two-state regime-switching with both mean-reverting and geometric Brownian motion states. Numerical examples are reported to illustrate the results.
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  OPTIMAL INVERSE LQG CONTROL FOR CERTAIN ODE AND PDESTATIONARY PROCESSES

  David L. RUSSELL

  Journal of Systems Science and Complexity. 2010, 23(3): 584-599. https://doi.org/10.1007/s11424-010-0147-6

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  Following work carried out earlier on linear-quadratic optimal control for linear finite dimensional stationary systems we report, in this article, on extension of some of those results to certain infinite dimensional systems; in particular a class of PDE systems of elliptic type. These systems are studied in the now familiar
  framework developed by J. L. Lions and E. Magenes, specialized to a subclass of such systems important in a variety of applications. As an extended example this paper studies an optimal redistribution problem in a groundwater flow system governed by Darcy's equation, presenting both analytic and computational work related to such problems.
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  CONVERGENCE RATES OF MARKOV CHAIN APPROXIMATION METHODS FORCONTROLLED DIFFUSIONS WITH STOPPING

  Qingshuo SONG;Gang George YIN

  Journal of Systems Science and Complexity. 2010, 23(3): 600-621. https://doi.org/10.1007/s11424-010-0148-5

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  This work is concerned with rates of convergence of numerical methods using Markov chain approximation for controlled diffusions with stopping (the first exit time from a bounded region). In lieu of considering the associated finite difference schemes for Hamilton-Jacobi-Bellman (HJB) equations, a purely probabilistic
  approach is used. There is an added difficulty due to the boundary condition, which requires the continuity of the first exit time with respect to the discrete parameter. To prove the convergence of the algorithm by Markov chain approximation method, a tangency problem might arise. A common approach uses certain conditions to avoid the tangency problem. Here, by modifying the value function, it is demonstrated that the tangency problem will not arise in the sense of convergence in probability and in $L^1$. In addition, controlled diffusions with a discount factor is also treated.
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  SIGNAL ESTIMATION WITH BINARY-VALUED SENSORS

  Leyi WANG;Gang George YIN ;Chanying LI ;Weixing ZHENG

  Journal of Systems Science and Complexity. 2010, 23(3): 622-639. https://doi.org/10.1007/s11424-010-0149-4

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  This paper introduces several algorithms for signal estimation using binary-valued output sensing. The main idea is derived from the empirical measure approach for quantized identification, which has been shown to be convergent and asymptotically efficient when the unknown parameters are constants. Signal estimation under binary-valued observations must take into consideration of time
  varying variables. Typical empirical measure based algorithms are modified with exponential weighting and threshold adaptation to accommodate time-varying natures of the signals. Without any information on signal generators, the authors establish estimation algorithms, interaction between noise reduction by averaging and signal tracking, convergence rates, and asymptotic efficiency. A threshold adaptation algorithm is introduced. Its convergence and convergence rates are analyzed by using the ODE method for stochastic approximation problems.
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  ESTIMATION OF TIME DEPENDENT CARBON TRANSFER COEFFICIENTSUSING NET ECOSYSTEM EXCHANGE DATA

  Luther WHITE

  Journal of Systems Science and Complexity. 2010, 23(3): 640-664. https://doi.org/10.1007/s11424-010-0150-y

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  Time dependent carbon transfer coefficients are estimated using ecosystem exchange data by minimizing over variable observational intervals, Kalman filter, and variational minimization techniques. Transfer coefficients are determined by
  application of estimation procedures to subintervals from a partition of the observational time period, minimizing the variance of analyzed errors without the imposition of a priori transfer coefficient models in Kalman filters, and minimization
  with respect to transfer coefficients in variational fit-to-data functionals. Results are compared between methods and seasonal variability is observed in the transfer coefficients.
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  STABILITY FOR THE MIX-DELAYED COHEN-GROSSBERG NEURAL NETWORKS WITH NONLINEAR IMPULSE

  Yong ZHAO;Qishao LU ;Zhaosheng FENG

  Journal of Systems Science and Complexity. 2010, 23(3): 665-680. https://doi.org/10.1007/s11424-010-0151-x

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  In this paper, the authors are concerned with the stability of the mix--delayed Cohen-Grossberg neural networks with nonlinear impulse by the nonsmooth analysis. Some novel sufficient conditions are obtained for the existence and the globally asymptotic stability of the unique equilibrium point, which include the well-known results on some impulsive systems and non-impulsive systems as its
  particular cases. The authores also analyze the globally exponential stability of the equilibrium point. Two examples are exploited to illustrate the feasibility and effectiveness of our results.