自抗扰控制纵横谈

首先从不确定系统控制的角度,将自抗扰控制与其它一些有关不确定系统控制的理论与方法进行比较和讨论,然后围绕自抗扰控制理论分析方面的进展,以及需要进一步研究的课题进行深入讨论与总结.通过纵横两方面的讨论揭示自抗扰控制对推进不确定系统控制研究的贡献,以及自抗扰控制方法的突出特点.  

General Uniqueness Results and Variation Speed for Blow-Up Solutions of Elliptic Equations

Let be a smooth bounded domain in R^N. We prove general uniquenessresults for equations of the form – u = au – b(x)f(u) in , subject to u = on . Our uniqueness theorem is establishedin a setting involving Karamata's theory on regularly varyingfunctions, which is used to relate the blow-up behavior of u(x)with f(u) and b(x), where b 0 on and a certain ratio involvingb is bounded near . A key step in our proof of uniqueness usesa modification of an iteration technique due to Safonov. 2000Mathematics Subject Classification 35J25 (primary), 35B40, 35J60(secondary).  

Robust numerical methods for contingent claims under jump diffusion processes

An implicit method is developed for the numerical solution ofoption pricing models where it is assumed that the underlyingprocess is a jump diffusion. This method can be applied to avariety of contingent claim valuations, including American options,various kinds of exotic options, and models with uncertain volatilityor transaction costs. Proofs of timestepping stability and convergenceof a fixed-point iteration scheme are presented. For typicalmodel parameters, it is shown the error is reduced by two ordersof magnitude at each iteration. The correlation integral iscomputed using a fast Fourier transform method. Numerical testsof convergence for a variety of options are presented.  

A Tabu-Search Hyperheuristic for Timetabling and Rostering

Hyperheuristics can be defined to be heuristics which choose between heuristics in order to solve a given optimisation problem. The main motivation behind the development of such approaches is the goal of developing automated scheduling methods which are not restricted to one problem. In this paper we report the investigation of a hyperheuristic approach and evaluate it on various instances of two distinct timetabling and rostering problems. In the framework of our hyperheuristic approach, heuristics compete using rules based on the principles of reinforcement learning. A tabu list of heuristics is also maintained which prevents certain heuristics from being chosen at certain times during the search. We demonstrate that this tabu-search hyperheuristic is an easily re-usable method which can produce solutions of at least acceptable quality across a variety of problems and instances. In effect the proposed method is capable of producing solutions that are competitive with those obtained using state-of-the-art problem-specific techniques for the problems studied here, but is fundamentally more general than those techniques.  

Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix

The Lanczos algorithm for tridiagonalizing a symmetric matrixis the basis for several methods for solving sets of linearequations as well as for solving the eigenproblem. These methodsare very useful when the matrix is large and sparse. A completerounding error analysis of the algorithm is presented here,giving among other results an important expression for the lossof orthogonality of the computed vectors. The results here canbe used to analyze the many methods which are basedon the Lanczosalgorithm.  

A New Characterization of Semi-bent and Bent Functions on Finite Fields*

We present a new characterization of semi-bent and bent quadratic functions on finite fields. First, we determine when a GF(2)-linear combination of Gold functions Tr(x²ⁱ+1) is semi-bent over GF(2ⁿ), n odd, by a polynomial GCD computation. By analyzing this GCD condition, we provide simpler characterizations of semi-bent functions. For example, we deduce that all linear combinations of Gold functions give rise to semi-bent functions over GF(2^p) when p belongs to a certain class of primes. Second, we generalize our results to fields GF(pⁿ) where p is an odd prime and n is odd. In that case, we can determine whether a GF(p)-linear combination of Gold functions Tr(x^pi+1) is (generalized) semi-bent or bent by a polynomial GCD computation. Similar to the binary case, simple characterizations of these p-ary semi-bent and bent functions are provided. Parts of this paper were presented at the 2002 IEEE International Symposium on Information Theory [10]  

The Inverse Resonance Problem for Jacobi Operators

It is proved in this paper that super-exponentially decaying,possibly non-selfadjoint perturbations of the free Jacobi operatorare uniquely determined by the location of all their eigenvaluesand resonances. 2000 Mathematics Subject Classification 39A70,34K29.  

Numerical convergence properties of option pricing PDEs with uncertain volatility

The pricing equations derived from uncertain volatility modelsin finance are often cast in the form of nonlinear partial differentialequations. Implicit timestepping leads to a set of nonlinearalgebraic equations which must be solved at each timestep. Tosolve these equations, an iterative approach is employed. Inthis paper, we prove the convergence of a particular iterativescheme for one factor uncertain volatility models. We also demonstratehow non-monotone discretization schemes (such as standard Crank–Nicolsontimestepping) can converge to incorrect solutions, or lead toinstability. Numerical examples are provided.  

Group decision making using fuzzy sets theory for evaluating the rate of aggregative risk in software development

The purpose of this study is not only to build a group decision making structure model of risk in software development but also to propose two algorithms to tackle the rate of aggregative risk in a fuzzy environment by fuzzy sets theory during any phase of the life cycle. While evaluating the rate of aggregative risk, one may adjust or improve the weights or grades of the factors until she/he can accept it. Moreover, our result will be more objective and unbiased since it is generated by a group of evaluators.