Numerical stabilization of polynomial and matrix

Email: jdhan{at}sia.cn Email: zhjiang{at}sia.cn Corresponding author Email: nyy{at}sia.cn Received on March 6, 2006; Accepted on September 4, 2006 In this paper, the conception of numerical stabilization, whichis related to mantissa digits of computer and dimensions ofsystem, is described; and several strategies for the numericalstabilization of polynomial and matrix are presented.     

Estimating vaccine coverage by using computer algebra

Email: altmannd{at}rki.deEmail: altmann{at}mathematik.hu-berlin.de The approach of N Gay for estimating the coverage of a multivalentvaccine from antibody prevalence data in certain age cohortsis complemented by using computer aided elimination theory ofvariables. Hereby, Gay's usage of numerical approximation canbe replaced by exact formulae which are surprisingly nice, too.     

Necessary conditions for infinite-horizon Volterra optimal control problems with time delay

Email: csfvega{at}dm.uba.ar Received on August 17, 2006; Accepted on September 8, 2007 Necessary conditions are proved for optimal control problemsinvolving an infinite horizon and terminal conditions at infinitywhose states are governed by Volterra integral equations withnon-linear time delay.     

Estimates of the region of attraction of continuous-time cascade systems

Xiao-Song Yang Department of Mathematics, Huazhong University of Science and Technology Wuhan, Hubei 430074, People's Republic of China Huimin Li Departments of Mathematics and Control and Engineering, Huazhong University of Science and Technology Wuhan, Hubei 430074, People's Republic of China Corresponding author. Email: yangxs{at}cqupt.edu.cn Received on May 1, 2006; Accepted on October 6, 2006 In this paper, we first present some new sufficient conditionsfor global asymptotic stability of continuous-time cascade systems.Then, we give some detailed results on the region of attractionof continuous-time cascade systems. Some examples are presentedto illustrate these results.     

Post-processing with computable error bounds for the finite element approximation of a nonlinear heat conduction problem

Email: ain{at}mcs.le.ac.uk Email: D.Kelly{at}unsw.edu.au^* Email: I.Sloan{at}unsw.edu.au^** Email: swang{at}cs.curtin.edu.au It is shown how the finite element approximation of a nonlinearheat conduction problem may be post-processed to yield enhancedapproximations to the solution and the flux at any point inthe domain. Sharp computable bounds on the accuracy of the post-processedapproximations are derived. A criterion is identified for guidingadaptive refinements of the finite element discretization. Anumerical example is given illustrating the theoretical results.     

Error estimates for the finite-element solution of an elliptic singularly perturbed problem

e-mail:ang{at}am.uni-erlangen.de The paper deals with an upwind discretization of finite-volume-typefor singularly perturbed elliptic boundary value problems. Stability,inverse monotonicity and convergence are considered. The mainobjective is to pursue the dependence of the error estimateon the perturbation parameter.     

An LMI-based approach for robust stabilization of time delay systems containing saturating actuators

Email: elhaous_fati{at}yahoo.fr Corresponding author. Email: elh_tissir{at}yahoo.fr Received on September 8, 2005; Accepted on July 24, 2006 This paper deals with the problem of robust stabilization foruncertain systems with input saturation and time delay in thestate. The parameter uncertainties are time-varying and unknownbut are norm bounded. Sufficient conditions obtained via a linearmatrix inequality formulation are stated to guarantee the localstabilization. The method of synthesis consists in determiningsimultaneously a state feedback control law and an associateddomain of safe admissible states for which the stability ofthe closed-loop system is guaranteed when control saturationseffectively occur. Numerical examples are used to demonstratethe effectiveness of the proposed design technique.     

Direct approximation of observer error linearization for nonlinear forced systems

Email: klaus{at}roebenack.de In this paper, we discuss a generalization of the extended Luenbergerobserver. Our approach can be interpreted as an approximateerror linearization. The design procedure which is formulatedin terms of Lie derivatives and Lie brackets can easily be implementedusing computer algebra software.     

Time optimal control of retarded parabolic systems

Email: skrakowi{at}usk.pk.edu.pl Received on June 15, 2005; Accepted on July 12, 2006 In this paper, the time-optimal control problem for parabolicsystems in which time lags appear in the integral form bothin the state equation and in the Neumann boundary conditionis presented. The particular properties of the optimal controlare discussed.     

Multiple criteria models for evaluation of competitive bids

Email: slliu{at}mail.east.net.cnAuthor for correspondence Email: mskklai{at}cityu.edu.hkEmail: sywang{at}iss02.iss.ac.cn In this paper, two general bidding systems are proposed to aidan owner to select one contractor based on multiple-attributedecision making models. They are named the general multiple-attributelower-bidder system and the general multiple-attribute average-bid system and are an extension (and refreshment) of the multiparameterbidding system and the average-bid method, respectively. Thepreference of the owner over the criteria (or attributes) relevantto construction work award is incorporated into the two newsystems if necessary and required by the owner. The values ofthe attributes (excluding the cost) required to be determinedby the owner in the multiparameter bidding system are not necessarilydetermined in the general multiple-attribute lower-bidder system.This reduces the burden to the owner. The two new bidding systemsare demonstrated via an example, and are compared with the multiparameterbidding system and the average-bid method. The comparisons showthat the preference of the owner in regard to the attributesrelevant to selection of contractors has a significant effecton bid evaluation. The two new systems preserve the form ofthe competitive bidding concept and can easily be applied topractice.     

Controllability and observability of impulsive hybrid dynamic systems

Corresponding author, Email: cbsoh{at}auto.eee.ntu.ac.sg This paper considers the controllability and observability ofhybrid dynamic systems with impulsive switching of the otherwisecontinuously evolving state. It derives necessary and sufficientconditions for impulsive hybrid dynamic systems to be controllableand observable.     

Computation and parametrization of periodic and connecting orbits

Email: g.moore{at}ma.ic.ac.uk or na.gmoore New algorithms for the computation of periodic and connectingorbits of autonomous differential equations are developed. Previousmethods have parametrized these curves by the independent timevariable, but our procedure is based on the canonical arclengthparametrization.     

Gaussian factor models futures and forward prices

Email: hyndman{at}mathstat.concordia.ca Received on 31 July 2006. Accepted on 19 March 2007. We completely characterize the futures price and forward priceof a risky asset (commodity) paying a stochastic dividend yield(convenience yield). The asset (commodity) price is modelledas an exponential affine function of a Gaussian factors process,while the interest rate and dividend yield are affine functionsof the factors process. The characterization we provide is basedon the method of stochastic flows. We believe this method leadsto simpler and more clear-cut derivations of the futures priceand forward price formulae than alternative methods. Hedginga long-term forward contract with shorter term futures contractsand bonds is also examined.     

The Convergence of Operator Approximations at Turning Points

Present address: Department of Mathematics, University of Reading, Reading RG6 2AX. We consider the convergence of solution curves of approximationsto parameter-dependent operator equations of the form G(, x)= 0. Provided G_x(, x) remains non-singular this problem is cateredfor by a simple extension to standard theory. In this paper,however, attention is concentrated on solution curves throughcertain singular points (⁰, x⁰), and the main result is thatconvergence depends on consistency and stability results forthe linear eigenvalue problem G_x(⁰, x⁰)0 = 0.     

Therapy burden, drug resistance, and optimal treatment regimen for cancer chemotherapy

Email: boldrini{at}ime.unicamp.brAuthor to whom correspondence should be addressed. Email: michel{at}Incc.br Three nonlinear models of tumour cell growth under continuousdelivery of cycle nonspecific anticancer agents are studied.A dynamical optimization problem with the objective of minimizingthe final level of tumour cells is posed for these mathematicalsetups. The simplest setup does not possess toxicity constraints,whereas the other setups contain a dynamical equation describingthe therapy burden as a toxicity criterion. In addition, thethird setting contains the dynamics of drug resistant cells.A discussion conceming the optimal strategies of the respectivemodels is performed.     

Delay-dependent conditions for guaranteed cost observer-based control of uncertain neutral systems with time-varying delays

Email: chlien{at}mail.nkmu.edu.tw Received on August 10, 2006; Accepted on September 6, 2006 In this paper, delay-dependent guaranteed cost observer-basedcontrol for neutral systems with time-varying delays is considered.Control and observer gains will be given from the linear matrixinequality feasible solutions. Optimal guaranteed cost observer-basedcontrol which will minimize the guaranteed cost of the systemis provided.     

Optimal control for the thermistor problem with a current limiting device

Email: cimatti{at}dm.unipi.it Received on September 26, 2005; Accepted on August 2, 2006 The problem of finding in the thermistor problem the optimaldifference of applied potential in order to minimize a suitablecost functional involving the temperature is studied. We findthe optimal system in the elementary case of constant electricconductivity. In addition, a theorem of existence of the optimalsolution is given in the general case of conductivities dependingon the temperature.     

Properties of the weighted logarithmic matrix norms

Mingzhu Liu Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China Email: ghu{at}hit.edu.cn, ghuca{at}yahoo.ca Email: mzliu{at}hit.edu.cn Received on January 31, 2006; Accepted on December 9, 2006 In this paper, we are concerned with the properties of the weightedlogarithmic matrix norms. A relation between the elliptic logarithmicmatrix norm and the weighted logarithmic matrix norm is given.Based on Lyapunov equations, two weighted logarithmic matrixnorms are constructed which are less than 1-logarithmic matrixnorm and -logarithmic matrix norm, respectively. Then, an iterativescheme is presented to obtain the logarithmically -efficientmatrix norm. Numerical examples are given to illustrate theresults.     

An analysis of the coupling of finite-element and Nystrm methods in acoustic scattering

In this paper we analyze the use of a combined Nystrm and finite-elementprocedure for approximating the scattered time-harmonic acousticfield produced when an incident wave interacts with a boundedinhomogeneity. The coupling technique uses a smooth artificialboundary and explicitly decouples the integral equation andfinite-element computations. We prove convergence of the method.One highlight of this analysis is that we prove Sobolev spaceerror estimates for the Nystrm scheme (which is usually analyzedin Hlder spaces). We also present some numerical results. E-mail: kirsch{at}am.uni-erlangen.de E-mail: monk{at}math.udel.edu     

Optimal control problems of parabolic equations with an infinite number of variables and with equality constraints

Email: bahaa_gm{at}hotmail.com Received on December 6, 2005; Accepted on December 7, 2006 Optimal control problems of systems governed by parabolic equationswith an infinite number of variables and with additional equalityconstraints are considered. The extremum principle, as wellas sufficient condition of optimality, is formulated for theNeumann problem by using certain extensions of Dubovitskii–Milyutinmethod.