Synthesis of the Optimal Control of Linear Logical-Dynamical Systems Under Instant Multiple Switchings of the Automaton Part

We consider a dynamic system controlled by an automaton with memory. The continuous part of the system is described by linear differential equations and the logical (automaton) part is described by linear recurrence equations. The moments of the state change of the automaton part are not known in advance and they are determined in the process of optimization. Modes with instant multiple switchings of the automaton part are admitted. Based on sufficient optimality conditions, we develop a technique for the synthesis of a feedback control. The application of the technique is demonstrated in an example.     

Vector field reconstruction via quaternionic setting

We propose the reconstruction of the solenoidal part of a vector field supported in the unit ball in 3 dimensions by using cone beam data from a curve surrounding it, and this curve satisfies the Tuy's condition of order 3. We use the quaternionic inversion formula to decompose the solenoidal part of a vector field into 2 parts. To recover the first one, which is the main part of the solenoidal component, another definition of a cone beam transform containing both Doppler and transverse data will be introduced. The second part will be reconstructed by using information from the first part as in Katsevich and Schuster's work with less data.     

Weakly coupled semilinear parabolic evolution systems

Summary We obtain a priori bounds, global existence results, and a variation of parameters representation for classical solutions to weakly coupled semilinear parabolic systems which include spatial and temporal inhomogeneities.Supported in part by NSF Grant #DMS-8803151.Supported in part by NSF Grant #DMS-8813071.Supported in part by Texas Advanced Research Grant #1100.     

Adaptive control of discounted Markov decision chains

In this paper, we consider discounted-reward finite-state Markov decision processes which depend on unknown parameters. An adaptive policy inspired by the nonstationary value iteration scheme of Federgruen and Schweitzer (Ref. 1) is proposed. This policy is briefly compared with the principle of estimation and control recently obtained by Schäl (Ref. 4).This research was supported in part by the Consejo Nacional de Ciencia y Tecnología under Grant No. PCCBBNA-005008, in part by a grant from the IBM Corporation, in part by the Air Force Office of Scientific Research under Grant No. AFOSR-79-0025, in part by the National Science Foundation under Grant No. ECS-0822033, and in part by the Joint Services Electronics Program under Contract No. F49620-77-C-0101.     

Necessary conditions for the optimality of the automaton part of a logical-dynamical system

A dynamical system controlled by an automaton with memory is considered. The continuous part of the system is described by differential equations, and the automaton part, by recurrence inclusions. The instants of time at which the state of the automaton part is changed are not known in advance and are determined during the optimization process. Moreover, modes with multiple switchings of the automaton part at a given instant of time are admitted. Necessary conditions for the optimality of a program control are obtained. The application of the optimality conditions is illustrated by examples.     

On the rate of convergence in the entropic central limit theorem

We study the rate at which entropy is produced by linear combinations of independent random variables which satisfy a spectral gap condition.Mathematics Subjects Classification (2000):94A17; 60F05Supported in part by the EU Grant HPMT-CT-2000-00037, The Minkowski center for Geometry and the Israel Science Foundation.Supported in part by NSF Grant DMS-9796221.Supported in part by EPSRC Grant GR/R37210.Supported in part by the BSF, Clore Foundation and EU Grant HPMT-CT-2000-00037.     

The subgaussian constant and concentration inequalities

We study concentration inequalities for Lipschitz functions on graphs by estimating the optimal constant in exponential moments of subgaussian type. This is illustrated on various graphs and related to various graph constants. We also settle, in the affirmative, a question of Talagrand on a deviation inequality for the discrete cube. Research supported in part by NSF Grant No. DMS-0405587 and by EPSRC Visiting Fellowship. Research supported in part by NSF Grant No. DMS-9803239, DMS-0100289. Research supported in part by NSF Grant No. DMS-0401239.     

Volume comparison à la Aleksandrov

Sans résumé Supported in part by a grant from the National Science Foundation. Supported in part by a grant from the National Science Foundation and the Sloan Foundation.     

An improved part grouping model for minimizing makespan in FMS

In some flexible manufacturing systems (FMSs), limited tool magazine capacity requires grouping of parts into subsets for production. Although several studies have addressed the part grouping issue, research comparing the performance of models is scanty. Moreover, there is no congruency in the objectives of the present part grouping models and subsequent loading models. Traditionally, part grouping is addressed before machine loading. In this study, we overcome the drawbacks by proposing two models: model LM, which does not require part grouping, and model PGLRM (part grouping, loading and routing model), which requires part grouping. The performance of model LM serves as a benchmark. These two models also address machine loading and part routing issues concurrently. Model PGLRM's performance is then compared with the performance of model LM and few other existing part grouping models in terms of makespan and routing flexibility. Our analysis shows that model PGLRM not only results in a lower value of makespan but also imparts higher routing flexibility as compared to existing part grouping models.     

Simulation of Deep Drawing of Carbon Fibre Prepregs

The simulation of prepregs must regard highly anisotropic, viscoelastic and thermal-chemical properties. To this end a constitutive model is split into an anisotropic elastic part, which represents the fibre fraction and an isotropic, viscoelastic part, representing the matrix. The second part also contains curing, causing a dependency on time and temperature. During real deep-drawing processes large deformations up to 50 % occur, which is considered in a formulation at large strains. This model contains an anisotropic elastic part based on a Neo-Hooke law enhanced by an anisotropic part. A viscoelastic part is added using Hencky-strains and the work-conjugate Hill-stress to transfer a model for small strains into large strains. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Covariate selection for semiparametric hazard function regression models

We study a flexible class of nonproportional hazard function regression models in which the influence of the covariates splits into the sum of a parametric part and a time-dependent nonparametric part. We develop a method of covariate selection for the parametric part by adjusting for the implicit fitting of the nonparametric part. Asymptotic consistency of the proposed covariate selection method is established, leading to asymptotically normal estimators of both parametric and nonparametric parts of the model in the presence of covariate selection. The approach is applied to a real data set and a simulation study is presented.     

Methods to solve multi-skill project scheduling problem

This is a summary of the author’s PhD thesis supervised by P. Martineau and E. Néron and defended on 28 November 2006 at the Université François-Rabelais de Tours. The thesis is written in French, and is available upon request from the author. This work deals with the problem of scheduling a project. The activities of this project requires skills that may not be mastered by all persons involved. First of all, the problem is defined in the introduction part. Then we propose different methods to solve it: lower bounds in part 2, different heuristics and meta-heuristics in part 3, and finally a branch-and-bound procedure in the last part.     

Computing fence designs for orienting parts

A common task in automated manufacturing processes is to orient parts prior to assembly. We consider sensorless orientation of a polygonal part by a sequence of fences. We show that any polygonal part can be oriented by a sequence of fences placed along a conveyor belt, thereby settling a conjecture by Wiegley et al. (1997), and present the first polynomial-time algorithm to compute the shortest such sequence. The algorithm is easy to implement and runs in time O(n³ logn), where n is the number of vertices of the part.     

Portfolio Optimization in a Semi-Markov Modulated Market

We address a portfolio optimization problem in a semi-Markov modulated market. We study both the terminal expected utility optimization on finite time horizon and the risk-sensitive portfolio optimization on finite and infinite time horizon. We obtain optimal portfolios in relevant cases. A numerical procedure is also developed to compute the optimal expected terminal utility for finite horizon problem. This work was supported in part by a DST project: SR/S4/MS: 379/06; also supported in part by a grant from UGC via DSA-SAP Phase IV, and in part by a CSIR Fellowship.     

Modeling and Simulation of Polyoxymethylene

This essay is aimed at a brief representation of a constitutive model for a plastic called polyoxymethylene. This kind of plastic shows phenomena like tension-compression asymmetry, non-linear rate-dependence as well as a pronounced relaxation behaviour. The tension-compression asymmetry is modelled by the elastic part of the equilibrium stress state whereas the hysteretic part is described by an Armstrong&Frederick-type evolution equation. A particular viscosity function is used for describing the evolution of the viscous strains occuring in the overstress part. The model is able to represent most of the aforementioned phenomena in tension, compression and torsion experiments. In the second part of the article, the implementation of the constitutive model into the .nite element program ANSYS is described followed by a test calculation treating a nut of a bolt. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An efficiency frontier approach for the design of cellular manufacturing systems in a lumpy demand environment

A new multi-objective approach for the cell formation problem in a lumpy demand environment is presented. The objectives addressed in this paper are grouping efficiency and capacity requirements. In lumpy demand the required capacity is affected by demand variability and the correlation between the part types assigned to the cells. We claim that since the required capacity is determined by part types grouping, part type demands variability and their correlation should be taken into consideration as part of the cell formation. This new approach is discussed and formulated as a mixed integer programming model and illustrated by a wide range of typical examples. These examples demonstrate that when using traditional approaches designers do not obtain optimal solutions and may make decisions on the basis of wrong results. The proposed approach helps designers eliminate these problems and produce a reasonable cell design. A genetic algorithm is proposed and examined for designing large-scale systems.     

Hybrid neural network shock absorber model

A hybrid neural network model is presented and described. The model is composed of a mechanical and thermodynamical part. The mechanical part is described by Akima spline in combination with a feed-forward neural network, while in the case of the thermodynamic part differential equation of dissipative heating is formulated. The interface between both part is provided by the neural network. To identify a proper parameter set of the hybrid model a shock absorber of a middle class passenger car is measured on a servo-hydraulic testing machine. As an excitation a stochastic signal with a predefined power spectral density (PSD) is used. Subsequently the hybrid shock absorber is implemented into a full vehicle model in ADAMS/Car to test its numerical performance and influence on the vertical vehicle dynamics. As reference a standard spline shock absorber model is taken. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The range of the gradient of a LipschitzC 1-smooth bump in infinite dimensions

If a Banach space has a LipschitzC ¹-smooth bump function, then it admits other bumps of the same smoothness whose gradients exactly fill the dual unit ball and other reasonable figures. This strengthens a result of Azagra and Deville who were able to cover the dual unit ball. Supported in part by NSERC and the Canada Research Chair Programme. Supported in part by grants NATO CRG-973982, GAĈR 201-01-1198, and AV 1019003 (Czech Republic). Supported in part by NATO CRG-973982 and NSERC.     

Tauberian relations between the Abel-type and the Borel-type methods of summability

We consider the conditions underwhich a series, summable by an Abel-type method, is also summable by a Borel-type method. This extends and improves the known result of G. Doetsch.Supported in part by the National Research Council of Canada.Supported in part by the Mathematics Research Center, National Science Council, Taiwan, Republic of China.     

Partial expansion of a Lipschitz domain and some applications

We show that a Lipschitz domain can be expanded solely near a part of its boundary, assuming that the part is enclosed by a piecewise C ¹ curve. The expanded domain as well as the extended part are both Lipschitz. We apply this result to prove a regular decomposition of standard vector Sobolev spaces with vanishing traces only on part of the boundary. Another application in the construction of low-regularity projectors into finite element spaces with partial boundary conditions is also indicated.