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.     

Review Article On Current Developments in Partial Differential Equations

The first part of this article is an overview on some recent major developments in the field of analysis and partial different equations.It is a brief presentation given by the author at a round table discussion.The second part is a supplement of various details provided by several outstanding researchers on subjects.     

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)     

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)     

Index-aware model order reduction for differential-algebraic equations

We introduce a model order reduction (MOR) procedure for differential-algebraic equations, which is based on the intrinsic differential equation contained in the starting system and on the remaining algebraic constraints. The decoupling procedure in differential and algebraic part is based on the projector and matrix chain which leads to the definition of tractability index. The differential part can be reduced by using any MOR method, we use Krylov-based projection methods to illustrate our approach. The reduction on the differential part induces a reduction on the algebraic part. In this paper, we present the method for index-1 differential-algebraic equations. We implement numerically this procedure and show numerical evidence of its validity.     

Identification of non-minimum phase transfer function using higher-order spectrum

The present paper treats the identification of parametric nonminimum phase transfer function. We propose a method of identification based on the inner outer factorization of stable transfer function. It consists of identifying the outer and inner parts of a transfer function separately. The outer part is identified by the use of the second-order spectral estimate from the observed linear process, while the inner part is identified by the use of a higher-order cumulant spectral estimate from the observed process. Respective parameter estimators are determined in the light of asymptotic efficiency. In order to estimate the order of the inner part of a transfer function, a criterion is proposed. It is introduced based on the same principle as in the case of Akaike's AIC.     

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.     

The Goursat problem for a generalized Helmholtz operator in the plane

We consider the Goursat problem in the plane for partial differential operators whose principal part is the pth power of the standard Laplace operator. The data is posed on a union of 2p distinct lines through the origin. We show that the solvability of this Goursat problem depends on Diophantine properties of the geometry of lines on which the data is posed. The first author is supported in part by DMS-0401215. The second author is supported in part by Grant MTM2006-13000-C03-03 of the D.G.I. of Spain.     

A class of Nevanlinna functions related to singular Sturm-Liouville problems

The class of Nevanlinna functions consists of functions which are holomorphic off the real axis, which are symmetric with respect to the real axis, and whose imaginary part is nonnegative in the upper halfplane. The Kac subclass of Nevanlinna functions is defined by an integrability condition on the imaginary part. In this note a further subclass of these Kac functions is introduced. It involves an integrability condition on the modulus of the Nevanlinna functions (instead of the imaginary part). The characteristic properties of this class are investigated. The definition of the new class is motivated by the fact that the Titchmarsh-Weyl coefficients of various classes of Sturm-Liouville problems (under mild conditions on the coefficients) actually belong to this class.

     

Steady state scheduling of a flexible manufacturing system with periodic releasing and flow time constraints

This paper deals with the dynamic behaviour of an FMS when parts are released periodically. The minimal release period is induced by the most critical machine or fixture pallet type. Moreover, with a fixed period, the limited number of available pallets induces a maximal flow time for every part type. Thus, the objective of this paper is to determine a part release strategy and an activity schedule on every machine which allows to control every part flow time for steady state. An analysis method for this objective is presented in this paper. Its purpose is to obtain releasing and scheduling conditions ensuring a workshop steady state compatible with the considered constraints, especially part flow times. This method is based on the resolution of conflicts between activities processed on a common machine. This resolution uses limit times associated with each activity and it can modify these limit times. These modifications in turn can induce modifications for other activity limit times due to part routing, steady-state periodicity, and part flow time constraints. Thus, an iterative procedure has been defined. It refines steady-state feasibility conditions through limit times and sequencing conditions of activities processed on a common machine. The method is illustrated with two examples.     

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.     

Triangulate flat cones on simplices

The convex hull of the vertices of a simplex and a point lying on the hyperplane spanned by the simplex is called a flat cone on the simplex. This paper proposes a natural way to simplicially triangulate flat cones on simplices and develops its applications to PL homotopy methods. This work is supported in part by the Fund of the National Committee of Education of China and in part by the National Natural Science Foundation of China.     

A Dual Variational Approach to a Class of Nonlocal Semilinear Tricomi Problems

The existence of at least one nontrivial solution to a class of semilinear Tricomi problems is established via an application of the dual variational method which captures the solution as the preimage of a minimum of a suitable dual action functional. The boundary conditions are homogeneous Dirichlet conditions on a suitable part of the boundary, as dictated by uniqueness theorems for the linear problem. While there are good compactness properties for the inverse operator for the linear problem, there is a manifest asymmetry in the linear part due to the form of the boundary conditions. The linear part is symmetrized by introducing suitable re ection operators on symmetric domains, which then results in a nonlocal character of the nonlinearity. Received July 1997; Revised February 1998     

Cournot equilibrium uniqueness via demi-concavity

A family of oligopolies that possess a unique equilibrium was identified in the second authors doctoral dissertation. For such a family, it is therein specified a class of functions-economically related to the price function of a Cournot oligopoly – that satisfy a particular type of quasi-concavity. The first part of the present article (i) conceptualizes that type of quasi-concavity by introducing the notion of demi-concavity, (ii) considers two possible variants and (iii) provides some calculus properties. The second part, by relying on the results on demi-concavity, proves a Cournot equilibrium uniqueness theorem which is new for the journal literature and subsumes various results thereof. A third part shows an example that illustrates the novelty of the result.     

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.     

A problem of the bending of a plate for a doubly connected domain with a partially unknown boundary

The problem of the bending of an isotropic elastic plate, bounded by two rectangles with vertices lying on the same half-line, drawn from the common centre, is considered. The vertices of the inner rectangle are cut by convex smooth arcs (we will call the set of these arcs the unknown part of the boundary). It is assumed that normal bending moments act on each rectilinear section of the boundary contours in such a way that the angle of rotation of the midsurface of the plate is a piecewise-constant function. The unknown part of the boundary is free from external forces. The problem consists of determining the bending of the midsurface of the plate and the analytic form of the unknown part of the boundary when the tangential normal moment acting on it takes a constant value, while the shearing force and the normal bending moments and torques are equal to zero. The problem is solved by the methods of the theory of boundary-value problems of analytical functions.     

求解鲁棒主成分分析的新交替下降方向法

鲁棒主成分分析作为统计与数据科学领域的基本工具已被广泛研究,其核心原理是把观测数据分解成低秩部分和稀疏部分.本文基于鲁棒主成分分析的非凸模型,提出了一种新的基于梯度方法和非单调搜索技术的高斯型交替下降方向法.在新算法中,交替更新低秩部分和稀疏部分相关的变量,其中低秩部分的变量是利用一步带有精确步长的梯度下降法进行更新,...     

Semicoercive Variational-hemivariational Inequalities with Unilateral Growth Conditions

A variational-hemivariational inequality on a vector valued functions space is studied with the nonlinear part satisfying the unilateral growth condition. The higher order term is assumed to be pseudo-monotone and semicoercive. The existence result has been obtained by making use of the theory of pseudo-monotone operators combined with the Lipschitz regulariza-tion of the nonlinear part.