bluuebunny/crossref_metadata_2025 huggingface dataset:
Robustness with respect to disturbance model uncertainty: Theory and application to autopilot performance analysis
Authors: Davison Daniel E. , Kabamba Pierre T. , Meerkov Semyon M.
Published: September 2005

This paper deals with the notion of disturbance model uncertainty. The disturbance is modeled as the output of a first‐order filter which is driven by white noise and whose bandwidth and gain are uncertain. An analytical expression for the steady‐state output variance as a function of the uncertain bandwidth and gain is derived, and several properties of this variance function are analyzed. Two notions, those of disturbance bandwidth margin and disturbance gain margin are also introduced. These tools are then applied to the analysis of a simple altitude‐hold autopilot system in the presence of turbulence where the turbulence scale is treated as an uncertain parameter. It is shown that the autopilot, which is satisfactory for nominal turbulence scale, may be inadequate when the uncertainty is taken into account. Moreover, it is proven that, in order to obtain a design that provides robust performance in the face of turbulence scale uncertainty, it is necessary to substantially increase the controller bandwidth, even if one is willing to sacrifice the autopilot′s holding ability and stability robustness.
Generalized S‐procedure and finite frequency KYP lemma
Authors: Iwasaki Tetsuya , Meinsma Gjerrit , Fu Minyue
Published: September 2005

The contribution of this paper is twofold. First we give a generalization of the S‐procedure which has been proven useful for robustness analysis of control systems. We then apply the generalized S‐procedure to derive an extension of the Kalman – Yakubovich – Popov lemma that converts a frequency domain condition within a finite interval to a linear matrix inequality condition suitable for numerical computations.
Improvability of assembly systems I: Problem formulation and performance evaluation
Authors: Chiang S.-Y. , Kuo C.-T. , Lim J.-T. , Meerkov S. M.
Published: September 2005

This work develops improvability theory for assembly systems. It consists of two parts. Part I includes the problem formulation and the analysis technique. Part II presents the so‐called improvability indicators and a case study.

Improvability theory addresses the questions of improving performance in production systems with unreliable machines. We consider both constrained and unconstrained improvability. In the constrained case, the problem consists of determining if there exists a re‐distribution of resources (inventory and workforce), which leads to an increase in the system′s production rate. In the unconstrained case, the problem consists of identifying a machine and a buffer, which impede the system performance in the strongest manner.

The investigation of the improvability properties requires an expression for the system performance measures as functions of the machine and buffer parameters. This paper presents a method for evaluating these functions and illustrates their practical utility using a case study at an automotive components plant. Part II uses the method developed here to establish conditions of improvability and to describe additional results of the case study.
Window observers for linear systems
Authors: Utkin Vadim , Li Shengming
Published: September 2005

Given a linear system with output y = Cx
and a window function ω(t), i.e., ∀t, ω(t)∈ {0,1 }, and assuming that the window function is Lebesgue measurable, we refer to the following observer,
as a window observer. The stability issue is treated in this paper. It is proven that for linear time‐invariant systems, the window observer can be stabilized by an appropriate design under a very mild condition on the window functions, albeit for linear time‐varying system, some regularity of the window functions is required to achieve observer designs with the asymptotic stability. The corresponding design methods are developed. An example is included to illustrate the possible applications
Vertical flow of a multiphase mixture in a channel
Authors: Massoudi Mehrdad , Rao C. Lakshmana
Published: September 2005

The flow of a multiphase mixture consisting of a viscous fluid and solid particles between two vertical plates is studied. The theory of interacting continua or mixture theory is used. Constitutive relations for the stress tensor of the granular materials and the interaction force are presented and discussed. The flow of interest is an ideal one where we assume the flow to be steady and fully developed; the mixture is flowing between two long vertical plates. The non‐linear boundary value problem is solved numerically, and the results are presented for the dimensionless velocity profiles and the volume fraction as functions of various dimensionless numbers.
Adaptive algorithm for noisy autoregressive signals
Authors: Zheng Wei Xing
Published: September 2005

This paper presents a new type of improved least‐squares (ILS) algorithm for adaptive parameter estimation of autoregressive (AR) signals from noisy observations. Unlike the previous ILS based methods, the developed algorithm can give consistent parameter estimates in a very direct manner that it does not involve dealing with an augmented noisy AR model. The new algorithm is demonstrated to outperform the previous ILS based methods in terms of its improved numerical efficiency.
Mixed H2/H∞ control of flexible structures
Authors: De Farias D. P. , De Oliveira M. C. , Geromel J. C.
Published: September 2005

This paper addresses the design of full order linear dynamic output feedback controllers for flexible structures. Unstructured H∞ uncertainty models are introduced for systems in modal coordinates and in reduced order form. Then a controller is designed in order to minimize a given H2 performance function while keeping the maximum supported H∞ perturbation below some appropriate level. To solve this problem we develop an algorithm able to provide local optimal solutions to optimization problems with convex constraints and non‐convex but differentiable objective functions. A controller design procedure based on a trade‐off curve is proposed and a simple example is solved, providing a comparison between the proposed method and the usual minimization of an upper bound H2 to the norm. The method is applied to two different flexible structure theoretical models and the properties of the resulting controllers are shown in several simulations.
Adaptive stabilization of continuous‐time systems guaranteeingthe controllability of a modified estimation model
Authors: de la Sen M.
Published: September 2005

This paper presents an indirect adaptive control scheme for continuous‐time systems. The estimated plant model is controllable while the estimation model is free from singularities. Such singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. This property is achieved by ensuring that the absolute value of its determinant does not lie below a prescribed positive threshold. A switching rule is used in the estimates modification algorithm to ensure the controllability of the modified estimated model while avoiding possible chattering. For that purpose, the switching rule takes values at two possible distinct prefixed thresholds. In the event when the Sylvester determinant takes the current value of the switching function then that one switches to
the alternative threshold. The convergence of both the unmodified and modified
estimates to finite limits guarantees that switching ends in finite time. Thus, the solution to the controlled plant exist so that all the signals within the loop are well‐posed.
Escape probability and mean residence time in random flows withunsteady drift
Authors: Brannan James R. , Duan Jinqiao , Ervin Vincent J.
Published: September 2005

We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then develop numerical algorithms to solve for escape probability and mean residence time, which are described by backward Fokker‐Planck type partial differential equations. A few computational issues are also discussed. Finally, we apply these ideas and numerical algorithms to a tidal flow model.
Quasi‐boundary value method for non‐well posed problem for aparabolic equation with integral boundary condition
Authors: Denche M. , Bessila K.
Published: September 2005

In this paper we study the problem of control by the initial conditions of the heat equation with an integral boundary condition. This problem is ill‐posed. Perturbing the final condition we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates.
Effect of rotation on wave propagation in a transversely isotropic medium
Authors: Ahmad F. , Khan A.
Published: September 2005

Wave propagation in a transversely isotropic unbounded medium rotating about its axis of symmetry is studied. For propagation at high frequencies, effects of rotation are negligible but for a frequency which is much smaller than the frequency of rotation, there is a fast wave and two very slow waves. When the two frequencies are equal, the speed of a wave becomes unbounded.
Sufficient conditions for Lagrange, Mayer, and Bolza optimization problems
Authors: Boltyanski V.
Published: September 2005

The Maximum Principle [2,13] is a well known necessary condition for optimality. This condition, generally, is not sufficient. In [3], the author proved that if there exists regular synthesis of trajectories, the Maximum Principle also is a sufficient condition for time‐optimality. In this article, we generalize this result for Lagrange, Mayer, and Bolza optimization problems.
Solution of nonlinear Volterra‐Hammerstein integral equations via rationalized Haar functions
Authors: Razzaghi M. , Ordokhani Y.
Published: September 2005

Rationalized Haar functions are developed to approximate the solutions of the nonlinear Volterra‐Hammerstein integral equations. Properties of Rationalized Haar functions are first presented, and the operational matrix of integration together with the product operational matrix are utilized to reduce the computation of integral equations to into some algebraic equations. The method is computationally attractive, and applications are demonstrated through illustrative examples.
Nonlinear analysis of flexible beams undergoing large rotations Via symbolic computations
Authors: Yuan Xiaofeng , Tada Yukio
Published: September 2005

In this paper, a two‐stage approach is presented for analyzing flexible beams undergoing large rotations. In the first stage, the symbolic forms of equations of motion and the Jacobian matrix are generated by means of MATLAB and written into a MATLAB script file automatically, where the flexible beams are described by the unified formulation presented in our previous paper. In the second stage, the derived equations of motion are solved by means of implicit numerical methods. Several comparison computations are performed. The two‐stage approach proves to be much more efficient than pure numerical one.
Analysis of the self‐similar solutions of a generalizedBurger′s equation with nonlinear damping
Authors: Rao Ch. Srinivasa , Sachdev P. L. , Ramaswamy Mythily
Published: September 2005

The nonlinear ordinary differential equation resulting from the self‐similar reduction of a generalized Burgers equation with nonlinear damping is studied in some detail. Assuming initial conditions at the origin we observe a wide variety of solutions – (positive) single hump, unbounded or those with a finite zero. The existence and nonexistence of positive bounded solutions with different types of decay (exponential or algebraic) to zero at infinity for specific parameter ranges are proved.
New schemes for a two‐dimensional inverse problem withtemperature overspecification
Authors: Dehghan Mehdi
Published: September 2005

Two different finite difference schemes for solving the two‐dimensional parabolic inverse problem with temperature overspecification are considered. These schemes are developed for indentifying the control parameter which produces, at any given time, a desired temperature distribution at a given point in the spatial domain. The numerical methods discussed, are based on the (3,3) alternating direction implicit (ADI) finite difference scheme and the (3,9) alternating direction implicit formula. These schemes are unconditionally stable. The basis of analysis of the finite difference equation considered here is the modified equivalent partial differential equation approach, developed from the 1974 work of Warming and Hyett [17]. This allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes. These schemes use less central processor times than the fully implicit schemes for two‐dimensional diffusion with temperature overspecification. The alternating direction implicit schemes developed in this report use more CPU times than the fully explicit finite difference schemes, but their unconditional stability is significant. The results of numerical experiments are presented, and accuracy and the Central Processor (CPU) times needed for each of the methods are discussed. We also give error estimates in the maximum norm for each of these methods.
Dissipativity theory and stability of feedback interconnectionsfor hybrid dynamical systems
Authors: Haddad Wassim M. , Chellaboina Vijaysekhar
Published: September 2005

In this paper we develop a unified dynamical systems framework for a general class of systems possessing left‐continuous flows; that is, left‐continuous dynamical systems. These systems are shown to generalize virtually all existing notions of dynamical systems and include hybrid, impulsive, and switching dynamical systems as special cases. Furthermore, we generalize dissipativity, passivity, and nonexpansivity theory to left‐continuous dynamical systems. Specifically, the classical concepts of system storage functions and supply rates are extended to left‐continuous dynamical systems providing a generalized hybrid system energy interpretation in terms of stored energy, dissipated energy over the continuous‐time dynamics, and dissipated energy over the resetting events. Finally, the generalized dissipativity notions are used to develop general stability criteria for feedback interconnections of left‐continuous dynamical systems. These results generalize the positivity and small gain theorems to the case of left‐continuous, hybrid, and impulsive dynamical systems.
A hybrid domain analysis for systems with delays in state and control
Authors: Razzaghi M. , Marzban H. R.
Published: September 2005

The solution of time‐delay systems is obtained by using a hybrid function. The properties of the hybrid functions consisting of block‐pulse functions and Chebyshev polynomials are presented. The method is based upon expanding various time functions in the system as their truncated hybrid functions. The operational matrix of delay is introduced. The operational matrices of integration and delay are utilized to reduce the solution of time‐delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
A new numerical scheme for non uniform homogenized problems: Application to the non linear Reynolds compressible equation
Authors: Buscaglia Gustavo C. , Jai Mohammed
Published: September 2005

A new numerical approach is proposed to alleviate the computational cost of solving non‐linear non‐uniform homogenized problems. The article details the application of the proposed approach to lubrication problems with roughness effects. The method is based on a two‐parameter Taylor expansion of the implicit dependence of the homogenized coefficients on the average pressure and on the local value of the air gap thickness. A fourth‐order Taylor expansion provides an approximation that is accurate enough to be used in the global problem solution instead of the exact dependence, without introducing significant errors. In this way, when solving the global problem, the solution of local problems is simply replaced by the evaluation of a polynomial. Moreover, the method leads naturally to Newton‐Raphson nonlinear iterations, that further reduce the cost.

The overall efficiency of the numerical methodology makes it feasible to apply rigorous homogenization techniques in the analysis of compressible fluid contact considering roughness effects. Previous work makes use of an heuristic averaging technique. Numerical comparison proves that homogenization‐based methods are superior when the roughness is strongly anisotropic and not aligned with the flow direction.
Aggregation of a class of large‐scale, interconnected, nonlineardynamical systems
Authors: Darbha Swaroop , Rajagopal K. R.
Published: September 2005

In this paper, the authors consider the issue of the construction of a meaningful average for a collection of nonlinear dynamical systems. Such a collection of dynamical systems may or may not have well defined ensemble averages as the existence of ensemble averages is predicated on the specification of appropriate initial conditions. A meaningful “average” dynamical system can represent the macroscopic behavior of the collection of systems and allow us to infer the behavior of such systems on an average. They
can also prove to be very attractive from a computational perspective. An advantage to the construction of the meaningful average is that it involves integrating a nonlinear differential equation, of the same order as that of any member in the collection. An average dynamical system can be used in the analysis and design of hierarchical systems, and will allow one to capture approximately the response of any member of the collection.
Absolute stability of nonlinear systems with time delays and applications to neural networks
Authors: Liu Xinzhi , shen Xuemin , Zhang Yi
Published: September 2005

In this paper, absolute stability of nonlinear systems with time delays is investigated. Sufficient conditions on absolute stability are derived by using the comparison principle and differential inequalities. These conditions are simple and easy to check. In addition, exponential stability conditions for some special cases of nonlinear delay systems are discussed. Applications of those results to cellular neural networks are presented.
Passivity analysis and synthesis for uncertain time‐delay systems
Authors: Mahmoud Magdi S. , Xie Lihua
Published: September 2005

In this paper, we investigate the robust passivity analysis and synthesis problems for a class of uncertain time‐delay systems. This class of systems arises in the modelling effort of studying water quality constituents in fresh stream. For the analysis problem, we derive a sufficient condition for which the uncertain time‐delay system is robustly stable and strictly passive for all admissible uncertainties. The condition is given in terms of a linear matrix inequality. Both the delay‐independent and delay‐dependent cases are considered. For the synthesis problem, we propose an observer‐based design method which guarantees that the closed‐loop uncertain time‐delay system is stable and strictly passive for all admissible uncertainties. Several examples are worked out to illustrate the developed theory.
Fundamental problems for infinite plate with a curvilinear holehaving finite poles
Authors: Abdou M. A. , El-Bary A. A.
Published: September 2005

In the present paper Muskhelishvili′s complex variable method of solving two‐dimensional elasticity problems has been applied to derive exact expressions for Gaursat′s functions for the first and second fundamental problems of the infinite plate weakened by a hole having many poles and arbitrary shape which is conformally mapped on the domain outside a unit circle by means of general rational mapping function. Some applications are investigated. The interesting cases when the shape of the hole takes different shapes are included as special cases.
On the inversion of the camber line problem
Authors: Mikolaitis David W.
Published: September 2005

Often airfoil shapes are given by specification of camber line and thickness functions. The camber line of an airfoil extends from the leading edge of the airfoil to the trailing edge and its position is given as a function of distance measured along the chord of the airfoil. The thickness function measures the perpendicular distance from the upper and lower surfaces of the airfoil to the camber line. The inverse problem where the upper and lower surfaces are specified and camber line and thickness functions are to be determined give rise to a first order semi‐explicit nonlinear differential algebraic equation with boundary conditions. Examples are given where there are no solutions and multiple solutions.
c‐Bottlenecks in serial production lines: Identification andapplication
Authors: Chiang S.-Y. , Kuo C.-T. , Meerkov S. M.
Published: September 2005

The bottleneck of a production line is a machine that impedes the system performance in the strongest manner. In production lines with the so‐called Markovian model of machine reliability, bottlenecks with respect to the downtime, uptime, and the cycle time of the machines can be introduced. The two former have been addressed in recent publications [1] and [2]. The latter is investigated in this paper. Specifically, using a novel aggregation procedure for performance analysis of production lines with Markovian machines having different cycle time, we develop a method for c‐bottleneck identification and apply it in a case study to a camshaft production line at an automotive engine plant.
A data‐based damping modeling technique
Authors: Zhang William , Lee S. G.
Published: September 2005

Damping mechanisms exist in all vibration systems, but their nature is little understood and there is no systematic method for modeling general damping. This paper describes a novel damping modeling method (the Method of Energy Approximation, or MEA). This method is novel because it is a unique damping modeling method without assumed damping linearity; it is based on experimental data instead of physical principles; hence it is applicable to vibration systems of various materials and configurations; and it is suitable for vibration system transient control. Among the three quantities essential to an understanding of the dynamics of a vibration system, mass, stiffness, and damping, the last is the most complex and least understood. Therefore, with recent technology advances in such areas as composite materials and smart materials, the need for a good damping modeling method is more urgent than ever.
Bulk input queues with quorum and multiple vacations
Authors: Dshalalow Jewgeni H. , Yellen Jay
Published: September 2005

The authors study a single‐server queueing system with bulk arrivals and batch service in accordance to the general quorum discipline: a batch taken for service is not less than
r
and not greater than
R(≥r). The server takes vacations each time the queue level falls below
r(≥1)
in accordance with the multiple vacation discipline. The input to the system is assumed to be a compound Poisson process. The analysis of the system is based on the theory of first excess processes developed by the first author. A preliminary analysis of such processes enabled the authors to obtain all major characteristics for the queueing process in an analytically tractable form. Some examples and applications are given.
Hybrid probabilistic and convex modeling of excitation and response of periodic structures
Authors: Zhu L. P. , Elishakoff I.
Published: September 2005

In this paper, a periodic finite‐span beam subjected to the stochastic acoustic pressure with bounded parameters is investigated. Uncertainty parameters exist in this acoustic excitation due to the deviation or imperfection. First, a finite‐span beams subjected to the random acoustic pressure field are studied, the exact analytic forms of the cross‐spectral density of both the transverse displacement and the bending moment responses of the structure are formulated. The combined probabilistic and convex modeling of acoustic excitation appears to be most suitable, since there is an insufficient information available on the acoustic excitation parameters, to justify the totally probabilitic analysis. Specifically, we postulate that the uncertainty parameters in the acoustic loading belong to a bounded, convex set. In the special case when this convex set is an ellipsoid, closed form solutions are obtained for the most and least favorable mean square responses of both the transverse displacement and bending moment of the structure. Several finite‐span beams are exemplified to gain insight into proposal methodology.
Solution and stability of a set of PTH order linear differential equations with periodic coefficients via Chebyshev polynomials
Authors: Sinha S. C. , Butcher Eric A.
Published: September 2005

Chebyshev polynomials are utilized to obtain solutions of a set of
pth order linear differential equations with periodic coefficients. For this purpose, the operational matrix of differentiation associated with the shifted Chebyshev polynomials of the first kind is derived. Utilizing the properties of this matrix, the solution of a system of differential equations can be found by solving a set of linear algebraic equations without constructing the equivalent integral equations. The Floquet Transition Matrix (FTM) can then be computed and its eigenvalues (Floquet multipliers) subsequently analyzed for stability. Two straightforward methods, the ‘differential state space formulation’ and the ‘differential direct formulation’, are presented and the results are compared with those obtained from other available techniques. The well‐known Mathieu equation and a higher order system are used as illustrative examples.
Analysis of nonlinear systems with time varying inputs and its application to gain scheduling
Authors: Lim J.-T. , Cho S.-K.
Published: September 2005

An analytical framework for analysis of a class of nonlinear systems with time varying inputs is presented. It is shown that the trajectories of the transformed nonlinear systems are uniformly bounded with an ultimate bound under certain conditions shown in this paper. The result obtained is useful for applications, in particular, analysis and design of gain scheduling.
A self‐consistent numerical method for simulation of quantum transport in high electron mobility transistor; part I: The Boltzmann‐Poisson‐Schrödinger solver
Authors: Khoie R.
Published: September 2005

A self‐consistent Boltzmann‐Poisson‐Schrödinger solver for High Electron Mobility Transistor is presented. The quantization of electrons in the quantum well normal to the heterojunction is taken into account by solving the two higher moments of Boltzmann equation along with the Schrödinger and Poisson equations, self‐consistently. The Boltzmann transport equation in the form of a current continuity equation and an energy balance equation are solved to obtain the transient and steady‐state transport behavior. The numerical instability problems associated with the simulator are presented, and the criteria for smooth convergence of the solutions are discussed. The current‐voltage characteristics, transconductance, gate capacitance, and unity‐gain frequency of a single quantum well HEMT is discussed. It has been found that a HEMT device with a gate length of 0.7
μm, and with a gate bias voltage of 0.625 V, has a transconductance of 579.2 mS/mm, which together with the gate capacitance of 19.28 pF/cm, can operate at a maximum unity‐gain frequency of 47.8 GHz.
A self‐consistent numerical method for simulation of quantum transport in high electron mobility transistor; part II: The full quantum transport
Authors: Khoie R.
Published: September 2005

In Part I of this paper we reported a self-consistent Boltzmann-Schrödinger-Poisson simulator for HEMT in which only electrons in the first subband were assumed to be quantized with their motion restricted to 2 dimensions. In that model, the electrons in the second and higher subbands were treated as bulk system behaving as a 3 dimensional electron gas. In Part II of this paper, we extend our simulator to a self-consistent full-quantum model in which the electrons in the second subband are also treated as quantized 2 dimensional gas. In this model, we consider the electrons in the lowest two subbands to be in the quantum well forming the 2‐dimensional electron gas, and the electrons in the third and higher subbands to behave as bulk electrons with no restrictions in their motion. We have further incorporated an additional self‐consistency by calculating the field‐dependent, energy‐dependent scattering rates due to ionized impurities and polar optical phonons. The two higher moments of Boltzmann transport equation are numerically solved for the two lowest subbands and the bulk system; six transport equations, four for the two subbands and two for the bulk system. The Schrödinger and Poisson equations are also solved self‐consistently. The wavefunctions obtained are used to calculate the ionized impurity scattering and the polar optical phonon scattering rates. The rates of transfer of electrons and their energies to and from each subband are calculated from these intersubband and intrasubband scattering rates.
Bottlenecks in serial production lines: A system‐theoretic approach
Authors: Kuo C.-T. , Lim J.-T. , Meerkov S. M.
Published: September 2005

In this work, a new definition of production systems bottlenecks is formulated and analyzed. Specifically, a machine is defined as the bottleneck if the sensitivity of the system′s performance index to this machine′s production rate in isolation is the largest. Although appealing from the systems point of view, this definition suffers a deficiency due to the fact that the sensitivities involved cannot be either measured on‐line or efficiently calculated off‐line. To avoid this, the paper develops a method based on indirect but real‐time data. From this point of view, the main result of the work is as follows: The bottleneck machine in a serial production line can be identified by analyzing relationships between the so‐called manufacturing blockage and manufacturing starvation of each machine. This leads to a simple rule for bottleneck identification. The rule requires neither the calculation of the production rate sensitivities nor the production rate itself. When the probabilities of manufacturing blockages and starvations are not available from on‐line measurements, the paper presents their analytical estimates which, under certain conditions, can be used for bottleneck identification. Finally, a case study at an automotive component plant is described.
A new technique in constructing closed‐form solutions for nonlinear PDEs appearing in fluid mechanics and gas dynamics
Authors: Panayotounakos D. E.
Published: September 2005

We develop a new unique technique in constructing closed‐form solutions for several nonlinear partial differential systems appearing in fluid mechanics and gas dynamics. The obtained solutions include fewer arbitrary functions than needed for general solutions, fact that permits us to specify them according to the initial state, or the geometry, of each specific problem under consideration. In order to apply the before mentioned technique we construct closed‐form solutions concerning the gas‐dynamic equations with constant pressure, the dynamic equations of an ideal gas in isentropic flow, and the two‐dimensional incompressible boundary layer flow.
Discrete Riccati equation solutions: Distributed algorithms
Authors: Lainiotis D. G. , Plataniotis K. N. , Papanikolaou Michail , Papaparaskeva Paraskeuas
Published: September 2005

In this paper new distributed algorithms for the solution of the discrete Riccati equation are introduced. The algorithms are used to provide robust and computational efficient solutions to the discrete Riccati equation. The proposed distributed algorithms are theoretically interesting and computationally attractive.
High frequency asymptotic solutions of the reduced wave equation on infinite regions with non‐convex boundaries
Authors: Bloom Clifford O.
Published: September 2005

The asymptotic behavior as λ → ∞ of the function U(x, λ) that satisfies the reduced wave equation Lλ[U] = ∇⋅(E(x)∇U) + λ2N2(x)U = 0 on an infinite 3‐dimensional region, a Dirichlet condition on
∂V
, and an outgoing radiation condition is investigated. A function
UN(x, λ)
is constructed that is a global approximate solution as
λ → ∞ of the problem satisfied by U(x, λ)
. An estimate for
WN(x, λ) = U(x, λ) − UN(x, λ)
on V
is obtained, which implies that
UN(x, λ)
is a uniform asymptotic approximation of
U(x, λ)
as
λ → ∞, with an error that tends to zero as rapidly as
λ−N(N = 1, 2, 3, …). This is done by applying a priori estimates of the function
WN(x, λ) in terms of its boundary values, and the L2 norm of rLλ[WN(x, λ)]
on V. It is assumed that
E(x), N(x), ∂V
and the boundary data are smooth, that
E(x) − I and N(x) − 1 tend to zero algebraically fast as r → ∞, and finally that
E(x) and
N(x) are slowly varying;
∂V may be finite or infinite.

The solution
U(x, λ) can be interpreted as a scalar potential of a high frequency acoustic or electromagnetic field radiating from the boundary of an impenetrable object of general shape. The energy of the field propagates through an inhomogeneous, anisotropic medium; the rays along which it propagates may form caustics. The approximate solution (potential) derived in this paper is defined on and in a neighborhood of any such caustic, and can be used to connect local “geometrical optics” type approximate solutions that hold on caustic free subsets of V.

The result of this paper generalizes previous work of Bloom and Kazarinoff [C. O. BLOOM and N. D. KAZARINOFF, Short Wave Radiation Problems in Inhomogeneous Media: Asymptotic Solutions, SPRINGER VERLAG, NEW YORK, NY, 1976].
Eigenvalues of boundary value problems for higher order differential equations
Authors: Wong Patricia J. Y. , Agarwal Ravi P.
Published: September 2005

We shall consider the boundary value problem

urn:x-wiley:1024123X:media:mpe952346:mpe952346-math-0001

urn:x-wiley:1024123X:media:mpe952346:mpe952346-math-0002

urn:x-wiley:1024123X:media:mpe952346:mpe952346-math-0003

urn:x-wiley:1024123X:media:mpe952346:mpe952346-math-0004

where λ > 0, α, β, γ
and δ
are constants satisfying αγ + αδ + βγ > 0, β, δ ≥ 0, β + α > 0
and δ + γ > 0
to characterize the values of
λ
so that it has a positive solution. For the special case
λ = 1, sufficient conditions
are also established for the existence of positive solutions.
High‐rate wireless data communications: An underwater acoustic communications framework at the physical layer
Authors: Bessios Anthony G. , Caimi Frank M.
Published: September 2005

A variety of signal processing functions are performed by Underwater Acoustic Systems. These include: 1) detection to determine presence or absence of information signals in the presence of noise, or an attempt to describe which of a predetermined finite set of possible messages {mi, i, …, M}
the signal represents; 2) estimation of some parameter
associated with the received signal (i.e. range, depth, bearing angle, etc.); 3)
classification and source identification; 4) dynamics tracking; 5) navigation (collision avoidance and terminal guidance); 6) countermeasures; and 7) communications. The focus of this paper is acoustic communications.

There is a global current need to develop reliable wireless digital communications for the underwater environment, with sufficient performance and efficiency to substitute for costly wired systems. One possible goal
is a wireless system implementation that insures underwater terminal mobility. There is also a vital need to improve the performance of the existing systems in terms of data‐rate, noise immunity, operational range, and power consumption, since, in practice, portable high‐speed, long range, compact, low‐power systems are desired.

We concede the difficulties associated with acoustic systems and concentrate on the development of robust data transmission methods anticipating the eventual need for real time or near real time video transmission. An overview of the various detection techniques and the general statistical digital communication problem is given based on a statistical decision theory framework. The theoretical formulation of the underwater acoustic data communications problem includes modeling of the stochastic channel to incorporate a variety of impairments
and environmental uncertainties, and proposal of new compensation strategies for an efficient and robust receiver design.
Surface normals and barycentric coordinates
Authors: Mullineux Glen
Published: September 2005

The normal to a triangular parametric surface is investigated where the parameters used are barycentric coordinates. Formulae for the normal are obtained for non‐rational and rational surfaces.
Lyapunov analysis of sliding motions: Application to bounded control
Authors: Perruquetti W. , Richard J. P. , Borne P.
Published: September 2005

The results concern the fundamental problem of Lyapunov analysis of sliding motions. It consist first to estimate the useful part of the sliding surface (the so‐called “sliding domain”) and second to estimate the useful part of the state domain that is the domain of all initial conditions for which the corresponding solutions converge to the sliding domain. The application of such results concern the design of a realistic bounded control. Several examples are exposed in order to illustrate the obtained results.
Multisensor estimation: New distributed algorithms
Authors: Plataniotis K. N. , Lainiotis D. G.
Published: September 2005

The multisensor estimation problem is considered in this paper. New distributed algorithms, which are able to locally process the information and which deliver identical results to those generated by their centralized counterparts are presented. The algorithms can be used to provide robust and computationally efficient solutions to the multisensor estimation problem.
The proposed distributed algorithms are theoretically interesting and computationally attractive.
Performance analysis of multi‐hop wireless packet networks
Authors: Lim J.-T. , Meerkov S. M.
Published: September 2005

In this paper, a unified analytical framework for performance analysis of multi‐hop wireless packet networks is developed. The effect of coupling between the hops on the degradation of the delay‐throughput characteristics and the probability of blocking is investigated. The issue of hop decoupling is addressed.
On the solution of the differential equation occurring in the problem of heat convection in laminar flow through a tube with slip—flow
Authors: Wang Xanming , Gu Huaijin , Yu Duli
Published: September 2005

A technique is developed for evaluation of eigenvalues in solution of the differential equation

urn:x-wiley:1024123X:media:mpe913017:mpe913017-math-0001

which occurs in the problem of heat convection in laminar flow through a circular tube with silp‐flow (β > 1). A series solution requires the expansions of coeffecients involving extremely large numbers. No work has been reported in the case of β > 1, because of its computational complexity in the evaluation of the eigenvalues. In this paper, a matrix was constructed and a computational algorithm was obtained to calculate the first four eigenvalues. Also, an asymptotic formula was developed to generate the full spectrum of eigenvalues. The computational results for various values of β were obtained.
Improvability theory for assembly systems: Two component—one assembly machine case
Authors: Kuo C.-T , Lim J.-T , Meerkov S. M. , Park E.
Published: September 2005

Improvability theory for a simple assembly system consisting of two components and one
assembly machine is developed. Both constrained and unconstrained formulations are addressed. In the constrained case, it is shown that the assembly is unimprovable with respect to workforce if each component machine is blocked as frequently as the assembly machine is starved for parts produced by this particular assembly machine. The system is unimprovable with respect to work‐in‐process if, roughly speaking, all buffers have equal average steady state occupancy. In the unconstrained improvability case, it is shown that the bottleneck machine can be identified by analyzing the probabilities of the so‐called manufacturing blockages and starvations. A generalization to n component—one assembly machine system is also included.
Stochastic stability of linear time‐delay system with Markovian jumping parameters
Authors: Benjelloun K. , Boukas E. K.
Published: September 2005

This paper deals with the class of linear time‐delay systems with Markovian jumping parameters (LTDSMJP). We mainly extend the stability results of the deterministic class of linear systems with time‐delay to this class of systems. A delay‐independent necessary condition and sufficient conditions for checking the stochastic stability are established. A sufficient condition is also given. Some numerical examples are provided to show the usefulness of the proposed theoretical results.
Relaxation process modeling in a turbulent boundary layer with nonzero free stream turbulence
Authors: Dyban Eugen , Fridman Ella
Published: September 2005

In order to analyze the relaxation effects in a turbulent boundary layer with zero and nonzero free stream turbulence, the Reynolds‐averaged equations of motion and energy are solved. As the closure of the Reynolds‐averaged equations, the transport equation for turbulent shear stresses is used. The proposed approach leads to calculation of the relaxation scales in the turbulent boundary layer with zero and nonzero free stream turbulence. Results for friction coefficients, velocity profiles, shear stresses, thickness of the boundary layer and so called “superlayer” in a flat‐plate turbulent boundary layer are presented. The results obtained are in agreement with those available from the experimental data.
Analytical stability analysis of periodic systems by Poincaré mappings with application to rotorcraft dynamics
Authors: Flashner Henryk , Guttalu Ramesh S.
Published: September 2005

A point mapping analysis is employed to investigate the stability of periodic systems. The method is applied to simplified rotorcraft models. The proposed approach is based on a procedure to obtain an analytical expression for the period‐to‐period mapping description of system′s dynamics, and its dependence on system′s parameters. Analytical stability and bifurcation conditions are then determined and expressed as functional relations between important system parameters. The method is applied to investigate the parametric stability of flapping motion of a rotor and the ground resonance problem encountered in rotorcraft dynamics. It is shown that the proposed approach provides very accurate results when compared with direct numerical results which are assumed to be an “exact solution” for the purpose of this study. It is also demonstrated that the point mapping method yields more accurate results than the widely used classical perturbation analysis. The ability to perform analytical stability studies of systems with multiple degrees‐of‐freedom is an important feature of the proposed approach since most existing analysis methods are applicable to single degree‐of‐freedom systems. Stability analysis of higher dimensional systems, such as the ground resonance problems, by perturbation methods is not straightforward, and is usually very cumbersome.
On the structure of a distinguished‐limit quasi‐isothermal deflagration for the generalized reaction‐rate model
Authors: Bush W. B. , Krishnamurthy L.
Published: September 2005

The structure of the quasi‐isothermal deflagration is examined by means of an asymptotic analysis of the physical‐plane boundary‐value problem, with Lewis–Semenov number unity, in the limit of the activation‐temperature ratio, β = Ta/Tb, greater than order unity, for the generalized reaction‐rate‐model case of: (1) the heat‐addition‐temperature ratio, α = (Tb − Tu)/Tu, of order β−1/2, less than order unity
[where Ta, Tb, and Tu
are the activation, adiabatic‐flame (and/or burned‐gas), and unburned‐gas temperatures, respectively]; and (2) the exponent, a, which characterizes the pre‐exponential thermal dependence of the reaction‐rate term, unity. The examination indicates that, as in the order‐unity heat‐addition case, this deflagration has a four‐region structure: the upstream diffusion‐convection and downstream diffusion‐reaction regions, and the far‐upstream (or cold‐boundary) and the far‐downstream (or hot‐boundary) regions.
Nonlinear unsteady supersonic flow analysis for slender bodies of revolution: Series solutions, convergence and results
Authors: Markakis M. , Panayotounakos D. E.
Published: September 2005

In Ref. [6] the authors constructed analytical solutions including one arbitrary function for the problem of nonlinear, unsteady, supersonic flow analysis concerning slender bodies of revolution due to small amplitude oscillations. An application describing a flow past a right circular cone was presented and the constructed solutions were given in the form of infinite series through a set of convenient boundary and initial conditions in accordance with the physical problem. In the present paper we develop an appropriate convergence analysis concerning the before mentioned series solutions for the specific geometry of a rigid right circular cone. We succeed in estimating the limiting values of the series producing velocity and acceleration resultants of the problem under consideration. Several graphics for the velocity and acceleration flow fields are presented. We must underline here that the proposed convergence technique is unique and can be applied to any other geometry of the considered body of revolution.
A collocation method for optimal control of linear systems with inequality constraints
Authors: Razzaghi M. , Nazarzadeh J. , Nikravesh K. Y.
Published: September 2005

A numerical method for solving linear quadratic optimal control problems with control inequality constraints is presented in this paper. The method is based upon hybrid function approximations. The properties of hybrid functions which are the combinations of block‐pulse functions and Legendre polynomials are first presented. The operational matrix of integration is then utilized to reduce the optimal control problem to a set of simultaneous nonlinear equations. The inequality constraints are first converted to a system of algebraic equalities, these equalities are then collocated at Legendre–Gauss–Lobatto nodes. An illustrative example is included to demonstrate the validity and
applicability of the technique.
Variational Lyapunov method and stability theory
Authors: Lakshmikantham V. , Liu X. , Leela S.
Published: September 2005

By unifying the method of variation of parameters and Lyapunov′s second method, we develop a fruitful technique which we call variational Lyapunov method. We then consider the stability theory in this new framework showing the advantage of this unification.