Mathematical Problems in Engineering

https://www.hindawi.com/journals/mpe/

List of Papers (Total 43,672)

A high-precision algorithm for axisymmetric flow

We present a new algorithm for highly accurate computation of axisymmetric potential flow. The principal feature of the algorithm is the use of orthogonal curvilinear coordinates. These coordinates are used to write down the equations and to specify quadrilateral elements following the boundary. In particular, boundary conditions for the Stokes

A nested decomposition algorithm for parallel computations of very large sparse systems

In this paper we present a generalization of the balanced border block diagonal (BBD) decomposition algorithm, which was developed for the parallel computation of sparse systems of linear equations. The efficiency of the new procedure is substantially higher, and it extends the applicability of the BBD decomposition to extremely large problems. Examples of the decomposition are...

A unified approach to fixed-order controller design via linear matrix inequalities

We consider the design of fixed-order (or low-order) linear controllers which meet certain performance and/or robustness specifications. The following three problems are considered; covariance control as a nominal performance problem,𝒬-stabilization as a robust stabilization problem, and robust L∞ control problem as a robust performance problem. All three control problems are...

On adaptive control of mobile slotted aloha networks

An adaptive control scheme for mobile slotted ALOHA is presented and the effect of capture on the adaptive control scheme is investigated. It is shown that with the proper choice of adaptation parameters the adaptive control scheme can be made independent of the effect of capture.

Mathematical theory of improvability for production systems

A mathematical model for continuous improvement processes in production systems is formulated. Both constrained and unconstrained cases are addressed. A solution for the case of a serial production line with finite buffers and a Bernoulli model of machines reliability is given. In particular, it is shown that a production line is unimprovable under constraints if each buffer is...

Global asymptotic stability of a passive juggling strategy: A possible parts-feeding method

In this paper we demonstrate that a passive vibration strategy can bring a one-degree-of-freedom ball to a specified periodic trajectory from all initial conditions. We draw motivation from the problem of parts feeding in sensorless assembly. We provide simulation results suggesting the relevance of our analysis to the parts feeding problem.

System-theoretic analysis of due-time performance in production systems

Along with the average production rate, the due-time performance is an important characteristic of manufacturing systems. Unlike the production rate, the due-time performance has received relatively little attention in the literature, especially in the context of large volume production. This paper is devoted to this topic. Specifically, the notion of due-time performance is...

Mathematical problems in modeling artificial heart

In this paper we discuss some problems arising in mathematical modeling of artificial hearts. The hydrodynamics of blood flow in an artificial heart chamber is governed by the Navier-Stokes equation, coupled with an equation of hyperbolic type subject to moving boundary conditions. The flow is induced by the motion of a diaphragm (membrane) inside the heart chamber attached to a...

Nonlinear singularly perturbed systems of differential equations: A survey

In this paper a survey of the most effective methods in singular perturbations is presented. Many applied problems can be modeled by nonlinear singularly perturbed systems, as, for example, problems in kinetics, biochemistry, semiconductors theory, theory of electrical chains, economics, and so on. In this survey we consider averaging and constructive methods that are very useful...

A modeling and control framework for operating large-scale electric power systems under present and newly evolving competitive industry structures

This paper introduces a systematic, structure-based modeling framework for analysis and control of electric power systems for processes evolving over the mid-term and long-term time horizons. Much simpler models than the detailed dynamics specifically for control design at different hierarchical levels are obtained by applying both temporal and spatial separation. These simple...

A data-based damping modeling technique

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...

A note on the convergence of quantizers

Several questions concerning the convergence of quantized estimators are considered based upon points of accuracy. Examples are considered in which quantizers converge and in which they fail to converge, and points of accuracy are shown to provide explanations for both types of behavior.

Bulk input queues with quorum and multiple vacations

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...

Vibration suppression in a flexible gyroscopic system using modal coupling strategies

Several recent studies have shown that vibrations in a two-degree-of-freedom system can be suppressed by using modal coupling based control techniques. This involves making the first two natural frequencies commensurable (e.g, in a ratio of 1:1 or 1:2) to establish a state of Internal Resonance (IR). When the system exhibits IR, vibrations in the two directions are strongly...

Discrete-time adaptive control using a sliding mode

Adaptive control using a sliding mode in discrete time systems is proposed as a means of achieving robustness with respect to parameter variations, fast tracking to a desired trajectory, and fast parameter convergence, without increasing the chattering of the control inputs. We first prove the stability of a system in which the control inputs consist of equivalent control driven...

Hybrid probabilistic and convex modeling of excitation and response of periodic structures

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...

Solution and stability of a set of PTH order linear differential equations with periodic coefficients via Chebyshev polynomials

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...

Asymptotic performance characteristics of CSMA and CSMA←CD→CSMA/CD networks

This paper presents analytical formulae for performance evaluation of CSMA and CSMA/CD networks with a finite number of buffered users. The asymptotic theory developed in [1] is extended to local area networks so as to investigate the resulting steady state throughput, time delay, probability of blocking, and local stability of each equilibrium. In particular, the stabilization...

Bottlenecks in serial production lines: A system-theoretic approach

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...

Impulsive controllability of linear dynamical systems with applications to maneuvers of spacecraft

Necessary and sufficient conditions for impulsive controllability of linear dynamical systems are obtained, which provide a novel approach to problems that are basically defined by continuous dynamical systems, but on which only discrete-time actions are exercised. As an application, impulsive maneuvering of a spacecraft is discussed.

Nonlinear filtering for LIDAR signal processing

LIDAR (Laser Integrated Radar) is an engineering problem of great practical importance in environmental monitoring sciences. Signal processing for LIDAR applications involves highly nonlinear models and consequently nonlinear filtering. Optimal nonlinear filters, however, are practically unrealizable. In this paper, the Lainiotis's multi-model partitioning methodology and the...

On the structure of the deflagration for the generalized reaction-rate model

The structure of the 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 unity [where Ta, Tb, and...

Surface normals and barycentric coordinates

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

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...

Multisensor estimation: New distributed algorithms

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...