A unified approach to the modelling of holonomic and nonholonomic mechanical systems

An alternative technique, called projection method, for solving constrained system problems is presented. This approach can be used to derive equations of motion of both holonomic and nonholonomic systems, and the dynamic equations can be expressed in generalized velocities and/or quasi-velocities. Compared against the other methods of classical mechanics (Lagrange's, Gibbs-Appell, Kane's,...), the present method turns out to be extraordinarily short, elementary and general. As such, it deserves to be promoted as a generally accepted method in academic and engineering applications. Three examples are reported to illustrate advantages of the technique     

Hybrid coordinate approach for the modelling and simulation of multibody systems

The main goal of the present work is to provide an add-on scheme for the formulation of multibody dynamics, based on natural coordinates, in regard to ideally balanced rigid bodies with high rotational spin, e.g. gyroscopes. The underlying aim of this approach is to achieve higher numerical accuracy whenever the preferred axis of rotation coincides with the balanced main axis of the body. This will be achieved by seperating the spin of the balanced rigid body along the denoted axis as an additional angular coordinate, whereas the other rotations will be covered by a carried frame, parameterized via natural coordinates. At the same time the carried frame provides a link to the existing modelling framework in terms of natural coordinates, enabling a straightforward implementation into existing multibody systems (e.g. rotary crane [2]). (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An efficacious dynamic mathematical modelling approach for creation of best collaborative groups

In many disciplines, including business, publishing, management, health, sports, arts and education, there is a population of people which should be optimally divided into multiple groups based on certain attributes to collaboratively perform a particular task. The problem becomes more complex when some other requirements are also added. They might be importance degrees of grouping criteria, homogeneity, heterogeneity or a mixture of teams, amount of consideration to the preferences of individuals, variability or invariability of group size, having moderators, aggregation or distribution of persons, overlapping level of teams, and so forth. Several researchers have addressed the problem, but they suffered from failure to satisfy all the requirements and/or developed inexact solutions and/or had very long process times. This work reveals how these problems can be mathematically formulated through a binary integer programming approach to construct an effective model which is solvable by exact methods in an acceptable time. The suggested model was validated through data obtained from collaboration of a set of learners in an online learning discussion forum grouped by means of the provided method. The achieved outcomes confirmed that the new approach is satisfactory and promising.     

A new algebraic approach to stabilization for boundary control systems of parabolic type

We study the stabilization problem of linear parabolic boundary control systems. While the control system is described by a pair of standard linear differential operators (L,τ), the corresponding semigroup generator generally admits no Riesz basis of eigenvectors. In the sense that very little information on the fractional powers of this generator is needed, our approach has enough generality as a prototype to be used for other types of parabolic systems. We propose in this paper a new algebraic approach to the stabilization, which gives—to the best of the author's knowledge—the simplest framework of the problem. The control system with the scheme of boundary observation/boundary feedback is turned into the differential equations with no boundary input in usual and standard L²-spaces in a readable manner.     

Hybrid stochastic approach for the modelling and analysis of fire safety systems

This paper approaches the problem of analysing control strategies for Fire Safety Systems. The components of Fire Safety Systems present behaviours of different nature and therefore the use of a hybrid modelling formalism is necessary. Petri net is used to model the discrete dynamics. Algebraic and differential equations are used for the continuous one. In order to realistically evaluate the performance of Fire Safety Systems, failures and other uncertainties, such as people’s behaviour, should be included in the model. Due to the model complexity, results are obtained by Monte Carlo simulation.     

Instability results for slowly time varying linear dynamic systems on time scales

We develop eigenvalue criteria under which the solutions of a “slowly” time varying linear dynamic system of the form xΔ(t)=A(t)x(t) are unstable.     

Improved stability criteria for time-varying delayed T-S fuzzy systems via delay partitioning approach

This paper focuses on the stability analysis for uncertain Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. The uncertainties of system parameter matrices are assumed to be time-varying and norm-bounded. Some new Lyapunov-Krasovskii functionals (LKFs) are constructed by nonuniformly dividing the whole delay interval into multiple segments and choosing different Lyapunov functionals to different segments in the LKFs. By employing these LKFs, some new delay-derivative-dependent stability criteria are established for the nominal and uncertain T-S fuzzy systems in a convex way. These stability criteria are derived that depend on both the upper and lower bounds of the time derivative of the delay. By employing the new delay partitioning approach, the obtained stability criteria are stated in terms of linear matrix inequality (LMI). They are equivalent or less conservative while involving less decision variables than the existing results. Finally, numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results.     

Satisfactory solutions approach to parameter optimization of dynamic systems with vector performance index

A novel approach to parameter optimization of large dynamic systems using vector performance index is described. The approach entails characterizing and determining a set of satisfactory solutions to the multiobjective optimization problem. The satisfactory solutions are defined with respect to a prespecified and satisfactory set of bounds on the indices. A theoretical basis is provided to obtain a compact and connected set of satisfactory solutions in the parameter space. Compactness and connectedness are essential requirements, since they assure a range of values for the parameters. An expedient numerical technique for determining the range of satisfactory values for the parameters is illustrated with an example. The satisfactory solutions approach provides a basis for designing a system with multiple requirements when all of them cannot be formulated in the framework of a composite vector index problem.This work constitutes part of the first author's doctoral dissertation in the Department of Electrical Engineering and Computer Science, University of Illinois at Chicago, Chicago, Illinois. It was supported in part by the National Science Foundation, Grant No. ENG-76-09930. The first author is indebted to Drs. A. C. Raptis and T. P. Mulcahey of Argonne National Laboratory for their support and encouragement.     

A delay decomposition approach to stability analysis of neutral systems with time-varying delay

This paper presents novel stability criteria for neutral systems with time-varying delay. By developing a delayed decomposition approach, information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities (LMIs). Then, based on the Lyapunov method, delay-dependent stability criteria are devised by taking the relationship between terms in the Leibniz-Newton formula into account. Criteria are derived in terms of LMIs, which can be easily solved by using various convex optimization algorithms. Three illustrative numerical examples are given to show less conservatism of our obtained results and the effectiveness of the proposed method.     

An object-oriented hybrid symbolic/numerical approach for the development of finite element codes

The association of object-oriented programming and symbolic computation techniques introduces certain changes in finite element code organization. The purpose of this approach is to speed up the design of new formulations. Previous papers have described the basic concepts of the method. In this paper, the focus is placed on functional aspects of symbolic tools for the development of finite element formulations. Two practical examples are used to illustrate this point. The first is a space-time formulation for an incompressible flow driven by the Navier–Stokes equations, and the second is a finite element derivation of the total potential energy for linear elasticity.     

An LP-based algorithm for the correction of inconsistent linear equation and inequality systems

An algorithm based on linear programming is proposed, which finds for an inconsistent system minimal corrections of the matrix and RHS vector among those providing its consistency     

An approach to the solution of the vector optimization problem of dynamic systems

The optimal control problem with vector-valued criteria is considered. A new approach to the generalization of this problem and a method of constructing the Bellman function are given.Paper prepared during the author's visiting period at the Centro di Studio dei Sistemi di Controllo e Calcolo Automatici, Consiglio Nazionale delle Richerche, Roma, Italia; at Istituto di Mathematica Applicata; and at the Sezione Automatica, Informatica, e Sistemistica, Instituto di Elettronica, Facolta di Ingegneria, Universita di Firenze, Firenze, Italia.     

A network queuing approach for evaluation of performance measures in autonomous vehicle storage and retrieval systems

A network queuing approach is used to estimate performance measures for Autonomous Vehicle Storage and Retrieval (AVS/R) Systems using opportunistic interleaving. The model exploits the distribution of cycle types and random storage assumptions to estimate the proportion of single and dual command cycles in a system. Comparable in accuracy and computational efficiency to procedures based on standard queuing models, the proposed technique provides the additional advantage of flexibility for modeling the interfaces between a storage system and the overall material flow system in a facility. The procedure is demonstrated for a range of problem scenarios.     

A dynamic pricing approach for returned products in integrated forward/reverse logistics network design

During the last decade, the stringent pressures from environmental and social requirements have spurred an interest in designing a reverse logistics network. In this paper, we address the problem of designing and planning a multi-echelon, multi-period, multi-commodity and capacitated integrated forward/reverse logistics network. Returned products are categorized with respect to their quality levels, and a different acquisition price is offered for each return type. Furthermore, the reservation incentive of customers, the expected price of customers for one unit of used product described by uniform distribution, is applied to model the customers’ return willingness. Due to the fact that the remaining worthwhile value in the used products is the corporation’s key motivation for buying them from customers, a dynamic pricing approach is developed to determine the acquisition price for these products and based on it determine the percentage of returned products collected from customer zones. The used products’ acquisition prices at each time period are determined based on the customers’ return willingness by each collection center.     

Robust fault tolerant control of continuous-time switched systems: An LMI approach

The present paper proposes a new robust fault tolerant control (RFTC) design for continuous-time switched systems. The main objective is to design in an integrated way the couple (controller, observer) that allows to stabilize switched systems even in the presence of actuator faults. A state/fault estimation observer is designed to simultaneously estimate system state and actuator faults. Based on this observer, a fault tolerant controller is developed to stabilize the system and accommodate the actuator faults automatically. The RFTC problem is formalized in the form of linear matrix inequalities (LMI) rather than bilinear matrix inequalities (BMI), to avoid the difficulty of solving BMIs. Finally, a numerical example composed of unstable subsystems is studied to show the applicability and efficiency of the obtained results.     

A semi-analytic approach for the nonlinear dynamic response of circular plates

This paper presents a new semi-analytic perturbation differential quadrature method for geometrically nonlinear vibration analysis of circular plates. The nonlinear governing equations are converted into a linear differential equation system by using Linstedt–Poincaré perturbation method. The solutions of nonlinear dynamic response and the nonlinear free vibration are then sought through the use of differential quadrature approximation in space domain and analytical series expansion in time domain. The present method is validated against analytical results using elliptic function in several examples for both clamped and simply supported circular plates, showing that it has excellent accuracy and convergence. Compared with numerical methods involving iterative time integration, the present method does not suffer from error accumulation and is able to give very accurate results over a long time interval.