On delay-derivative-dependent stability of systems with fast-varying delays

Stability of linear systems with uncertain bounded time-varying delays is studied under the assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound of the L₂-norm of a certain integral operator. There exists a bound on this operator norm in two cases: in the case where the delay derivative is not greater than 1 and in the case without any constraints on the delay derivative. In the present note we fill the gap between the two cases by deriving a tight operator bound which is an increasing and continuous function of the delay derivative upper bound d?1. For d→∞ the new bound corresponds to the second case and improves the existing bound. As a result, for the first time, delay-derivative-dependent frequency domain and time domain stability criteria are derived for systems with the delay derivative greater than 1.     

Nonsmooth optimization for multiband frequency domain control design

Multiband frequency domain synthesis consists in the minimization of a finite family of closed-loop transfer functions on prescribed frequency intervals. This is an algorithmically difficult problem due to its inherent nonsmoothness and nonconvexity. We extend our previous work on nonsmooth H_∞ synthesis to develop a nonsmooth optimization technique to compute local solutions to multiband synthesis problems. The proposed method is shown to perform well on illustrative examples.     

A parametric bootstrap approach for ANOVA with unequal variances: Fixed and random models

This article is about testing the equality of several normal means when the variances are unknown and arbitrary, i.e., the set up of the one-way ANOVA. Even though several tests are available in the literature, none of them perform well in terms of Type I error probability under various sample size and parameter combinations. In fact, Type I errors can be highly inflated for some of the commonly used tests; a serious issue that appears to have been overlooked. We propose a parametric bootstrap (PB) approach and compare it with three existing location-scale invariant tests—the Welch test, the James test and the generalized F (GF) test. The Type I error rates and powers of the tests are evaluated using Monte Carlo simulation. Our studies show that the PB test is the best among the four tests with respect to Type I error rates. The PB test performs very satisfactorily even for small samples while the Welch test and the GF test exhibit poor Type I error properties when the sample sizes are small and/or the number of means to be compared is moderate to large. The James test performs better than the Welch test and the GF test. It is also noted that the same tests can be used to test the significance of the random effect variance component in a one-way random model under unequal error variances. Such models are widely used to analyze data from inter-laboratory studies. The methods are illustrated using some examples.     

Detecting change-points in Markov chains

Markov chains provide a flexible model for dependent random variables with applications in such disciplines as physics, environmental science and economics. In the applied study of Markov chains, it may be of interest to assess whether the transition probability matrix changes during an observed realization of the process. If such changes occur, it would be of interest to estimate the transitions where the changes take place and the probability transition matrix before and after each change. For the case when the number of changes is known, standard likelihood theory is developed to address this problem. The bootstrap is used to aid in the computation of p-values. When the number of changes is unknown, the AIC and BIC measures are used for model selection. The proposed methods are studied empirically and are applied to example sets of data.     

A reactive GRASP and path relinking for a combined production–distribution problem

An NP-hard production–distribution problem for one product over a multi-period horizon is investigated. The aim is to minimize total cost taking production setups, inventory levels and distribution into account. An integer linear model is proposed as a compact problem specification but it cannot be solved to optimality for large instances. Instead of using a classical two-phase approach (production planning and then route construction for each day), metaheuristics that simultaneously tackle production and routing decisions are developed: a GRASP (greedy randomized adaptive search procedure) and two improved versions using either a reactive mechanism or a path-relinking process. These algorithms are evaluated on 90 randomly generated instances with 50, 100 and 200 customers and 20 periods. The results confirm the interest of integrating production and distribution decisions, compared to classical two-phase methods. Moreover, reaction and path-relinking give better results than the GRASP alone.     

On the bounded-real and positive-real conditions for affine nonlinear state-delayed systems and applications to stability

In this paper, bounded-real conditions for affine nonlinear state-delayed systems are derived using the concept of dissipativeness. Necessary and sufficient conditions for the system to be dissipative and to have finite L₂-gain also referred to as the bounded-real condition are given. The implications on the stability of the system and feedback interconnections of such systems are also considered. Finally, an equivalent of the positive-real lemma is derived and its implications on stability of the system and feedback interconnections of such systems are similarly discussed.     

Exploring pre-service teachers' beliefs about using Web 2.0 technologies in K-12 classroom

This qualitative study explored pre-service teachers' behavioral, normative, and control beliefs regarding their intentions to use Web 2.0 technologies in their future classrooms. The Theory of Planned Behavior (TPB) was used as the theoretical framework (Ajzen, 1991) to understand these beliefs and pre-service teachers' intentions for why they want to use Web 2.0 technologies. According to Ajzen's TPB, the behavioral beliefs are based on attitude toward outcomes or consequences of using Web 2.0, the normative beliefs depend on social support and social pressure to use Web 2.0, and the control beliefs lay the foundation of perceived behavioral control over using Web 2.0 in a classroom. Data were collected from open-ended survey questions (n = 190), semi-structured interviews (n = 12) and end of semester reflections (n = 12). Findings suggest that pre-service teachers' intentions to use Web 2.0 technologies are related to their beliefs about the value of these technologies for improving student learning and engagement, its ease of use (behavioral beliefs), its ability to meet the needs/expectations of digital age students (normative beliefs), the participants' high self-efficacy in use, and its potential for affording students anytime/anywhere access to learning and interaction (control beliefs). From these results, we recommend that teacher educators should target these beliefs within teacher development programs to prepare pre-service teachers for successful use of Web 2.0 technologies in their future K-12 classrooms.     

Extending UML to model Web 2.0‐based context‐aware applications

Web 2.0 Mashups offer entirely new opportunities for context‐aware application (CAA) developers by integrating Web 2.0 technologies to facilitate interoperability among heterogeneous context‐aware systems. From a software engineering perspective, a visualized approach for Web 2.0‐based CAA modeling is crucial. Current CAA development, however, cannot provide a conceptual model for Web 2.0‐based CAA. Therefore, the development efficiency and potential for reuse are decreased. The UML is a general purpose modeling language with potential for use in many application domains. However, UML often lacks elements needed to model concepts in specific domains, such as Web 2.0‐based CAA modeling. To address the above issues, this study presents the Web 2.0‐based CAA UML profile, a UML profile for modeling Web 2.0‐based CAA. Copyright © 2011 John Wiley & Sons, Ltd.     

Geoadditive expectile regression

Quantile regression has emerged as one of the standard tools for regression analysis that enables a proper assessment of the complete conditional distribution of responses even in the presence of heteroscedastic errors. Quantile regression estimates are obtained by minimising an asymmetrically weighted sum of absolute deviations from the regression line, a decision theoretic formulation of the estimation problem that avoids a full specification of the error term distribution. Recent advances in mean regression have concentrated on making the regression structure more flexible by including nonlinear effects of continuous covariates, random effects or spatial effects. These extensions often rely on penalised least squares or penalised likelihood estimation with quadratic penalties and may therefore be difficult to combine with the linear programming approaches often considered in quantile regression. As a consequence, geoadditive expectile regression based on minimising an asymmetrically weighted sum of squared residuals is introduced. Different estimation procedures are presented including least asymmetrically weighted squares, boosting and restricted expectile regression. The properties of these procedures are investigated in a simulation study and an analysis on rental fees in Munich is provided where the geoadditive specification allows for an analysis of nonlinear effects of the size of flats or the year of construction and the spatial distribution of rents simultaneously.