Non-linear observer design for a class of singular time-delay systems with Lipschitz non-linearities

In this paper, we consider a class of time-delay singular systems with Lipschitz non-linearities. A method of designing full-order observers for the systems is presented which can handle non-linearities with large-Lipschitz constants. The Lipschitz conditions are reformulated into linear parameter varying systems, then the Lyapunov–Krasovskii approach and the convexity principle are applied to study stability of the new systems. Furthermore, the observers design does not require the assumption of regularity for singular systems. In case the systems are non-singular, a reduced-order observers design is proposed instead. In both cases, synthesis conditions for the observers designs are derived in terms of linear matrix inequalities which can be solved efficiently by numerical methods. The efficiency of the obtained results is illustrated by two numerical examples.

Partial state bounding with a pre-specified time of non-linear discrete systems with time-varying delays

In this study, the authors address a new problem of finding, with a pre-specified time, bounds of partial states of non-linear discrete systems with a time-varying delay. A novel computational method for deriving the smallest bounds is presented. The method is based on a new comparison principle, a new algorithm for finding the infimum of a fractal function, and linear programming. The effectiveness of our obtained results is illustrated through a numerical example.

Chemical structure based prediction of PAN and oxidized PAN fiber density through a non-linear mathematical model

The production of carbon fiber, particularly the oxidation/stabilization step, is a complex process. In the present study, a non-linear mathematical model has been developed for the prediction of density of polyacrylonitrile (PAN) and oxidized PAN fiber (OPF), as a key physical property for various applications, such as energy and material optimization, modeling, and design of the stabilization process. The model is based on the available functional groups in PAN and OPF. Expected functional groups, including [Formula presented], [Formula presented], –CH2, [Formula presented], and [Formula presented], were identified and quantified through the full deconvolution analysis of Fourier transform infrared attenuated total reflectance (FT-IR ATR) spectra obtained from fibers. These functional groups form the basis of three stabilization rendering parameters, representing the cyclization, dehydrogenation and oxidation reactions that occur during PAN stabilization, and are used as the independent variables of the non-linear predictive model. The k-fold cross validation approach, with k = 10, has been employed to find the coefficients of the model. This model estimates the density of PAN and OPF independent of operational parameters and can be expanded to all operational parameters. Statistical analysis revealed good agreement between the governing model and experiments. The maximum relative error was less than 1% for the present model.

Is guanxi always good for employee self-development in China? Examining non-linear and moderated relationships

The nature of work and careers in China are constantly evolving as a result of market-oriented economic transition in the country. Increasingly, employees are required to be proactive and self-starting in skill and competency improvement for employability. Employee self-development (ESD) involves considerations embedded in a wide range of relationships including both work and non-work domains. This research draws from social exchange theory and information processing theory to investigate how guanxi, a relational phenomenon unique to traditional Chinese culture, influences ESD. Drawing from the experience of a sample (n = 404) of employees in China, an inverted U-shaped relationship between guanxi and ESD is found, suggesting that initial positive influences of guanxi on ESD diminish after reaching an inflexion point. We also found that these influences are stronger for gender congruent employee-supervisor dyads. The theoretical and managerial implications that too much guanxi is not necessarily good for ESD, particularly in the presence of gender congruence, are also discussed.

Distribution Entropy (DistEn) : a complexity measure to detect arrhythmia from short length RR interval time series

Heart rate complexity analysis is a powerful non-invasive means to diagnose several cardiac ailments. Non-linear tools of complexity measurement are indispensable in order to bring out the complete non-linear behavior of Physiological signals. The most popularly used non-linear tools to measure signal complexity are the entropy measures like Approximate entropy (ApEn) and Sample entropy (SampEn). But, these methods become unreliable and inaccurate at times, in particular, for short length data. Recently, a novel method of complexity measurement called Distribution Entropy (DistEn) was introduced, which showed reliable performance to capture complexity of both short term synthetic and short term physiologic data. This study aims to i) examine the competence of DistEn in discriminating Arrhythmia from Normal sinus rhythm (NSR) subjects, using RR interval time series data; ii) explore the level of consistency of DistEn with data length N; and iii) compare the performance of DistEn with ApEn and SampEn. Sixty six RR interval time series data belonging to two groups of cardiac conditions namely `Arrhythmia' and `NSR' have been used for the analysis. The data length N was varied from 50 to 1000 beats with embedding dimension m = 2 for all entropy measurements. Maximum ROC area obtained using ApEn, SampEn and DistEn were 0.83, 0.86 and 0.94 for data length 1000, 1000 and 500 beats respectively. The results show that DistEn undoubtedly exhibits a consistently high performance as a classification feature in comparison with ApEn and SampEn. Therefore, DistEn shows a promising behavior as bio marker for detecting Arrhythmia from short length RR interval data.

Density based fuzzy c-means clustering of non-convex patterns

We propose a new technique to perform unsupervised data classification (clustering) based on density induced metric and non-smooth optimization. Our goal is to automatically recognize multidimensional clusters of non-convex shape. We present a modification of the fuzzy c-means algorithm, which uses the data induced metric, defined with the help of Delaunay triangulation. We detail computation of the distances in such a metric using graph algorithms. To find optimal positions of cluster prototypes we employ the discrete gradient method of non-smooth optimization. The new clustering method is capable to identify non-convex overlapped d-dimensional clusters.

Complexity theory and organizing form dualities

Purpose – The purpose of this paper is to describe how order-generated rules applied to organizing form dualities can assist in creating the conditions for emergent, self-organized behavior in organizations, thereby offering an operational deployment of complexity theory.

Design/methodology/approach – The paper begins by showing that the concept of dualities is consistent with complexity-thinking. In addition, when applied to organizing forms, dualities represent a practical way of affecting an organization's balance between chaos and order. Thus, when augmented with order-generating rules, organizing form dualities provide an access point for the practical instigation of edge of chaos conditions and the potential for emergence.

Findings – The paper maintains that many attempts to “manage” complexity have been associated with changes to organizing forms, specifically toward new forms of organizing. It is suggested that organizing form dualities provide some management guidance for encouraging the “edge of chaos” conditions advocated in complexity theory, although the details of self-organization cannot be prescribed given the assumptions of non-linearity associated with complexity theory perspectives. Finally, it is proposed that organizing dualities can elucidate the nature and application of order-generating rules in non-linear complex systems.

Practical implications – Dualities offer some guidance toward the practical implementation of complexity theory as they represent an accessible sub-system where the forces for order and chaos – traditional and new forms of organizing respectively – are accessible and subject to manipulation.

Originality/value – The commonalities between dualities and complexity theory are intuitive, but little conceptual work has shown how the former can be employed as a guide to managing organizing forms. Moreover, this approach demonstrates that managers may be able to stimulate “edge of chaos” conditions in a practical way, without making positivistic assumptions about the causality associated with their efforts.

Chaos theory and assessment of forest stakeholder attitudes towards Australian forest policy

The Regional Forest Agreement process has dominated Australian forest policy for the past decade. The RFA process set in place a mechanism by which benchmark conservation values were established for forest  ecosystems, whilst addressing the needs of the timber industry. The outcomes of a number of RFA's have been fraught with controversy. Key stakeholder groups have shown disagreement with processes and  outcomes of methods employed by government both in establishing conservation reserves and areas allocated to timber harvesting. This research uses non-linear techniques to examine the dynamical behavior in stakeholder responses and to identify patterns of behavior that may lead to prediction of stakeholder responses. The method developed in this research provides a bridge between social sciences and Chaos theory.¹

Ecology of arboreal marsupials in a network of remnant linear habitats

Linear strips of vegetation set within a less-hospitable matrix are common features of landscapes throughout the world. Depending on location, form and function, these linear landscape elements include hedgerows, fencerows, shelterbelts, roadside or streamside strips and wildlife corridors. In many anthropogenically-modified landscapes, linear strips are important components for conservation because they provide a large proportion of the remaining wooded or shrubby habitat for fauna. They may also function to provide connectivity across the landscape. In some districts, the linear strips form an interconnected network of habitat. The spatial configuration of remnant habitat (size, shape and arrangement) may influence habitat suitability, and hence survival, of many species of plant and animal in modified landscapes. Near Euroa in south-eastern Australia, the clearing and fragmentation of temperate woodlands for agriculture has been extensive and, at present, less than 5% tree cover remains, most of which (83%) occurs as linear strips along roads and streams. The remainder of the woodland occurs as relatively small patches and single isolated trees scattered across the landscape. As an assemblage, arboreal marsupials are woodland dependent and vary in their sensitivity to habitat loss and fragmentation. This thesis focusses on determining the conservation status of arboreal marsupials in the linear network and understanding how they utilise the landscape mosaic. Specifically, the topics examined in this thesis are: (1) the composition of the arboreal marsupial assemblage in linear and non-linear woodland remnants; (2) the status and habitat preferences of species of arboreal marsupial within linear remnants; and (3) the ecology of a population of the Squirrel Glider Petaurus norfolcensis in the linear network, focusing on population dynamics, spatial organisation, and use of den trees. The arboreal marsupial fauna in the linear network was diverse, and comprised seven out of eight species known to occur in the district. The species detected within the strips were P. norfolcensis, the Sugar Glider Petaurus breviceps, Common Brushtail Possum Trichosums vulpecula, Common Ringtail Possum Pseudocheirus peregrinus, Brush-tailed Phascogale Phascogale tapoatafa, Koala Phascolarctos cinereus and Yellow-footed Antechinus Antechinus flavipes. The species not detected was the Feathertail Glider Acrabates pygmaeus. Survey sites in linear remnants (strips of woodland along roads and streams) supported a similar richness and density of arboreal mammals to sites in non-linear remnants (large patches or continuous tracts of woodland nearby). Furthermore, the combined abundance of all species of arboreal marsupials was significantly greater in sites in the linear remnants than in the non-linear remnants. This initial phase of the study provided no evidence that linear woodland remnants support a degraded or impoverished arboreal marsupial fauna in comparison with the nonlinear remnants surveyed. Intensive trapping of arboreal marsupials within a 15 km linear network between February 1997 and June 1998 showed that all species of arboreal marsupial (except A. pygmaeus) were present within the linear strips. Further analyses related trap-based abundance estimates to measures of habitat quality and landscape structure. Width of the linear habitat was significantly positively correlated with the combined abundance of all arboreal marsupials, as well as with the abundance of P. norfolcensis and T. vulpecula. The abundance of T. vulpecula was also significantly positively correlated with variation in overstorey species composition, Acacia density and the number of hollow-bearing trees. The abundance of P. norfolcensis was positively correlated with Acacia density and canopy width, and negatively correlated with distance to the nearest intersection with another linear remnant. No significant variables were identified to explain the abundance of P. tapoatafa, and there were insufficient captures of the remaining species to investigate habitat preferences. Petaurus norfolcensis were resident within the linear network and their density (0.95 -1.54 ha-1) was equal to the maximum densities recorded for this species in continuous forest elsewhere in south-eastern Australia. Rates of reproduction were also similar to those in continuous forest, with births occurring between May and December, a mean natality rate of 1.9, and a mean litter size of 1.7. Sex ratios never differed significantly from parity. Overall, the population dynamics of P. norfolcensis were comparable with published results for the species in contiguous forest, clearly suggesting that the linear remnants currently support a self-sustaining, viable population. Fifty-one P. norfolcensis were fitted with radio transmitters and tracked intermittently between December 1997 and November 1998. Home ranges were small (1.3 - 2.8 ha), narrow (20 - 40 m) and elongated (322 - 839 m). Home ranges were mostly confined to the linear remnants, although 80% of gliders also utilised small clumps of adjacent woodland within farm paddocks for foraging or denning. Home range size was significantly larger at intersections between two or more linear remnants than within straight sections of linear remnants. Intersections appeared to be important sites for social interaction because the overlap of home ranges of members of adjacent social groups was significantly greater at intersections than straight sections. Intersections provided the only opportunity for members of three or more social groups to interact, while still maintaining their territories. The 51 gliders were radiotracked to 143 different hollow-bearing trees on 2081 occasions. On average, gliders used 5.3 den trees during the study (range 1-15), and changed den trees every 4.9 days. The number of den trees used by each glider is likely to be conservative because the cumulative number of den trees continued to increase over the full duration of the study. When gliders shifted between den trees, the mean distance between consecutive den sites was 247 m. Den trees were located throughout a glider's home range, thereby reducing the need to return to a central den site and potentially minimising energy expenditure. Dens were usually located in large trees (mean diameter 88.5 cm) and were selected significantly more often than expected based on their occurrence within the landscape. The overall conclusion of this thesis is that the linear network I studied provides high quality habitat for resident populations of arboreal marsupials. Important factors influencing the suitability of the linear remnants appear to be the high level of network connectivity, the location on soils of high nutrient status, the high density of large trees and an acacia understorey. In highly fragmented landscapes, linear habitats as part of the remaining woodland mosaic have the potential to be an integral component in the conservation of woodland-dependent fauna. The habitat value of linear strips of vegetation should not be underestimated.

The effect of recursive detrending on panel unit root tests

This paper analyzes the properties of panel unit root tests based on recursively detrended data. The analysis is conducted while allowing for a (potentially) non-linear trend function, which represents a more general consideration than the current state of affairs with (at most) a linear trend. A new test statistic is proposed whose asymptotic behavior under the unit root null hypothesis, and the simplifying assumptions of a polynomial trend and iid errors are shown to be surprisingly simple. Indeed, the test statistic is not only asymptotically independent of the true trend polynomial, but also is in fact unique in that it is independent also of the degree of the fitted polynomial. However, this invariance property does not carry over to the local alternative, under which it is shown that local power is a decreasing function of the trend degree. But while power does decrease, the rate of shrinking of the local alternative is generally constant in the trend degree, which goes against the common belief that the rate of shrinking should be decreasing in the trend degree. The above results are based on simplifying assumptions. To compensate for this lack of generality, a second, robust, test statistic is proposed, whose validity does not require that the trend function is a polynomial or that the errors are iid.

Primary voltage control of a single-phase inverter using linear quadratic regulator with integrator

This paper proposes a linear quadratic regulator with integral action, ensuring fast dynamic response and resisting capability of voltage deviation from instantaneous reference grid voltage, to control the inverter voltage that can also be used in a microgrid. The proposed control strategy is based on a linear quadratic regulator, minimizing the cost function of the system, with integral action used to impede voltage degradation from a reference voltage for outside disturbances of the system, such as abrupt load change. The combined integral term assists to recover the voltage difference between grid and reference grid voltage. The validity of the proposed controller has been tested with linear and non-linear loads under various conditions. In both cases, the effectiveness of the controller has been proved. The result of the proposed controller is good to track the instantaneous reference grid voltage.

Linear optimization for ecological indices based on aggregation functions

We consider an optimization problem in ecology where our objective is to maximize biodiversity with respect to different land-use allocations. As it turns out, the main problem can be framed as learning the weights of a weighted arithmetic mean where the objective is the geometric mean of its outputs. We propose methods for approximating solutions to this and similar problems, which are non-linear by nature, using linear and bilevel techniques.