Differential inclusions and robust control theory

Uncontrolled systems (x) over dot is an element of Ax, where A is a non-empty compact set of matrices, and controlled systems (x) over dot is an element of Ax + Bu are considered. Higher-order systems 0 is an element of Px - Du, where and are sets of differential polynomials, are also studied. It is shown that, under natural conditions commonly occurring in robust control theory, with some mild additional restrictions, asymptotic stability of differential inclusions is guaranteed. The main results are variants of small-gain theorems and the principal technique used is the Krasnosel'skii-Pokrovskii principle of absence of bounded solutions.

Should optional properties be used in conceptual modelling? A theory and three empirical tests

An important feature of some conceptual modelling grammars is the features they provide to allow database designers to show real-world things may or may not possess a particular attribute or relationship. In the entity-relationship model, for example, the fact that a thing may not possess an attribute can be represented by using a special symbol to indicate that the attribute is optional. Similarly, the fact that a thing may or may not be involved in a relationship can be represented by showing the minimum cardinality of the relationship as zero. Whether these practices should be followed, however, is a contentious issue. An alternative approach is to eliminate optional attributes and relationships from conceptual schema diagrams by using subtypes that have only mandatory attributes and relationships. In this paper, we first present a theory that led us to predict that optional attributes and relationships should be used in conceptual schema diagrams only when users of the diagrams require a surface-level understanding of the domain being represented by the diagrams. When users require a deep-level understanding, however, optional attributes and relationships should not be used because they undermine users' abilities to grasp important domain semantics. We describe three experiments which we then undertook to test our predictions. The results of the experiments support our predictions.

Estimates of the real structured radius of stability of linear dynamic systems

A question is examined as to estimates of the norms of perturbations of a linear stable dynamic system, under which the perturbed system remains stable in a situation R:here a perturbation has a fixed structure.

Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Theory and applications of fuzzy Volterra integral equations

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations. The investigation is restricted to Volterra type equations with mildly restrictive conditions, but the methods are capable of extensive generalization to other types and more general assumptions. The results are illustrated by integral equations relating to control models with fuzzy uncertainties.

Object transportation by multiple mobile robots controlled by attractor dynamics: theory and implementation

Dynamical systems theory is used as a theoretical language and tool to design a distributed control architecture for teams of mobile robots, that must transport a large object and simultaneously avoid collisions with (either static or dynamic) obstacles. Here we demonstrate in simulations and implementations in real robots that it is possible to simplify the architectures presented in previous work and to extend the approach to teams of n robots. The robots have no prior knowledge of the environment. The motion of each robot is controlled by a time series of asymptotical stable states. The attractor dynamics permits the integration of information from various sources in a graded manner. As a result, the robots show a strikingly smooth an stable team behaviour.

Fractional Dynamics and Control of Distributed Parameter Systems

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of some distributed parameter systems.

A Small World Perspective on Urban Systems

The theory of small-world networks as initiated by Watts and Strogatz (1998) has drawn new insights in spatial analysis as well as systems theory. The theoryâeuro?s concepts and methods are particularly relevant to geography, where spatial interaction is mainstream and where interactions can be described and studied using large numbers of exchanges or similarity matrices. Networks are organized through direct links or by indirect paths, inducing topological proximities that simultaneously involve spatial, social, cultural or organizational dimensions. Network synergies build over similarities and are fed by complementarities between or inside cities, with the two effects potentially amplifying each other according to the âeurooepreferential attachmentâeuro hypothesis that has been explored in a number of different scientific fields (Barabási, Albert 1999; Barabási A-L 2002; Newman M, Watts D, Barabàsi A-L). In fact, according to Barabási and Albert (1999), the high level of hierarchy observed in âeurooescale-free networksâeuro results from âeurooepreferential attachmentâeuro, which characterizes the development of networks: new connections appear preferentially close to nodes that already have the largest number of connections because in this way, the improvement in the network accessibility of the new connection will likely be greater. However, at the same time, network regions gathering dense and numerous weak links (Granovetter, 1985) or network entities acting as bridges between several components (Burt 2005) offer a higher capacity for urban communities to benefit from opportunities and create future synergies. Several methodologies have been suggested to identify such denser and more coherent regions (also called communities or clusters) in terms of links (Watts, Strogatz 1998; Watts 1999; Barabási, Albert 1999; Barabási 2002; Auber 2003; Newman 2006). These communities not only possess a high level of dependency among their member entities but also show a low level of âeurooevulnerabilityâeuro, allowing for numerous redundancies (Burt 2000; Burt 2005). The SPANGEO project 2005âeuro"2008 (SPAtial Networks in GEOgraphy), gathering a team of geographers and computer scientists, has included empirical studies to survey concepts and measures developed in other related fields, such as physics, sociology and communication science. The relevancy and potential interpretation of weighted or non-weighted measures on edges and nodes were examined and analyzed at different scales (intra-urban, inter-urban or both). New classification and clustering schemes based on the relative local density of subgraphs were developed. The present article describes how these notions and methods contribute on a conceptual level, in terms of measures, delineations, explanatory analyses and visualization of geographical phenomena.

Analyzing dynamic intellectual capital: System-based theory and application

This research report presents an application of systems theory to evaluating intellectual capital (IC) as organization's ability for self-renewal. As renewal ability is a dynamic capability of an organization as a whole, rather than a static asset or an atomistic competence of separate individuals within the organization, it needs to be understood systemically. Consequently, renewal ability has to be measured with systemic methods that are based on a thorough conceptual analysis of systemic characteristics of organizations. The aim of this report is to demonstrate the theory and analysis methodology for grasping companies' systemic efficiency and renewal ability. The volume is divided into three parts. The first deals with the theory of organizations as self-renewing systems. In the second part, the principles of quantitative analysis of organizations are laid down. Finally, the detailed mathematics of the renewal indices are presented. We also assert that the indices produced by the analysis are an effective tool for the management and valuation of knowledge-intensive companies.

Towards input/output-free modelling of linear infinite-dimensional systems in continuous time

This dissertation describes a networking approach to infinite-dimensional systems theory, where there is a minimal distinction between inputs and outputs. We introduce and study two closely related classes of systems, namely the state/signal systems and the port-Hamiltonian systems, and describe how they relate to each other. Some basic theory for these two classes of systems and the interconnections of such systems is provided. The main emphasis lies on passive and conservative systems, and the theoretical concepts are illustrated using the example of a lossless transfer line. Much remains to be done in this field and we point to some directions for future studies as well.

Methods for construction and analysis of computational models in systems biology : applications to the modelling of the heat shock response and the self-assembly of intermediate filaments

Systems biology is a new, emerging and rapidly developing, multidisciplinary research field that aims to study biochemical and biological systems from a holistic perspective, with the goal of providing a comprehensive, system- level understanding of cellular behaviour. In this way, it addresses one of the greatest challenges faced by contemporary biology, which is to compre- hend the function of complex biological systems. Systems biology combines various methods that originate from scientific disciplines such as molecu- lar biology, chemistry, engineering sciences, mathematics, computer science and systems theory. Systems biology, unlike “traditional” biology, focuses on high-level concepts such as: network, component, robustness, efficiency, control, regulation, hierarchical design, synchronization, concurrency, and many others. The very terminology of systems biology is “foreign” to “tra- ditional” biology, marks its drastic shift in the research paradigm and it indicates close linkage of systems biology to computer science. One of the basic tools utilized in systems biology is the mathematical modelling of life processes tightly linked to experimental practice. The stud- ies contained in this thesis revolve around a number of challenges commonly encountered in the computational modelling in systems biology. The re- search comprises of the development and application of a broad range of methods originating in the fields of computer science and mathematics for construction and analysis of computational models in systems biology. In particular, the performed research is setup in the context of two biolog- ical phenomena chosen as modelling case studies: 1) the eukaryotic heat shock response and 2) the in vitro self-assembly of intermediate filaments, one of the main constituents of the cytoskeleton. The range of presented approaches spans from heuristic, through numerical and statistical to ana- lytical methods applied in the effort to formally describe and analyse the two biological processes. We notice however, that although applied to cer- tain case studies, the presented methods are not limited to them and can be utilized in the analysis of other biological mechanisms as well as com- plex systems in general. The full range of developed and applied modelling techniques as well as model analysis methodologies constitutes a rich mod- elling framework. Moreover, the presentation of the developed methods, their application to the two case studies and the discussions concerning their potentials and limitations point to the difficulties and challenges one encounters in computational modelling of biological systems. The problems of model identifiability, model comparison, model refinement, model inte- gration and extension, choice of the proper modelling framework and level of abstraction, or the choice of the proper scope of the model run through this thesis.

Educational Leadership: Exploring the Influence of Managed and Living Systems in Educational Leadership Discourse

A conceptual analysis of educational leadership explored the influence of managed and living systems on 21st century leadership discourse. Drawing on a detailed understanding of managed and living systems theory compiled from the work of Capra (2002), Morgan (1997), Mitchell and Sackney (2009), and Wheatley (2007), this study draws attention to the managed systems systemic concepts of efficiency, control, and standardization, and the living systems concepts of collaboration, shared meaning, change, and interconnection as markers of systems theory that find resonance within leadership literature. Using these systemic concepts as a framework, this study provides important insights into the espousal of managed and living systems concepts within the leadership discourse.

Private industrial project management: a systems-based case study

The technique of linear responsibility analysis is used for a retrospective case study of a private industrial development consisting of an extension to existing buildings to provide a warehouse, services block and packing line. The organizational structure adopted on the project is analysed using concepts from systems theory which are included in Walker's theoretical model of the structure of building project organizations (Walker, 1981). This model proposes that the process of building provision can be viewed as systems and subsystems which are differentiated from each other at decision points. Further to this, the subsystems can be viewed as the interaction of managing system and operating system. Using Walker's model, a systematic analysis of the relationships between the contributors gives a quantitative assessment of the efficacy of the organizational structure used. The causes of the client's dissatisfaction with the outcome of the project were lack of integration and complexity of the managing system. However, there was a high level of satisfaction with the completed project and this is reflected by the way in which the organization structure corresponded to the model's propositions.

A conventionally managed project: a systems based case study

The technique of linear responsibility analysis is used for a retrospective case study of a private development consisting of an extension to an existing building to provide a wholesale butchery facility. The project used a conventionally organized management process. The organization structure adopted on the project is analysed using concepts from the systems theory, which are included in Walkers theoretical model of the structure of building project organizations. This model proposes that the process of building provision can be viewed as systems and sub-systems that are differentiated from each other at decision points. Further to this, the sub-systems can be viewed as the interaction of managing system and operating system. Using Walkers model, a systematic analysis of the relationships between the contributors gives a quantitative assessment of the efficiency of the organizational structure used. The project's organization structure diverged from the models propositions resulting in delay to the project's completion and cost overrun but the client was satisfied with the project functionally.

A project managed by a multi disciplinary practice: a systems based case study.

The technique of linear responsibility analysis is used for a retrospective case study of a private industrial development consisting of an engineering factory and offices. A multi-disciplinary professional practice was used to manage and design the project. The organizational structure adopted on the project is analysed using concepts from systems theory which are included in Walker's theoretical model of the structure of building project organizations (Walker, 1981). This model proposes that the process of buildings provision can be viewed as systems and sub-systems which are differentiated form each other at decision points. Further to this, the sub-systematic analysis of the relationship between the contributors gives a quantitative assessment of the efficiency of the organizational structure used. There was a high level of satisfaction with the completed project and this is reflected by the way in which the organization structure corresponded to the model's proposition. However, the project was subject to string environmental forces which the project organization was not capable of entirely overcoming.