Минимаксная рекурсивная оценка состояния линейных дескрипторных систем с дискретным временем

Розглянуто підхід до оцінювання стану системи, що описується дескрипторним рівнянням із дискретним часом за спостереженнями, що надходять у реальному часі. Підхід базується на понятті лінійної мінімаксної оцінки та індексу причинності, що вводяться у статті для сингулярних різницевих рівнянь. Рекурсивний оцінювач стану будується шляхом застосування методу «Київського віника» та теорії псевдоінверсних матриць до проблеми мінімаксного оцінювання.This paper describes an approach to the online state estimation of systems described by a general class of linear noncausal time-varying difference descriptor equations subject to uncertainties. An approach is based on the notions of a linear minimax estimation and an index of causality introduced here for singular difference equations. The online minimax observer is derived by the application of the dynamical programming and Moore's pseudoinverse theory to the minimax estimation problem.Рассмотрен подход к оцениванию состояния системы, описываемой дескрипторным уравнением с дискретным временем по наблюдениям, поступающим в реальном времени. Подход основан на понятии линейной минимаксной оценки и индекса причинности, введенных в статье для сингулярных разностных уравнений. Рекурсивный оцениватель строится путем применения метода «Киевского веника» и теории псевдообратных матриц к проблеме минимаксного оценивания

Minimax recursive state estimation for linear discrete-time descriptor systems

This paper describes an approach to the online state estimation of systems described by a general class of linear noncausal time-varying difference descriptor equations subject to uncertainties. An approach is based on the notions of a linear minimax estimation and an index of causality introduced here for singular difference equations. The online minimax observer is derived by the application of the dynamical programming and Moore's pseudoinverse theory to the minimax estimation problem.Розглянуто підхід до оцінювання стану системи, що описується дескрипторним рівнянням із дискретним часом за спостереженнями, що надходять у реальному часі. Підхід базується на понятті лінійної мінімаксної оцінки та індексу причинності, що вводяться у статті для сингулярних різницевих рівнянь. Рекурсивний оцінювач стану будується шляхом застосування методу «Київського віника» та теорії псевдоінверсних матриць до проблеми мінімаксного оцінювання.Рассмотрен подход к оцениванию состояния системы, описываемой дескрипторным уравнением с дискретным временем по наблюдениям, поступающим в реальном времени. Подход основан на понятии линейной минимаксной оценки и индекса причинности, введенных в статье для сингулярных разностных уравнений. Рекурсивный оцениватель строится путем применения метода «Киевского веника» и теории псевдообратных матриц к проблеме минимаксного оценивания

The best of both worlds? : An exploratory study on forms and effects of new qualitative-quantitative scenario methodologies

This study analyzes new forms of combined and integrated scenario methodologies, which are used to construct exploratory socio-environmental scenarios. It makes conceptual and empirical contributions to futures studies and to inter- and transdisciplinary environmental and sustainability research. For 15 years, scenario approaches for the construction of socio-environmental scenarios have been established, which combine qualitative scenario methods with numerical modeling and simulation. They have become state of the art by replacing scenario approaches based on modeling alone. Combined scenario approaches are used to explore the future of socio-environmental systems scientifically, and to supply society and policy makers with the best possible information on possible alternative future developments in climate, biodiversity, land use, water, resources and energy, etc. Combined scenarios are characterized by a deep methodological and epistemological hybridity, as they combine approaches and perspectives from different realms. This makes their appeal but also raises enormous challenges. At the same time, literature on combined scenarios has thus far provided little conceptual orientation for the comparison, design, assessment and implementation of different forms of combined approaches. In practice, the so-called Story and Simulation (SAS) approach is dominant, coupling intuitive scenarios with simulation, and postulating an iterative refinement of both components. Against this background, this study explores new avenues: Cross-impact balance analysis (CIB), a systematic-formalized yet qualitative form of systems analysis, is combined with numerical modeling and simulation (CIB&S). As yet, this approach was explored neither empirically nor conceptually in a systematic way. Still, in energy and climate research, the expectation is formulated that this approach might balance the difficulties of combined scenario approaches of the SAS type, especially with regard to traceability and consistency. This study asks whether and how CIB can be combined with numerical modeling and simulation to support inter- and transdisciplinary research teams in constructing qualitative and quantitative or integrated exploratory scenarios of socio-environmental systems. It focuses on forms of the combination of CIB&S; on effects on traceability and consistency as well as on further (unintended) effects of the use of CIB within such combinations; and finally on factors influencing these effects. Combined scenario approaches are conceptualized in this study as inter- and transdisciplinary methodologies. Each application is characterized by an individual social, technical and data-related organization. Based on a review of the literature on combined scenario approaches, central dimensions to characterize forms of the combination of qualitative and quantitative scenario methods are developed. In addition, a model of the typical phases of a CIB&S process is designed. To assess effects, working definitions of scenario traceability and scenario consistency are proposed and operationalized. This conceptual framework structures the empirical analysis of two exploratory case studies. The first case studies a method demonstration for the German Federal Environment Agency (UBA). In this case, CIB is used to analyze societal framework assumptions of environmental models and to construct plausible sets of assumptions until the year 2030. The second case studies a full pioneer application of CIB&S in the context of a megacity project for the German Federal Ministry for Education and Research (BMBF). In the latter case, CIB is combined with a material flow simulator, to construct integrated scenarios on the possible water futures of Lima, Peru, until the year 2040. Both cases are qualitatively analyzed and interpreted, based on participant observation, interviews with process participants as well as process documents. The study shows that in different (ideal typical) forms of its combination with numerical modeling and simulation, CIB takes over different functions. The combined form, in turn, is mainly influenced by the position of both components within the process as well as by their degree of integration. CIB&S methodologies can successfully support scenario traceability, and contribute to both the internal consistency of the qualitative scenario component and the consistency between qualitative and quantitative scenario components. The stronger the degree of integration between CIB and simulation model, the stronger these effects. However, integration requires that the models underlying the scenarios, i.e. the conceptual CIB model as well as the numerical modeling and simulation, are made explicit and accessible, are compared with and, if applicable, adapted to each other. In addition, CIB&S approaches can create new checks and balances within combined scenario methodologies, when the definition of scenarios as well as the selection of scenario samples is assigned to the CIB and to the CIB participants. CIB&S approaches seem to be less suitable for the construction of explicitly normative or participatory scenarios. Instead, CIB&S approaches do support the participating experts in better analyzing, structuring and reflecting their knowledge, their assumptions and their ideas on possible future developments of socio-environmental systems. The external users of CIB&S-based scenarios can benefit from the improved accessibility of assumptions on uncertainty and complexity, which underlie the qualitative and quantitative or integrated scenarios, as these become criticizable in the first place. Overall, this study makes steps toward more conceptually grounded and more reflective research on the diversity of possible variants of combined and integrated scenario methodologies

Classification Algorithms based on Generalized Polynomial Chaos

Classification is one of the most important tasks in process system engineering. Since most of the classification algorithms are generally based on mathematical models, they inseparably involve the quantification and propagation of model uncertainty onto the variables used for classification. Such uncertainty may originate from either a lack of knowledge of the underlying process or from the intrinsic time varying phenomena such as unmeasured disturbances and noise. Often, model uncertainty has been modeled in a probabilistic way and Monte Carlo (MC) type sampling methods have been the method of choice for quantifying the effects of uncertainty. However, MC methods may be computationally prohibitive especially for nonlinear complex systems and systems involving many variables. Alternatively, stochastic spectral methods such as the generalized polynomial chaos (gPC) expansion have emerged as a promising technique that can be used for uncertainty quantification and propagation. Such methods can approximate the stochastic variables by a truncated gPC series where the coefficients of these series can be calculated by Galerkin projection with the mathematical models describing the process. Following these steps, the gPC expansion based methods can converge much faster to a solution than MC type sampling based methods. Using the gPC based uncertainty quantification and propagation method, this current project focuses on the following three problems: (i) fault detection and diagnosis (FDD) in the presence of stochastic faults entering the system; (ii) simultaneous optimal tuning of a FDD algorithm and a feedback controller to enhance the detectability of faults while mitigating the closed loop process variability; (iii) classification of apoptotic cells versus normal cells using morphological features identified from a stochastic image segmentation algorithm in combination with machine learning techniques. The algorithms developed in this work are shown to be highly efficient in terms of computational time, improved fault diagnosis and accurate classification of apoptotic versus normal cells

Optimization methods for deadbeat control design: a state space approach

This thesis addresses the synthesis problem of state deadbeat regulator using state space techniques. Deadbeat control is a linear control strategy in discrete time systems and consists of driving the system from any arbitrary initial state to a desired final state infinite number of time steps. Having described the framework for development of the thesis which is in the form of a lower linear-fractional transformation (LFT), the conditions for internal stability based on the notion of coprime factorization over the set of proper and stable transfer matrices, namely RH, is discussed. This leads to the derivation of the class of all stabilizing linear controllers, which are parameterized affinely in terms of a stable but otherwise free parameter Q, usually known as the Q-parameterization. In this work, the classical Q- parameterization is generalized to deliver a parameterization for the family of deadbeat regulators. Time response characteristics of the deadbeat system are investigated. In particular, the deadbeat regulator design problem in which the system must satisfy time domain specifications and minimize a quadratic (LQG-type) performance criterion is examined. It is shown that the attained parameterization for deadbeat controllers leads to the formulation of the synthesis problem in a quadratic programming framework with Q regarded as the design variable. The equivalent formulation of this objective as a quadratic integral in the frequency domain provides the means for shaping the frequency response characteristics of the system. Using the LMI characterization of the standard H problem, a new scheme for shaping the system frequency response characteristics by minimizing the infinity norm of an appropriate closed-loop transfer function is introduced. As shown, the derived parameterization of deadbeat compensators simplifies considerably the formulation and solution of this problem. The last part of the work described in this thesis is devoted to addressing the synthesis problem of deadbeat regulators in a robust way, when the plant is subject to structured norm-bounded parametric uncertainties. A novel approach which is expressed as an LMI feasibility condition has been proposed and analysed

Proceedings. 27. Workshop Computational Intelligence, Dortmund, 23. - 24. November 2017

Dieser Tagungsband enthält die Beiträge des 27. Workshops Computational Intelligence. Die Schwerpunkte sind Methoden, Anwendungen und Tools für Fuzzy-Systeme, Künstliche Neuronale Netze, Evolutionäre Algorithmen und Data-Mining-Verfahren sowie der Methodenvergleich anhand von industriellen und Benchmark-Problemen

Of evolution, information, vitalism and entropy: reflections of the history of science and epistemology in the works of Balzac, Zola, Queneau, and Houellebecq

This dissertation proposes the application of rarely-used epistemological and scientific lenses to the works of four authors spanning two centuries: Honoré de Balzac, Émile Zola, Raymond Queneau, and Michel Houellebecq. Each of these novelists engaged closely with questions of science and epistemology, yet each approached that engagement from a different scientific perspective and epistemological moment. In Balzac’s La Peau de chagrin, limits of determinism and experimental method tend to demonstrate that there remains an inscrutable yet guided excess in the interactions between the protagonist Raphaël and his enchanted skin. This speaks to an embodiment of the esprit préscientifique, a framework that minimizes the utility of scientific practice in favor of the unresolved mystery of vitalism. With Zola comes a move away from undefinable mystery to a construction of the novel consistent with Claude Bernard’s deterministic experimental medicine. Yet Zola’s Roman expérimental project is only partially executed, in that the Newtonian framework that underlies Bernard’s method yields to contrary evidence in Zola’s text of entropy, error, and loss of information consistent with the field of thermodynamics. In Queneau’s texts, Zola’s interest in current science not only remains, but is updated to reflect the massive upheaval in scientific thought that took place in the last half of the nineteenth and early part of the twentieth centuries. If Queneau’s texts explicitly mention advances like relativity, however, they often do so in a humorously dismissive manner that values pre-entropic and even early geometric constructs like perpetual motion machines and squared circles. Queneau’s apparent return to the pre-scientific ultimately yields to Houellebecq’s textual abyss. For Houellebecq, science is not only to be embraced in its entropic and relativistic constructs; it is these very constructs - and the style typically used to present them – that serve as a reminder of the abjection, decay, and hopelessness of human existence. Gone is the mystery of life in its totality. In its place remain humans acting as a series of particles mechanically obeying deterministic laws. The parenthesis that opened with Balzac’s positive coding of pre-scientific thought closes with Houellebecq’s negative coding of modern scientific theory