Relaxed LMI conditions for control of nonlinear Takagi-Sugeno models

Los problemas de optimización de desigualdades matriciales lineales en control borroso se han convertido en la herramienta más utilizada en dicha área desde los años 90. Muchos sistemas no lineales pueden ser modelados como sistemas borrosos de modo que el control borroso puede considerarse como una técnica de control no lineal. Aunque se han obtenido muchos y buenos resultados, quedan algunas fuentes de conservadurismo cuando se comparan con otros enfoques de control no lineal. Esta tesis discute dichas cuestiones de conservadurismo y plantea nuevos enfoques para resolverlas. La principal ventaja de la formulación mediante desigualdades matriciales lineales es la posibilidad de asegurar estabilidad y prestaciones de un sistema no lineal modelado como un sistema borroso Takagi-Sugeno. Estos modelos están formados por un conjunto de modelos lineales eligiendo el sistema a aplicar mediante el uso de unas reglas borrosas. Estas reglas se traducen en funciones de interpolación o de pertenecía que nos indican el grado de validez de un modelo lineal respecto del resto. El mayor problema que presentan estas técnicas basadas en desigualdades matriciales lineales es que las funciones de pertenencia no están incluidas en las condiciones de estabilidad del sistema, lo que significa que se prueba la estabilidad y prestaciones para cualquier forma de interpolación entre los diferentes modelos lineales. Esto genera una fuente de conservadurismo que sería conveniente limitar. En la tesis doctoral se presentan varias metodologías capaces de trasladar la información de las funciones de pertenencia del sistema al problema basado en desigualdades matriciales lineales de estabilidad y prestaciones. Las dos principales aportaciones propuestas se basan, respectivamente, en introducir una serie de matrices de relajación que permitan incorporar esta información y en aprovechar la descripción de una amplia clase de sistemas borrosos en productos tensoriales de...Ariño Latorre, CV. (2008). Relaxed LMI conditions for control of nonlinear Takagi-Sugeno models [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8301Palanci

Control of nonlinear systems using n-fuzzy models

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2015.A utilização de modelos fuzzy Takagi-Sugeno (T-S) tem sido extensivamente investigada no decorrer das últimas décadas, principalmente por propiciarem o desenvolvimento de metodologias de projeto de sistemas de controle não lineares que possuem caráter sistemático e solução numérica, fazendo-se uso de propriedades inerentes como a de aproximação universal e/ou de convexidade dos modelos. Nota-se, entretanto, que as técnicas de modelagem fuzzy T-S atuais, em geral, garantem a convexidade do modelo e/ou a sua precisão de representação somente para uma determinada região do espaço de estados. Desta forma, para estratégias de controle baseadas em propriedades de convexidade, a estabilidade do sistema de malha fechada formado pelo sistema não linear realimentado pela lei de controle fuzzy deve ser estudada no contexto de estabilidade local, sendo fundamental a determinação de regiões de estabilidade para o sistema de malha fechada. Esta importante característica dos modelos fuzzy T-S raramente é considerada na literatura, podendo implicar em perda de desempenho e até mesmo instabilidade do sistema em malha fechada. Outro problema inerente à utilização de modelos fuzzy T-S diz respeito ao aumento exponencial de complexidade do modelo com o número de não linearidades presentes no sistema, principalmente quando se busca descrever de forma exata a dinâmica do sistema a controlar, o que implica no aumento da complexidade numérica dos algoritmos para análise e projeto, assim como do aumento da complexidade de implementação de leis de controle. Neste contexto, esta tese busca evidenciar a importância da consideração da validade regional dos modelos fuzzy de tipo T-S para o desenvolvimento de ferramentas de análise e síntese de sistemas de controle não lineares, assim como considerar outras restrições físicas presentes no sistema de controle como limites nos atuadores, e discutir a problemática associada à complexidade dos modelos fuzzy T-S. Um método de modelagem baseado no uso de regras não lineares locais é desenvolvido permitindo, além de uma representação compacta e precisa da planta não linear original, o tratamento do problema de projeto de controladores dinâmicos por realimentação de saídas na presença de não linearidades dependentes de estados não mensuráveis do sistema. Utilizando-se funções de Lyapunov fuzzy (FLF), são desenvolvidas condições de estabilidade e estabilização para o sistema em malha fechada que podem ser verificadas em termos de factibilidade de um conjunto de desigualdades matriciais lineares. Os controladores propostos são baseados na realimentação de estados e do vetor de não linearidades de setor, ao qual são consideradas perturbações limitadas em energia ou amplitude, e na realimentação dinâmica de saídas, para sistemas não perturbados com atuadores saturantes ou para sistemas sujeitos a perturbações persistentes. Exemplos numéricos são apresentados ao longo do trabalho com o objetivo de ilustrar a eficiência dos métodos propostos. Ainda, objetivando auxiliar estudantes, engenheiros e pesquisadores na análise e projeto de controle de sistemas não lineares, apresenta-se o desenvolvimento de uma ferramenta computacional interativa para a modelagem e controle fuzzy. Aspectos práticos e um estudo da complexidade de implementação digital de controladores fuzzy também são discutidos através da simulação Hardware-in-the-Loop (HIL) com utilização de uma placa de desenvolvimento FPGA (do inglês Field Programmable Gate Array).Abstract : Takagi-Sugeno (T-S) fuzzy models have been extensively investigated over the last decade to develop the so-called fuzzy model based (FMB) control techniques, providing nonlinear control design methodologies with a systematic aspect and numerical solution. However, the actual T-S fuzzy modeling techniques, in general, only guarantee the convexity of the model and/or their accuracy of representation for a specific domain of the state space. Thus, for control strategies based on convexity properties, the stability of the closed-loop system composed of the nonlinear system and the fuzzy controller should be analyzed in a local context, being fundamental to determining stability regions for the closed-loop system. This inherent local characteristic is often not considered in most FMB control design results, which may lead to poor performance or even instability of the closed-loop system. In this sense, this thesis aims to consider the regional validity of the T-S fuzzy models for the development of nonlinear control systems analysis and design tools, to consider other physical constraints and to discuss the problems associated with the complexity of T-S fuzzy models. A modeling method based on the use of nonlinear local rules that provides a compact and accurate representation is presented, allowing also to handle with the dynamic output feedback control problem for systems with nonlinearities that may depend on unmeasurable states. Using fuzzy Lyapunov functions (FLF), closed-loop stability conditions are provided, which can be verified in terms of the feasibility of a set of linear matrix inequalities (LMIs). The proposed controllers are based on a state and sector nonlinearities feedback, for systems subject to disturbances bounded in energy or amplitude, and on a dynamic output feedback, for systems with saturating actuators. Numerical examples are presented throughout this document to illustrate the effectiveness of the proposed design methodologies. Further, aiming to assist students and engineers in the nonlinear control system design, an interactive computational tool is presented for fuzzy modeling and control. Practical aspects and a study of the digital implementation of fuzzy controllers are discussed using a Hardware-in-the-Loop (HIL) simulation with a Field Programmable Gate Array (FPGA) development board

3D modelling and inversion of airborne gravity gradiometry and aeromagnetic data from Budgell Harbour, North-Central Newfoundland

Airborne gravity surveys have been become a popular tool for mineral exploration in the past three decades, mostly because of considerable improvements in equipment. Airborne methods make the data acquisition process rapid, more straightforward, and potentially cheaper than ground surveys. 3D modeling and inversion of gravity gradiometry and aeromagnetic datasets from Budgell Harbour, located in north-central Newfoundland, are carried out. Reef-type platinum group mineralization is present in the area, as well as a large scale, deep igneous intrusion (the Budgell Harbour Stock). The intrusion is thought to be related to the same tectonic activity that resulted in the formation of the basins offshore Newfoundland that are now being actively explored for hydrocarbons. 3D modeling and inversion, specifically taking into account topography, are done for the gravity gradiometry and magnetic data-sets. The inversions are typical unconstrained, minimum-structure inversions. Joint inversion of the gravity gradiometry and magnetic data-sets is also considered. The Earth model is parameterized in terms of an unstructured tetrahedral mesh, which allows the topography to be modeled to the same accuracy with which it is known. The goal is to develop 3D density and susceptibility models of the area, thus further assessing the mineral potential of the area and better delineating the Budgell Harbour Stock

Development of an Optimal Replenishment Policy for Human Capital Inventory

A unique approach is developed for evaluating Human Capital (workforce) requirements. With this approach, new ways of measuring personnel availability are proposed and available to ensure that an organization remains ready to provide timely, relevant, and accurate products and services in support of its strategic objectives over its planning horizon. The development of this analysis and methodology was established as an alternative approach to existing studies for determining appropriate hiring and attrition rates and to maintain appropriate personnel levels of effectiveness to support existing and future missions. The contribution of this research is a prescribed method for the strategic analyst to incorporate a personnel and cost simulation model within the framework of Human Resources Human Capital forecasting which can be used to project personnel requirements and evaluate workforce sustainment, at least cost, through time. This will allow various personnel managers to evaluate multiple resource strategies, present and future, maintaining near “perfect” hiring and attrition policies to support its future Human Capital assets

Deconstructing the glass transition through critical experiments on colloids

The glass transition is the most enduring grand-challenge problem in contemporary condensed matter physics. Here, we review the contribution of colloid experiments to our understanding of this problem. First, we briefly outline the success of colloidal systems in yielding microscopic insights into a wide range of condensed matter phenomena. In the context of the glass transition, we demonstrate their utility in revealing the nature of spatial and temporal dynamical heterogeneity. We then discuss the evidence from colloid experiments in favor of various theories of glass formation that has accumulated over the last two decades. In the next section, we expound on the recent paradigm shift in colloid experiments from an exploratory approach to a critical one aimed at distinguishing between predictions of competing frameworks. We demonstrate how this critical approach is aided by the discovery of novel dynamical crossovers within the range accessible to colloid experiments. We also highlight the impact of alternate routes to glass formation such as random pinning, trajectory space phase transitions and replica coupling on current and future research on the glass transition. We conclude our review by listing some key open challenges in glass physics such as the comparison of growing static lengthscales and the preparation of ultrastable glasses, that can be addressed using colloid experiments.Comment: 137 pages, 45 figure

Contributions to fuzzy polynomial techniques for stability analysis and control

The present thesis employs fuzzy-polynomial control techniques in order to improve the stability analysis and control of nonlinear systems. Initially, it reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems, such as the more relevant results about polynomial and fuzzy polynomial systems. The basic framework uses fuzzy polynomial models by Taylor series and sum-of-squares techniques (semidefinite programming) in order to obtain stability guarantees. The contributions of the thesis are: ¿ Improved domain of attraction estimation of nonlinear systems for both continuous-time and discrete-time cases. An iterative methodology based on invariant-set results is presented for obtaining polynomial boundaries of such domain of attraction. ¿ Extension of the above problem to the case with bounded persistent disturbances acting. Different characterizations of inescapable sets with polynomial boundaries are determined. ¿ State estimation: extension of the previous results in literature to the case of fuzzy observers with polynomial gains, guaranteeing stability of the estimation error and inescapability in a subset of the zone where the model is valid. ¿ Proposal of a polynomial Lyapunov function with discrete delay in order to improve some polynomial control designs from literature. Preliminary extension to the fuzzy polynomial case. Last chapters present a preliminary experimental work in order to check and validate the theoretical results on real platforms in the future.Pitarch Pérez, JL. (2013). Contributions to fuzzy polynomial techniques for stability analysis and control [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34773TESI

Uncertainty propagation in nonlinear systems.

This thesis examines the effects of uncertainty on a variety of different engineering systems. Uncertainty can be best described as a lack of knowledge for a particular system, and can come from a variety of different sources. Within this thesis the possibilistic branch of uncertainty quantification is used. A combination of simulated and real-life engineering systems are studied, covering some of the most popular types of computational models. An outline of various background topics is presented first, as these topics are all subsequently used within the thesis. The most important of these is the transformation method, a possibilistic uncertainty approach derived from fuzzy arithmetic. Most of the work here examines uncertain systems by implementing Ben-Haim's information gap theory. Uncertainty is deliberately introduced into the parameters of the various computational models to use the concept of “opportunity”. The basic rationale is that if some degree of tolerance can be accepted on a model prediction of a system, it is possible to obtain a lower value of prediction error than with a standard crisp-valued model. For the use of interval-valued computational models there is generally a trade-off to be made between minimising the prediction error of the model and minimising the range of predicted outputs, to reduce the tolerance on the solution. The studied models all use a “degree of uncertainty” parameter that allows any user to select the suitable trade-off level for their particular application. The thesis then concludes with a real-life engineering study, undertaken as a nine month placement on a European Union project entitled MADUSE. The work was done at Centro Ricerche Fiat, and examined the dynamic effects of uncertainties related to automotive spot welds. This study used both finite element modelling and experimental modal testing of manufactured specimens

Abstracts of Papers Schedueled for Presentation at the 86th Session of the Iowa Acedemy of Science, April 19-20, 1974

Presentation abstracts from the annual meeting of the Iowa Academy of Sciencehttps://scholarworks.uni.edu/ias_docs/1060/thumbnail.jp

Applied Mathematics to Mechanisms and Machines

This book brings together all 16 articles published in the Special Issue "Applied Mathematics to Mechanisms and Machines" of the MDPI Mathematics journal, in the section “Engineering Mathematics”. The subject matter covered by these works is varied, but they all have mechanisms as the object of study and mathematics as the basis of the methodology used. In fact, the synthesis, design and optimization of mechanisms, robotics, automotives, maintenance 4.0, machine vibrations, control, biomechanics and medical devices are among the topics covered in this book. This volume may be of interest to all who work in the field of mechanism and machine science and we hope that it will contribute to the development of both mechanical engineering and applied mathematics