On relaxed LMI-based designs for fuzzy regulators and fuzzy observers

Relaxed conditions for stability of nonlinear, continuous and discrete-time systems given by fuzzy models are presented. A theoretical analysis shows that the proposed methods provide better or at least the same results of the methods presented in the literature. Numerical results exemplify this fact. These results are also used for fuzzy regulators and observers designs. The nonlinear systems are represented by fuzzy models proposed by Takagi and Sugeno. The stability analysis and the design of controllers are described by linear matrix inequalities, that can be solved efficiently using convex programming techniques. The specification of the decay rate, constrains on control input and output are also discussed.

Caracterização geomorfométrica multiescala de modelos digitais de terreno.

O estudo das formas de relevo através da geomorfometria ciência que quantifica as superfícies topográficas demanda que múltiplas escalas sejam consideradas simultaneamente. Esse fato soma-se à continuidade espacial inerente à topografia, a qual raramente apresenta limites naturais abruptos, para conceder um caráter vago às formas de relevo. Essa dupla vagueza, no entanto, é raramente abordada de forma explícita em trabalhos científicos que, usualmente, valem-se de limiares e definições subjetivas e arbitrárias para descreverem o relevo. Dentro desse contexto, o trabalho apresenta um método inovador de caracterização geomorfométrica multiescala de modelos digitais de terreno (MDTs). A abordagem proposta baseia-se no método de extração de feições morfométricas de Wood (1996), mas o modifica em um número de maneiras: (i) expandindo o número de classes identificadas; (ii) transformando-o em um sistema fuzzy, cujos conjuntos fuzzy são parametrizados automaticamente e; (iii) limitando localmente a escala máxima de análise de maneira não-supervisionada. Como resultado, obtém-se um mapa de feições fundamentais e um mapa de escalas fundamentais que, juntos, sintetizam a estrutura multiescala das superfícies. Além disso, são produzidos mapas de pertinências fuzzy e de índice de confusão para cada escala analisada, assim como versões multiescala dos mesmos. Para avaliar a transferibilidade e o caráter não-supervisionado do método, foram analisados cinco MDTs oriundos de bases de dados distintas, com diferentes resoluções e extensões espaciais, compreendendo regiões continentais, do fundo dos oceanos e do planeta Marte. Os resultados obtidos foram avaliados em relação à utilização de escalas e parametrizações fixas, atestando a capacidade do método de empreender caracterizações geomorfométricas mais completas do que abordagens convencionais. Duas aplicações foram ainda propostas: a parametrização geomorfométrica multiescala e o desenvolvimento de uma assinatura morfométrica multiescala, demonstrando claros caminhos para a continuidade da pesquisa. Como conclusão geral, não obstante a algumas limitações apontadas, considerou-se que o trabalho apresentado alcançou seu objetivo de prover a caracterização geomorfométrica multiescala de modelos digitais de terreno.

Modelos de presupuestación de capital en finanzas corporativas y utilidad de los mismos

La siguiente investigación describe una aproximación teórica al tema de los modelos de presupuestación de capital, el objetivo fundamental se basa en comprender su enfoque e importancia al momento de tomar decisiones de inversión por parte de los directores de una empresa, así como de prever los efectos de esta en un futuro. Al respecto, y sobre la base de que los modelos de presupuestación de capital son herramientas para analizar posibles erogaciones de capital por parte de una empresa, es necesario para efectos del presente proyecto de investigación, definir sus diferentes modelos desde lo teórico y metodológico, explicando los diferentes conceptos relacionados con el tema. Así mismo, se explican algunos de los indicadores financieros utilizados en las compañías para medir y estimar la “salud financiera” de la empresa, además de puntualizar su impacto en la perdurabilidad de las entidades, lo cual permite dar una visión más general sobre la importancia que trasciende de los indicadores financieros, generando un impacto positivo en la evolución o crecimiento de la organización. En complemento, la investigación aborda la presupuestación de capital de manera particular aplicado en la gestión empresarial, sean estas privadas o públicas (estatal y gubernamental). En este sentido, se abordan conceptos elaborados por diferentes académicos en los que se exponen algunas aproximaciones respecto al posible mejoramiento de la presupuestación para los sectores a los que pertenecen determinadas entidades. Finalmente, se presenta de manera explícita las conclusiones que surgieron a lo largo de la construcción del documento de investigación, con el fin de dar cumplimiento concreto al objetivo general del trabajo, el cual constituye una respuesta a la pregunta de investigación que se enunciará en el desarrollo del documento.

Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.

A neurofuzzy network knowledge extraction and extended gram-Schmidt algorithm for model subspace decomposition

This paper introduces a new neurofuzzy model construction and parameter estimation algorithm from observed finite data sets, based on a Takagi and Sugeno (T-S) inference mechanism and a new extended Gram-Schmidt orthogonal decomposition algorithm, for the modeling of a priori unknown dynamical systems in the form of a set of fuzzy rules. The first contribution of the paper is the introduction of a one to one mapping between a fuzzy rule-base and a model matrix feature subspace using the T-S inference mechanism. This link enables the numerical properties associated with a rule-based matrix subspace, the relationships amongst these matrix subspaces, and the correlation between the output vector and a rule-base matrix subspace, to be investigated and extracted as rule-based knowledge to enhance model transparency. The matrix subspace spanned by a fuzzy rule is initially derived as the input regression matrix multiplied by a weighting matrix that consists of the corresponding fuzzy membership functions over the training data set. Model transparency is explored by the derivation of an equivalence between an A-optimality experimental design criterion of the weighting matrix and the average model output sensitivity to the fuzzy rule, so that rule-bases can be effectively measured by their identifiability via the A-optimality experimental design criterion. The A-optimality experimental design criterion of the weighting matrices of fuzzy rules is used to construct an initial model rule-base. An extended Gram-Schmidt algorithm is then developed to estimate the parameter vector for each rule. This new algorithm decomposes the model rule-bases via an orthogonal subspace decomposition approach, so as to enhance model transparency with the capability of interpreting the derived rule-base energy level. This new approach is computationally simpler than the conventional Gram-Schmidt algorithm for resolving high dimensional regression problems, whereby it is computationally desirable to decompose complex models into a few submodels rather than a single model with large number of input variables and the associated curse of dimensionality problem. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.

Sistema fuzzy para estimativa do bem-estar de matrizes pesadas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Identificação não linear usando uma rede fuzzy wavelet neural network modificada

In last decades, neural networks have been established as a major tool for the identification of nonlinear systems. Among the various types of networks used in identification, one that can be highlighted is the wavelet neural network (WNN). This network combines the characteristics of wavelet multiresolution theory with learning ability and generalization of neural networks usually, providing more accurate models than those ones obtained by traditional networks. An extension of WNN networks is to combine the neuro-fuzzy ANFIS (Adaptive Network Based Fuzzy Inference System) structure with wavelets, leading to generate the Fuzzy Wavelet Neural Network - FWNN structure. This network is very similar to ANFIS networks, with the difference that traditional polynomials present in consequent of this network are replaced by WNN networks. This paper proposes the identification of nonlinear dynamical systems from a network FWNN modified. In the proposed structure, functions only wavelets are used in the consequent. Thus, it is possible to obtain a simplification of the structure, reducing the number of adjustable parameters of the network. To evaluate the performance of network FWNN with this modification, an analysis of network performance is made, verifying advantages, disadvantages and cost effectiveness when compared to other existing FWNN structures in literature. The evaluations are carried out via the identification of two simulated systems traditionally found in the literature and a real nonlinear system, consisting of a nonlinear multi section tank. Finally, the network is used to infer values of temperature and humidity inside of a neonatal incubator. The execution of such analyzes is based on various criteria, like: mean squared error, number of training epochs, number of adjustable parameters, the variation of the mean square error, among others. The results found show the generalization ability of the modified structure, despite the simplification performed

Controle fuzzy espacialmente diferenciado para um sistema de irrigação

Traditional irrigation projects do not locally determine the water availability in the soil. Then, irregular irrigation cycles may occur: some with insufficient amount that leads to water deficit, other with excessive watering that causes lack of oxygen in plants. Due to the nonlinear nature of this problem and the multivariable context of irrigation processes, fuzzy logic is suggested to replace commercial ON-OFF irrigation system with predefined timing. Other limitation of commercial solutions is that irrigation processes either consider the different watering needs throughout plant growth cycles or the climate changes. In order to fulfill location based agricultural needs, it is indicated to monitor environmental data using wireless sensors connected to an intelligent control system. This is more evident in applications as precision agriculture. This work presents the theoretical and experimental development of a fuzzy system to implement a spatially differentiated control of an irrigation system, based on soil moisture measurement with wireless sensor nodes. The control system architecture is modular: a fuzzy supervisor determines the soil moisture set point of each sensor node area (according to the soil-plant set) and another fuzzy system, embedded in the sensor node, does the local control and actuates in the irrigation system. The fuzzy control system was simulated with SIMULINK® programming tool and was experimentally built embedded in mobile device SunSPOTTM operating in ZigBee. Controller models were designed and evaluated in different combinations of input variables and inference rules base

A fuzzy logic system applied in lightning models

This paper describes a novel approach for mapping lightning processes using fuzzy logic. The estimation process is carried out using a fuzzy system based on Sugeno's architecture. Simulation results confirm that proposed approach can be efficiently used in these types of problem.

Segmentação Fuzzy de Texturas e Vídeos

The segmentation of an image aims to subdivide it into constituent regions or objects that have some relevant semantic content. This subdivision can also be applied to videos. However, in these cases, the objects appear in various frames that compose the videos. The task of segmenting an image becomes more complex when they are composed of objects that are defined by textural features, where the color information alone is not a good descriptor of the image. Fuzzy Segmentation is a region-growing segmentation algorithm that uses affinity functions in order to assign to each element in an image a grade of membership for each object (between 0 and 1). This work presents a modification of the Fuzzy Segmentation algorithm, for the purpose of improving the temporal and spatial complexity. The algorithm was adapted to segmenting color videos, treating them as 3D volume. In order to perform segmentation in videos, conventional color model or a hybrid model obtained by a method for choosing the best channels were used. The Fuzzy Segmentation algorithm was also applied to texture segmentation by using adaptive affinity functions defined for each object texture. Two types of affinity functions were used, one defined using the normal (or Gaussian) probability distribution and the other using the Skew Divergence. This latter, a Kullback-Leibler Divergence variation, is a measure of the difference between two probability distributions. Finally, the algorithm was tested in somes videos and also in texture mosaic images composed by images of the Brodatz album

Índice fuzzy de conforto térmico para frangos de corte

A estimativa de conforto térmico na avicultura moderna é importante para que sistemas de climatização possam ser acionados no tempo correto, diminuindo perdas e aumentando rendimentos. Embora a literatura corrente apresente alguns índices de conforto térmico, que são aplicados para essa estimativa, estes são baseados apenas em condições do ambiente térmico e não consideram fatores importantes inerentes aos animais, tais como genética e capacidade de aclimatação, provendo, geralmente, uma estimativa inadequada do conforto térmico das aves. Este trabalho desenvolveu o Índice Fuzzy de Conforto Térmico (IFCT), com o intuito de estimar o conforto térmico de frangos de corte, considerando que o mecanismo usado pelas aves para perda de calor em ambientes fora da zona termoneutra é a vasodilatação periférica, que aumenta a temperatura superficial, e que pode ser usada como indicador do estado de conforto. O IFCT foi desenvolvido a partir de dois experimentos, que proporcionaram 108 cenários ambientais diferentes. Foram usadas imagens termográficas infravermelhas, para o registro dos dados de temperaturas superficiais das penas e da pele, e o grau de empenamento das aves. Para os mesmos cenários de ambiente térmico observados nos experimentos, foram comparados os resultados obtidos usando o IFCT e o Índice de Temperatura e Umidade (ITU). Os resultados validaram o IFCT para a estimativa do conforto térmico de frangos de corte, sendo específico na estimativa de condições de perigo térmico, usual em alojamentos em países de clima tropical. Essa característica é desejável em modelos que estimem o bem-estar térmico de frangos de corte, pois situações classificadas como perigo acarretam no dispêndio de recursos para evitar perdas produtivas.

Relação entre modelos de programação não-linear com incerteza no conjunto de restrições

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Uma abordagem fuzzy para a avaliação técnico-econômica de redes de acesso

O surgimento de novas tecnologias e serviços vem impondo mudanças substanciais ao tradicional sistema de telecomunicações. Múltiplas possibilidades de evolução do sistema fazem da etapa de planejamento um procedimento não só desejável como necessário, principalmente num ambiente de competitividade. A utilização de metodologias abrangentes e flexíveis que possam auxiliar no processo de decisão, fundadas em modelos de otimização, parece um caminho inevitável. Este artigo propõe um modelo de programação linear inteiro misto para ajudar no planejamento estratégico de sistemas de telecomunicações, e em particular da rede de acesso. Os principais componentes de custo e receita são identificados e o modelo é desenvolvido para determinar a configuração da rede (serviços, tecnologias, etc) que maximize a receita esperada pelo operador do sistema. O conceito de números fuzzy é adotado para avaliar o risco técnico-econômico em situações de imprecisão nos dados de demanda. Resultados de experimentos computacionais são apresentados e discutidos.

Mapping lightning processes using fuzzy inference system

This paper describes a novel approach for mapping lightning processes using fuzzy logic. The core regarding lightning process is to identify and to model those uncertain information on mathematical principles. In fact, the lightning process involves several nonlinear features that our current mathematical tools would not be able to model. The estimation process has been carried out using a fuzzy system based on Sugeno's architecture. Simulation results confirm that proposed approach can be efficiently used in these types of problem.

Classificação da curvatura de vertentes em perfil via Thin Plate Spline e Inferência Fuzzy

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)