Submitted by Gustavo Chaves Tanaka (gustavotanakachaves@gmail.com) on 2018-08-15T14:18:30Z No. of bitstreams: 1 Tanaka, G. C. - Dissertaação Mestrado_2018.pdf: 1815626 bytes, checksum: a2a89dc96cd728c12e9a3fbac8c5aa62 (MD5) / Approved for entry into archive by Minervina Teixeira Lopes null (vina_lopes@bauru.unesp.br) on 2018-08-15T16:21:19Z (GMT) No. of bitstreams: 1 tanaka_gc_me_bauru.pdf: 1773178 bytes, checksum: b9e8d25c3e3fd8f7e43072082a01b175 (MD5) / Made available in DSpace on 2018-08-15T16:21:19Z (GMT). No. of bitstreams: 1 tanaka_gc_me_bauru.pdf: 1773178 bytes, checksum: b9e8d25c3e3fd8f7e43072082a01b175 (MD5) Previous issue date: 2018-06-07 / Atualmente pesquisas sobre a produção de energia com menor impacto ambiental, com maior rendimento energético e, possivelmente, a um custo mínimo de produção, são de interesse mundial. Desta forma, a produção de energia renovável, com estas características, através de biodigestores torna-se uma alternativa relevante. Os biodigestores, em geral, consistem de biorreator que armazena matéria orgânica fresca (substrato ou biomassa) de origem humana, animal ou vegetal. A fermentação anaeróbica destes substratos produz um gás combustível (biogás) que pode ser utilizado como fonte de energia e o material remanescente no biodigestor pode ser usado como biofertilizante. O processo de biodigestão é complexo, pois envolve vários grupos de bactérias e o seu entendimento é importante para promoção de agentes que visam aumentar a eficiência dos biodigestores. Neste trabalho propõe-se um modelo dinâmico não linear para descrever o processo de fermentação da biomassa dentro do biodigestor. Realiza-se também uma análise do modelo mediante a técnica de Lyapunov, a qual possibilitou a investigação de soluções analíticas assintoticamente estáveis e um estudo de seu espaço de fase, que contempla a sua estabilidade assintótica. Simulações numéricas são realizadas para a validação dos resultados obtidos ao modelo proposto. / Nowadays, research on energy production with lower environmental impact, with higher energy efficiency and, possibly, at a minimum cost of production, is of worldwide interest. In this way, the production of renewable energy, with these characteristics, through biodigesters becomes a relevant alternative. Biodigesters generally consist of a chamber that stores fresh organic matter (substrate or biomass) of human, animal or plant origin. Anaerobic fermentation of these substrates produces a fuel gas (biogas) that can be used as an energy source and the remaining material in the biodigester can be used as biofertilizer. The biodigestion process is complex because it involves several groups of bacteria and its understanding is important to promote agents that aim to increase the efficiency of biodigesters. This essay proposes a dynamic non-linear model to describe the fermentation process of an Indian biodigester. It is also proposed an analysis of the model using the Lyapunov technique, which became possible the investigation of asymptotically stable analytical solutions and asymptotic stability and a study of its phase space, which contemplates its asymptotic stability. Numerical simulations are performed to convalidate the proposed model.

abstract: In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems - in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) - whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers - machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers. We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors, and analyze systems with 100+ dimensional state-space. Furthermore, we extend our algorithms to analyze robust stability over more complicated geometries such as hypercubes and arbitrary convex polytopes. Our algorithms can be readily extended to address a wide variety of problems in control such as Hinfinity synthesis for systems with parametric uncertainty and computing control Lyapunov functions. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2016

Orientadores: João Marcos Travassos Romano, Romis Ribeiro de Faissol Attux / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-19T00:40:42Z (GMT). No. of bitstreams: 1 SousaJunior_Celsode_D.pdf: 2582555 bytes, checksum: 4c20b08e97e42d51ea143f7651c91af4 (MD5) Previous issue date: 2011 / Resumo: O problema de equalização adaptativa se vincula à busca por soluções iterativas que permitam reduzir ou eliminar os efeitos nocivos do canal de comunicação sobre um sinal transmitido de interesse. Uma vez que os sistemas adaptativos se baseiam em algoritmos capazes de ajustar os parâmetros de um filtro, pode-se considerar o conjunto equalizador / algoritmo adaptativo como um sistema dinâmico, o que termina por relacionar a possibilidade de obter uma solução satisfatória à noção de convergência. A análise de convergência de algoritmos de equalização adaptativa se desenvolveu, tipicamente, considerando algumas hipóteses para viabilizar o tratamento matemático, mas nem sempre tais hipóteses são estritamente válidas. Um exemplo clássico nesse sentido é o uso da teoria da independência. Neste trabalho, buscamos uma abordagem distinta do estudo das condições de estabilidade de algoritmos de equalização clássica baseada na teoria de Lyapunov. Essa teoria é geralmente utilizada no estudo de sistemas não-lineares, e apresenta um amplo histórico de resultados sólidos na área de controle adaptativo. Isso motiva o uso no campo de processamento de sinais. A primeira contribuição deste trabalho consiste em determinar, por meio da teoria de Lyapunov, a faixa de valores de passo de adaptação que garantem estabilidade do sistema de equalização para algoritmos baseados no critério deWiener e para o algoritmo do módulo constante. A partir dos resultados para estabilidade, investigar-se-á também a região de convergência para os pesos do algoritmo LMS, o que trará uma produtiva relação com a idéia de misadjustment. Como segunda linha de contribuição, será apresentada uma análise de um limitante inferior para o custo atingível e uma proposta de inicialização capaz de aumentar a probabilidade de convergência para o melhor ótimo gerado pelo critério para o algoritmo do módulo constante. Essa estratégia se baseia numa formulação do critério não-supervisionado de filtragem linear em termos da aplicação do critério de Wiener a uma estrutura polinomial. Os resultados obtidos revelam que a idéia é capaz de levar a um desempenho melhor que os do clássico método center spike e de uma estratégia de inicialização aleatória / Abstract: The problem of adaptive equalization is related to the search for iterative solutions that allow the reduction or the elimination of the noxious effects of a communication channel on a transmitted signal of interest. Since adaptive systems are based on algorithms capable of adjusting the parameters of a filter, the combination between equalizer and learning algorithm can be considered to form a dynamical system, which relates the possibility of obtaining a satisfactory solution to the convergence issue. The analysis of the convergence of adaptive equalization algorithms was developed, typically, considering certain simplifying hypotheses that, however, are not always strictly valid. A classical example that illustrates this assertion is the use of the so-called independence theory. In this work, it has been investigated a distinct approach to the study of stability conditions of classical methods based on Lyapunov theory. This theory is generally employed in the study of nonlinear systems, and presents a significant framework of sound results in the field of adaptive control, which motivates its use in the context of signal processing. The first contribution of this work consists of determining, by means of Lyapunov theory, the range of step-size values that ensure stability of the equalization system for algorithms based on the Wiener criterion and for the constant modulus algorithm. Using the obtained stability results, the convergence region for the parameters estimated via LMS is also investigated, which establishes an interesting connection with the notion of misadjustment. In a second line of study, we present an analysis of the lower bound for the attainable CM cost and an initialization heuristic capable of increasing the probability of convergence to the best optimum engendered by the constant modulus criterion. This strategy is based on a formulation of the unsupervised linear filtering criterion in terms of the application of the Wiener criterion to a polynomial structure. The obtained results reveal that the proposal is able to effectively lead to a performance level that is better than that achieved using the classical center spike method and a random approach / Doutorado / Telecomunicações e Telemática / Doutor em Engenharia Elétrica

Cette thèse porte sur la modélisation et l’analyse de stabilité de certains mécanismes biologiques complexes en rapport avec le cancer. Un intérêt particulier est porté au cas de l’hématopoïèse et de la leucémie aiguë myéloblastique (LAM). Les modèles utilisés et/ou introduits dans cette thèse se décrivent par des équations aux dérivées partielles structurées en âge, qui se réduisent à des systèmes à retards de plusieurs types (retards ponctuels ou distribués, à support fini ou infini). Ces modèles à retards sont parfois couplés à des équations aux différences, et possiblement avec des paramètres variant dans le temps. Un des principaux challenges dans ce travail consiste à développer des méthodes temporelles, qui se basent sur la construction de fonctionnelles de Lyapunov-Krasovskii strictes, pour les systèmes non-linéaires à retards étudiés. Les principales notions abordées dans ces travaux incluent : l’analyse de stabilité/stabilisation et de robustesse, l’emploi de techniques de modélisation des populations cellulaires saines et malades, l’étude de différentes classes de systèmes dynamiques, (possiblement à temps variant ou à commutation), et également l’introduction de quelques outils issus de l’intelligence artificielle (planification et recherche de solution) dans un contexte de modèles biologiques. Ainsi, les méthodes de modélisation et d’analyse employées dans ce travail ont permis d’une part d’étendre les résultats de stabilité de cette classe de systèmes biologiques, et d’autre part de mieux comprendre certains mécanismes biologiques liés au cancer et sa thérapie. Plus précisément, certains concepts récemment établis en biologie et en médecine sont mis en évidence dans ce travail pour la première fois dans cette classe de systèmes, telles que : la dédifférenciation des cellules (plasticité), ou encore la dormance des cellules cancéreuses dans des modèles tenant compte de la cohabitation entre cellules saines et mutées. Les résultats obtenus sont interprétés dans le cas de l’hématopoïèse et de la LAM, mais ce travail s’applique également à d’autres types de tissus où le cycle cellulaire se produit de façon similaire. / Medical research is looking for new combined targeted therapies against cancer. Our research project -which involves intensive collaboration with hematologists from Saint-Antoine Hospital in Paris- is imbued within a similar spirit and fits the expectations of a better understanding of the behavior of blood cell dynamics. In fact, hematopoiesis provides a paradigm for studying all the mammalian stem cells, as well as all the mechanisms involved in the cell cycle. We address multiple issues related to the modeling and analysis of the cell cycle, with particular insights into the hematopoietic systems. Stability features of the models are highlighted, since systems trajectories reflect the most prominent healthy or unhealthy behaviors of the biological process under study. We indeed perform stability analysis of systems describing healthy and unhealthy situations, with a particular interest in the case of acute myeloblastic leukemia (AML). Thus, we pursue the objectives of understanding the interactions between the various parameters and functions involved in the mechanisms of interest. For that purpose, an advanced stability analysis of the cell fate evolution in treated or untreated leukemia is performed in several modeling frameworks, and our study suggests new anti-leukemic combined chemotherapy. Throughout the thesis, we cover many biological evidences that are currently undergoing intensive biological research, such as: cell plasticity, mutations accumulation, cohabitation between ordinary and mutated cells, control or eradication of cancer cells, cancer dormancy, etc.Among the contributions of Part I of the thesis, we can mention the extension of both modeling and analysis aspects in order to take into account a proliferating phase in which most of the cells may divide, or die, while few of them may be arrested during their cycle for unlimited time. We also introduce for the first time cell-plasticity features to the class of systems that we are focusing on.Next, in Part II, stability analyses of some differential-difference cell population models are performed through several time-domain techniques, including tools of Comparative and Positive Systems approaches. Then, a new age-structured model describing the coexistence between cancer and ordinary stem cells is introduced. This model is transformed into a nonlinear time-delay system that describes the dynamics of healthy cells, coupled to a nonlinear differential-difference system governing the dynamics of unhealthy cells. The main features of the coupled system are highlighted and an advanced stability analysis of several coexisting steady states is performed through a Lyapunov-like approach for descriptor-type systems. We pursue an analysis that provides a theoretical treatment framework following different medical orientations, among which: i) the case where therapy aims to eradicate cancer cells while preserving healthy ones, and ii) a less demanding, more realistic, scenario that consists in maintaining healthy and unhealthy cells in a controlled stable dormancy steady-state. Mainly, sufficient conditions for the regional exponential stability, estimate of the decay rate of the solutions, and subsets of the basins of attraction of the steady states of interest are provided. Biological interpretations and therapeutic strategies in light of emerging AML-drugs are discussed according to our findings.Finally, in Part III, an original formulation of what can be interpreted as a stabilization issue of population cell dynamics through artificial intelligence planning tools is provided. In that framework, an optimal solution is discovered via planning and scheduling algorithms. For unhealthy hematopoiesis, we address the treatment issue through multiple drug infusions. In that case, we determine the best therapeutic strategy that restores normal blood count as in an ordinary hematopoietic system.

The contributions of this thesis lie in the area of global finite-time observer design for a class of nonlinear systems with bounded rational and mixed rational powers imposed on the incremental rate of the nonlinear terms whose solutions exist and are unique for all positive time. In the thesis, two different kinds of nonlinear global finite-time observers are designed by employing of finite-time theory and homogeneity properties with different methods. The global finite-time stability of both proposed observers is derived on the basis of Lyapunov theory. For a class of nonlinear systems with rational and mixed rational powers imposed on the nonlinearities, the first global finite-time observers are designed, where the global finite-time stability of the observation systems is achieved from two parts by combining asymptotic stability and local finitetime stability. The proposed observers can only be designed for the class of nonlinear systems with dimensions greater than 3. The observers have a dynamic high gain and two homogenous terms, one homogeneous of degree greater than 1 and the other of degree less than 1. In order to prove the global finite-time stability of the proposed results, two homogeneous Lyapunov functions are provided, corresponding with the two homogeneous items. One is homogeneous of degree greater than 1, which makes the observation error systems converging into a spherical area around the origin, and the other is of degree less than 1, which ensures local finite-time stability. The second global finite-time observers are also proposed based on the high-gain technique, which does not place any limitation on the dimension of the nonlinear systems. Compared with the first global finite-time observers, the newly designed observers have only one homogeneous term and a new gain update law where two new terms are introduced to dominate some terms in the nonlinearities and ensure global finite-time stability as well. The global finite-time stability is obtained directly based on a sufficient condition of finite-time stability and only one Lyapunov function is employed in the proof. The validity of the two kinds of global finite-time observers that have been designed is illustrated through some simulation results. Both of them can make the observation error systems converge to the origin in finite-time. The parameters, initial conditions as well as the high gain do have some impact on the convergence time, where the high gain plays a stronger role. The bigger the high gain is, the shorter the time it needs to converge. In order to show the performance of the two kinds of observers more clearly, two examples are provided and some comparisons are made between them. Through these, it can be seen that under the same parameters and initial conditions, although the amplitude of the observation error curve is slightly greater, the global finite-time observers with a new gain update law can make the observation error systems converge much more quickly than the global finite-time observers with two homogeneous terms. In the simulation results, one can see that, as a common drawback of high gain observers, they are noise-sensitive. Finding methods to improve their robustness and adaptiveness will be quite interesting, useful and challenging. / Thesis (PhD)--University of Pretoria, 2013. / gm2014 / Electrical, Electronic and Computer Engineering / unrestricted

Les multiples applications liées aux systèmes multi-agents en réseau, tels que les satellites en formation, les oscillateurs couplés, les véhicules aériens sans pilote, entre autres, ont été, sans aucun doute, une motivation majeure dans le développement de cette thèse, qui est consacrée à l’étude du consensus de systèmes dynamiques et à la commande en formation de robots mobiles non holonomes. Dans le contexte du consensus, nous étudions la topologie en anneau avec de liens de communication variant dans le temps. Notamment, la communication peut être perdue pendant de longs intervalles de temps. Nous donnons de conditions suffisantes pour le consensus qui restent simples à vérifier, par exemple, en utilisant le théorème du petite gain. En suite, nous abordons le problème de consensus en supposant que la topologie de communication est variable. Nous établissons que le consensus est atteint à condition qu’il existe toujours un chemin de communication du type « spanning-tree » pendant un temps de séjour minimal. L'analyse s'appuie sur la théorie de stabilité des systèmes variant dans le temps et les systèmes à commutation. Dans le contexte de la commande en formation de véhicules autonomes nous adressons le problème de commande en suivi de trajectoire sur ligne droite en suivant une approche type maître-esclave. Nous montrons que le suivi global peut être obtenu à partir d’un contrôleur qui possède la propriété d’excitation persistante. En gros, le mécanisme de stabilisation dépend de l’excitation du système par une quantité qui est proportionnelle à l’erreur de suivi. Ensuite, la méthode est utilisée pour résoudre le problème de suivi de formation de plusieurs véhicules interconnectés sur la base d’une topologie « spanning-tree ». Nous donnons des conditions de stabilité concernant les modèles cinématique et dynamique, en utilisant la seconde méthode de Lyapunov. / The multiple applications related to networked multi-agent systems such as satellite formation flying, coupled oscillators, air traffic control, unmanned air vehicles, cooperative transport, among others, has been undoubtedly a watershed for the development of this thesis. The study of cooperative control of multi-agent systems is of great interest for his extensive field work and applications. This thesis is devoted to the study of consensus seeking of multi-agents systems and trajectory tracking of nonholonomic mobile robots.In the context of consensus seeking, first we study a ring topology of dynamic agents with time-dependent communication links which may disconnect for long intervals of time. Simple checkable conditions are obtained by using small-gain theorem to guarantee the achievement of consensus. Then, we deal with a network of dynamic agents with time-dependent communication links interconnected over a time-varying topology. We establish that consensus is reached provided that there always exists a « spanning-tree » for a minimal dwell-time by using stability theory of time-varying and switched systems. In the context of trajectory tracking, we investigate a simple leader-follower tracking controller for autonomous vehicles following straight lines. We show that global tracking may be achieved by a controller which has a property of persistency of excitation tailored for nonlinear systems. Roughly speaking the stabilisation mechanism relies on exciting the system by an amount that is proportional to the tracking error. Moreover, the method is used to solve the problem of formation tracking of multiple vehicles interconnected on the basis of a « spanning-tree » topology. We derive stability conditions for the kinematic and dynamic model by using a Lyapunov approach.

L’objectif principal de cette thèse est d’étudier le problème du contrôle de suivi distribué pour les systèmes de formation de multi-robots à contrainte non holonomique. Ce contrôle vise à entrainer une équipe de robots mobile de type monocycle pour former une configuration de formation désirée avec son centroïde se déplaçant avec une autre trajectoire de référence dynamique et pouvant être spécifié par le leader virtuel ou humain. Le problème du contrôle de suivi a été résolu au cours de cette thèse en développant divers contrôleurs distribués pratiques avec la considération d’un taux de convergence plus rapide, une précision de contrôle plus élevée, une robustesse plus forte, une estimation du temps de convergence explicite et indépendante et moins de coût de communication et de consommation d’énergie. Dans la première partie de la thèse nous étudions d’abord au niveau du chapitre 2 la stabilité à temps fini pour les systèmes de formation de multi-robots. Une nouvelle classe de contrôleur à temps fini est proposée dans le chapitre 3, également appelé contrôleur à temps fixe. Nous étudions les systèmes dynamiques de suivi de formation de multi-robots non holonomiques dans le chapitre 4. Dans la deuxième partie, nous étudions d'abord le mécanisme de communication et de contrôle déclenché par l'événement sur les systèmes de suivi de la formation de multi-robots non-holonomes au chapitre 5. De plus, afin de développer un schéma d'implémentation numérique, nous proposons une autre classe de contrôleurs périodiques déclenchés par un événement basé sur un observateur à temps fixe dans le chapitre 6. / The main aim of this thesis is to study the distributed tracking control problem for the multi-robot formation systems with nonholonomic constraint, of which the control objective it to drive a team of unicycle-type mobile robots to form one desired formation configuration with its centroid moving along with another dynamic reference trajectory, which can be specified by the virtual leader or human. We consider several problems in this point, ranging from finite-time stability andfixed-time stability, event-triggered communication and control mechanism, kinematics and dynamics, continuous-time systems and hybrid systems. The tracking control problem has been solved in this thesis via developing diverse practical distributed controller with the consideration of faster convergence rate, higher control accuracy, stronger robustness, explicit and independent convergence time estimate, less communication cost and energy consumption.In the first part of the thesis, we first study the finite-time stability for the multi-robot formation systems in Chapter 2. To improve the pior results, a novel class of finite-time controller is further proposed in Chapter 3, which is also called fixed-time controller. The dynamics of nonholonomic multi-robot formation systems is considered in Chapter 4. In the second part, we first investigate the event-triggered communication and control mechanism on the nonholonomic multi-robot formation tracking systems in Chapter 5. Moreover, in order to develop a digital implement scheme, we propose another class of periodic event-triggered controller based on fixed-time observer in Chapter 6.