A água é uma matéria-prima estratégica na indústria química, petroquímica e de alimentos, sendo utilizada em diversas etapas dos processos. Devido à importância econômica e ao impacto ambiental resultante do consumo da água na indústria, o uso racional da água vem sendo amplamente enfatizado. Nas últimas décadas, diversas metodologias foram propostas para a minimização do consumo de água e emissão de efluentes líquidos na indústria, baseadas em conceitos de integração mássica como reuso, reciclo e regeneração das correntes que conectam os processos. As metodologias propostas na literatura para a integração mássica dividem-se em dois grandes grupos: o primeiro utiliza a abordagem termodinâmica-heurística-evolutiva, enquanto que o segundo faz uso da programação matemática e otimização. Ambas as metodologias apresentam dificuldades para tratar do caso de múltiplos poluentes, sendo que na primeira, é necessário uma série de aproximações para tratar deste tipo de problema e na segunda estão presentes limitações relativas aos métodos de otimização. Além disso, sistemas integrados massicamente podem apresentar dificuldades operacionais devido ao maior número de reciclos e reusos de correntes. O presente trabalho através do uso de ferramentas de programação matemática e, baseado no problema padrão de síntese de redes proposto por Fontana (2002), propõe métodos para a redução da complexidade do problema de síntese e obtenção de redes integradas massicamente, considerando aspectos econômicos e operacionais. Inicialmente foi proposta a eliminação de variáveis inteiras do problema de otimização, transformando o problema de programação nãolinear inteira-mista (MINLP) em um problema de programação não-linear (NLP). Em seguida, foi proposta uma metodologia para a redução da complexidade do problema baseada na utilização das restrições de igualdade, reduzindo o número de variáveis de decisão. As formulações propostas apresentaram bons resultados, diminuindo consideravelmente o tempo computacional em relação ao problema MINLP original. Baseada nas metodologias desenvolvidas para redução da complexidade do problema, foi implementado ainda um gerador de estimativas iniciais viáveis utilizando números aleatórios. Também foram propostas três implementações para a síntese de redes com considerações econômicas e operacionais, resolvendo o problema de otimização em dois níveis: um externo para avaliação de critérios econômicos e um interno de onde é obtido o índice operacional. Das três formulações com considerações operacionais propostas, duas apresentaram redes com melhor desempenho operacional quando comparadas com os problemas somente com considerações econômicas. Tais resultados foram avaliados através de simulações dinâmicas com modelos linearizados, sendo observado, nestas duas implementações, aumento da robustez do sistema (redução da ação de controle sobre as variáveis manipuladas) frente a distúrbios positivos nas cargas de poluentes e mudanças nos set-points das variáveis controladas. / Water is an important raw material in the chemical, petrochemical, and food industry, being used in several stages of a process. Based on the economic importance of the water and the environmental impact through its employment in the industry, its rational consume has been receiving special attention. In the past decades, several methodologies have been proposed for the minimization of industrial water consume and wastewater emissions based on concepts of mass integration such as reuse, recycle, and regeneration of process streams. The methodologies proposed in the literature for the mass integration can be classified in two main groups: the first uses the themodynamic-heuristic-evolutive approach while the second uses mathematical programming and optimization. Both methodologies show difficulties to deal with the case of multiple pollutants: on the first one it is necessary to make some assumptions to solve this problem while the second, limitations relative to optimization methods are present. Another problem is the operational limitations due to streams recycle and reuse, that integrated processes can present. The present study, through the use of mathematical programming tools, based on the synthesis problem proposed by Fontana (2002), proposes methods to reduce the problem complexity and also for the synthesis of mass integration networks regarding economical and operational aspects. Initially it was proposed the elimination of the integer variables from the optimization problem, changing the problem from mixed-integer nonlinear programming (MINLP) to nonlinear programming (NLP). In the following, a methodology for the reduction of the problems complexity, based on the equality constraints, was applied to reduce the number of decision variables. The proposed formulations showed good results, reducing the computational time comparing to the MINLP problem. Based on the proposed methodologies for the reduction of the problem complexity described above, it was implemented a feasible initial guess generator based on random numbers. It was also proposed three formulations for the network synthesis with economic and operational considerations, solving the synthesis problem in two levels: an external level for the evaluation of economical criteria and an internal level where the operational index is obtained. Two out of the three implementations presented networks with better operational results comparing with problems only with economical aspects. These results were evaluated by dynamic simulations with linearized models and it was observed an increase in the systems robustness (reduction of the control action over the manipulated variables) when the system was subjected to positive disturbances in the pollutants loads and set-points changes.

Neste trabalho estudamos as noções de alcançabilidade e controlabilidade para sistemas lineares a tempo contínuo com perturbações aditivas e saltos nos parâmetros sujeitos a uma cadeia de Markov geral. Definimos conceitos de alcançabilidade e controlabilidade médios de maneira natural exigindo que os valores esperados dos gramianos correspondentes sejam definidos positivos. Visando obter uma condição testável para ambos os conceitos, introduzimos conjuntos de matrizes de alcançabilidade e de controlabilidade para esta classe de sistemas e usamos certas propriedades de invariância para mostrar que: o sistema é alcançável em média, e, analogamente, controlável em média, se e somente se as matrizes respectivas, de alcançabilidade e de controlabilidade, têm posto completo. Usamos alcançabilidade média de sistemas para mostrar que a matriz de segundo momento do estado é definida positiva com uma margem uniforme. Uma consequência deste resultado no problema de estimação linear do estado é que a matriz de covariância do erro de estimação é positiva definida em média, no sentido que existe um nível mínimo de ruído nas estimativas. Na sequência, para estimadores lineares markovianos, estudamos a limitação do valor esperado da matriz de covariância do erro para mostrar que o filtro é estável num certo sentido, sendo esta uma propriedade desejável em aplicações reais. Quanto às aplicações da controlabilidade média, usamos este conceito para estabelecer condições necessárias e suficientes que garantem a existência de um processo de controle que leva a componente contínua do estado do sistema para a origem em tempo finito e com probabilidade positiva. / In this work we study the reachability and controllability notions for continuous-time linear systems with exogenous inputs and jump parameters driven by a quite general Markov chain. We define a rather natural average reachability and controllability concepts by requiring that the associated gramians are average positive definite, respectively. Aiming at testable conditions for each concept, we introduce certain sets of matrices linked with the gramians, and employ some invariance properties to find rank-based conditions. We show for average reachable systems that the state second moment is positive definite. One consequence of this result in the context of linear estimation for reachable systems is that the expectation of the error covariance matrix is positive definite. Moreover, for linear markovian filters we study the average boundedness of the error covariance matrix to show that the filter is stable in an appropriate sense, which consists in a property that is desirable in real applications. Regarding the average controllability concept, we show that it is a necessary and sufficient condition for the feasibility of the following control problem: find a control process that drives the continuous component of the state to zero in finite time with positive probability.

Le sujet abordé dans cette thèse concerne la contrôlabilité d’une classe de systèmes spatio-temporels, entièrement discrets de type automates cellulaires (AC). Le but de cette étude est de mettre en lumière de nouvelles pistes pour prouver la contrôlabilité des systèmes complexes. Plus spécifiquement, cette thèse se focalise sur la contrôlabilité régionale qui consiste à se restreindre à une région du domaine où le système devra atteindre un objectif donné à travers des actions ciblées. Le cas d’AC Booléens a été particulièrement examiné tout au long de cette thèse. La première partie est consacrée à l’étude du problème de la contrôlabilité régionale des AC déterministes lorsque les actions sont exercées sur la frontière de la régioncontrôlée. Une première démarche que nous avons utilisée s’appuie sur les chaines de Markov et la contrôlabilité est caractérisée en établissant une matrice similaire à leur matrice de transition en utilisant les définitions d’une chaîne ergodique et régulière. Cette étude a été étendue au cas des AC probabilistes qui sont largement utilisés pour modéliser de nombreux phénomènes réels. Le même problème a été appréhendé en utilisant des outils de la théorie des graphes. Nous proposons des conditions nécessaires et suffisantes pour la contrôlabilité régionale des AC déterministes en utilisant les notions de circuit hamiltonien et de composante fortement connexe. Le contrôle qui assure la contrôlabilité régionale est défini à travers un algorithme préimages. La deuxième partie est dédiée au problème de la contrôlabilité régionale frontière des AC Booléens qui consiste à agir sur la frontière du domaine pour atteindre un objectif sur une région cible. Nous considérons d’abord des AC linéaires pour lesquels nousdonnons un résultat de caractérisation grâce à la condition de Kalman. Nous proposons un algorithme pour déterminer le contrôle qui permet de forcer l’apparition d’une configuration désirée dans la région d’étude. Le cas des AC non linéaires a été également considéré en utilisant un algorithme de recherche des préimages. / The issue addressed in this thesis concerns the controllability of a class of discrete spatio-temporal systems named cellular automata (CA). The purpose of this study is to highlight new ways to prove the controllability of complex systems. Morespecifically, this thesis focuses on regional controllability which consists in restricting the study to a subregion of the domain where the system will have to achieve a given objective through targeted actions. The case of Boolean CA have been particularly examined throughout this thesis. The first part is devoted to the study of the problem of the regional controllability of deterministic CAs when the actions are exerted on the boundaries of the controlled region. A first approach that we used relies on Markov chains and controllability is characterized by establishing a matrix similar to their transition matrix using the definitions of a regular and ergodic chain. This study has been extended to the case of probabilistic CAs that are widely used tomodel many real phenomena. The same problem has been apprehended using tools of graph theory. We proposenecessary and sufficient conditions for the regional controllability of deterministic CAs using the notions of Hamiltonian circuit and strongly connected component. The control that ensures regional controllability is defined through a preimage algorithm.The second part is devoted to the problem of the boundary regional controllability of Boolean CAs, which consists of acting on the boundary of the domain in order to reach a desired goal in a target region. We first consider linear CAs for which we givea characterization result using the Kalman condition. We propose an algorithm to determine the control that allows to force the appearance of a desired configuration in the study area. The case of nonlinear CAs was also considered using a preimagesearch algorithm.

Cette thèse est consacrée à trois sujets dans le domaine du contrôle, qui sont la contrôlabilité exacte frontière, la stabilisation frontière et la synchronisation exacte frontière, des systèmes hyperboliques de lois de bilan. Pour la partie sur la contrôlabilité exacte frontière, on améliore le temps de contrôlabilité exacte pour les systèmes hyperboliques de lois de conservation pour des conditions aux limites générales. On montre aussi que ce temps est optimal. En ce qui concerne les systèmes hyperboliques couplés avec une vitesse caractéristique nulle, nous prouvons que l'on n'a pas la contrôlabilité exacte, même avec des couplages internes dans les équations. Cependant, on montre que l'on peut stabiliser les systèmes par les lois de rétroaction à la frontière du domaine. Dans la deuxième partie, nous nous intéressons à la stabilisation frontière des systèmes hyperboliques de lois de bilan. En utilisant une approche "backstepping", on montre comment stabiliser des systèmes d'abord dans les cas linéaires puis dans les cas quasi-lin éaires. La troisième partie concerne la synchronisation exacte frontière. Nous rappelons d'abord les résultats de contrôlabilité et d'observabilité exacte frontière pour les systèmes couplés d' équations des ondes quasi-linéaires. Puis nous introduisons plusieurs types de synchronisations pour un système d' équations des ondes linéaires, puis quasi-linéaires, couplées avec des conditions aux limites de type Dirichlet, de type Neumann, de type Robin et de type dissipatif dans le cadre de solutions de classe C2. Nous montrons que toutes ces synchronisations peuvent être réalisées en imposant peu de contrôles aux frontières. / This thesis is devoted to three topics in the control field, namely, exact boundary controllability, boundary stabilization and exact boundary synchronization, for hyperbolic systems of balance laws. For the exact boundary controllability part, we first improve the boundary control time for hyperbolic systems of conservation laws with general boundary conditions and show that this control time is sharp. Then for a coupled hyperbolic system with zero characteristic speed, we prove that it is impossible to achieve the corresponding exact boundary controllability even with inner couplings in the equation. However, one can stabilize the system in infinite time by means of boundary feedback laws. For the boundary stabilization part, we show how to stabilize both the n×n linear and quasilinear hyperbolic systems by means of one-sided closed-loop boundary controls. For that a backstepping method is developed. For the exact boundary synchronization part, we first recall both the exact boundary controllability and observability results for coupled systems of quasilinear wave equations. Then several kinds of exact synchronizations are introduced for a coupled system of 1-D linear and quasilinear wave equations with boundary conditions of Dirichlet type, Neumann type, coupled third type and coupled dissipative type in the framework of C2 solutions. We show that all these synchronizations can be realized by means of few boundary controls.

Dans cette thèse, nous nous intéressons à la contrôlabilité interne et à son coût pour une ou plusieurs équations aux dérivées partielles conservatives. ?Dans la première partie, nous introduisons et détaillons deux méthodes permettant d'estimer le coût du contrôle (et par dualité, de la constante d'observabilité) de l'équation des ondes avec potentiel $l^{\infty}$ en dimension un d'espace. La première utilise la propagation des ondes le long des caractéristiques en s'appuyant sur le rôle symétrique de la variable de temps et d'espace. La deuxième méthode repose sur la décomposition spectrale de l'équation des ondes et sur l'utilisation des inégalités d'ingham. L'estimation de la constante d'observabilité se ramène alors à l'étude d'un problème d'optimisation faisant intervenir les vecteurs propres du laplacien-dirichlet avec potentiel. Nous fournissons ensuite des propriétés qualitatives sur le minimiseurs ainsi qu'une estimation du minimum ne dépendant que de la mesure de l'ensemble d'observation. ?Dans la deuxième partie, nous étudions la contrôlabilité de certains systèmes d'équations avec un nombre de contrôles réduits, autrement dit le nombre de contrôles est plus petit que le nombre d'équations. En particulier, nous caractérisons exactement les données initiales qui peuvent être contrôlées pour des systèmes d'équations couplées de type schrödinger et nous énonçons une condition nécessaire et suffisante de type kalman pour des systèmes d'équations des ondes couplées. La preuve repose sur une méthode de contrôle fictif combinée à la résolution algébrique d'un système sous-déterminé et sur certains résultats de régularité. / In this work, we focus on the internal controllability and its cost for some linear partial differential equations. In the first part, we introduce and describe two methods to provide precise estimates of the cost of control (and by duality, of the observability constant) for general one dimensional wave equations with potential. The first one is based on a propagation argument along the characteristics relying on the symmetrical roles of the time and space variables. The second one uses a spectral decomposition of the solution of the wave equation and ingham's inequalities. This relates the estimation of the observability constant to the study of an optimal problem involving dirichlet eigenfunctions of laplacian with potential. We provide some qualitative properties of the minimizers, and also precise bounds on the minimum. In the second part, we are concerned with the controllability of some systems of equations by a reduced number of controls (i.e. the number of controls is less that the number of equations). In particular, in the case of coupled systems of schrödinger equations, we exactly characterize the initial conditions that can be controlled and we give a necessary and sufficient condition of kalman type for the controllability of coupled systems of wave equations. The proof relies on the fictitious control method coupled with the proof of an algebraic solvabilityproperty for some related underdetermined system, as well as on some regularity results.

Cette thèse est consacrée la contrôlabilité lagrangienne, l'étude du champ de vitesse de l'Équation de Korteweg-de Vries, le problème de stabilisation rapide d'une équation aux dérivées partielles linéaires et aux méthodes numériques permettant d'obtenir la convergence des contrôles numériques vers les contrôles optimaux. Dans la première partie, on montre, l'aide de la solution de N-solitons de l'équation de Korteweg-de Vries, qu'il est possible de faire sortir des particules du fluide l’extérieur d'un domaine déterminé en temps arbitrairement petit. Une meilleure approximation du champ de vitesse associée la solution de N-solitons est également présentée, permettant de retrouver en particulier une propriété typique des trajectoires des particules soumises des ondes solitaires : les particules situées plus haut dans le fluide ont un plus grand déplacement. Dans la deuxième partie, la stabilisation rapide d'une équation de Schrödinger est obtenue grâce une méthode inspirée du backstepping en dimension infinie. Une équation de Schrödinger stable est considérée comme l'image d'une transformation ayant comme domaine de définition les solutions de l'équation de Schrödinger stabilisé. La stabilisation de l'équation de Schrödinger est obtenue en montrant l'inversibilité de la transformation. La nouveauté du travail présentée est l'introduction d'une condition d’unicité sur la transformation. Finalement, un filtre spectral, une formulation mixte et une formulation de Nitsche sont proposées comme technique afin d'obtenir numériquement l’observabilité uniforme de l'équation des ondes semi-discrétisée avec une méthode spectrale de Legendre-Galerkin. Une étude numérique de la convergence des contrôles numériques sans l’admissibilité uniforme de l’opérateur de contrôle est également présentée. / This thesis is devoted to the Lagrangian controllability and the analysis of the particle trajectories for the Korteweg-de Vries equation, to the rapid stabilization problem of the bilinear Schrödinger equation and to the convergence of the numerical controls of the wave equation. In the first part, we prove that the N-solitons solution of the Korteweg-de Vries equation allows one to move the particles outside an arbitrarily long domain in an arbitrarily small time. A higher approximation of the velocity field associated to the N-soliton is also presented, allowing to recover a typical property of solitary waves: the higher the particle is located in the fluid, the greater its displacement. These results are of a nonlinear nature since there exists no linear approximation of solitons. In the second part, inspired by the backstepping method, the rapid stabilization of a linearized Schrödinger equation is obtained. The proof consists to prove the invertibility of a transformation mapping the equation to stabilize to a stable linearized Schrödinger equation. The key ingredient of this proof is the introduction of a uniqueness condition. In the last part, a spectral filter, a mixed method and the Nitsche's method are proposed as a remedy to the lack of uniformness of the discrete observability constant for the Legendre-Galerkin semi-discretization of the wave equation. A numerical study of the convergence of the numerical controls is also presented.

The master’s thesis is dealt with the design of rebuilding of VUT 051 RAY which is equipped electric powerplant to twin-engine conception named VUT 051 RAY-DUO. In the thesis was verified the range of centre of gravity position of VUT 051 RAY-DUO then powerplant in ducted fan configuration was designed, performances of the airplane were appointed and controllability during fail one of the engines was analysed. The design of new powerplant was verified by strength analysis and then costing calculation was established.

In this thesis the issue with the description, modeling and analysis of hybrid dynamic systems is solved. The main goal is to select appropriate method for solving hybrid dynamic systems and to aim to question on solving controllability, observability and stability of these systems. Two types of hybrid systems are covered in this work. In the first part, the description and simulation of hybrid systems that are compiled of continous and discrete parts with the systems of discrete affair are specified. For the description and modeling of hybrid automata and hybrid Petri nets have been used. The possibilities mentioned above are showned on the simple examples. Second part of this work covers the description, modeling and analysis of hybrid systems that are compiled of links continous and discreate dynamic system. The state space has been used. The universal state equations are mentioned and have been used for the description of the hybrid system and the structure of the matrixes A, B, C, D. The relation and basic method are spin off for the analysis of hybrid dynamic systems. From the analysis point of view, these are general methods for the controllability, observability, stability and steady state of hybrid dynamic systems. The examples of hybrid control systems for mentioned methods are specified. If it is allowed, the results are verified by the simulation in MATLAB Simulink background.

This diploma thesis deals with a stability and manoeuvrability of experimental aircraft VUT 001 MARABU. It contains calculation of aerodynamic stability derivations and other data necessary for evaluation of static and dynamic stability. Assessment of convenient autopilot.

Dans cette thèse, nous étudions la stabilisation et la contrôlabilité exacte de certains problèmes distribués avec différents types d’amortissement. Dans la première partie, nous étudions la stabilité d'un système Bresse mono-dimensionnel avec un contrôle de type mémoire infini et/ou avec une conduction de chaleur donnée par la loi de Cattaneo agissant sur le déplacement de l'angle de cisaillement. Nous considérons le cas intéressant de conditions aux bords de types entièrement Dirichlet. En effet, sous la condition d'égalité de la vitesse de propagation des ondes, nous établissons la stabilité exponentielle du système. Cependant, dans le cas physique naturel lorsque les vitesses de propagation sont différentes, en utilisant une méthode de décomposition de spectre, nous montrons que le système de Bresse n'est pas uniformément stable. Dans ce cas, nous établissons un taux de décroissance énergétique polynomiale. Notre étude est valable pour toutes les autres conditions aux bords mixtes. Dans la deuxième partie, nous étudions la stabilisation d'un système élastique faiblement amorti d’un système couplé abstrait du second ordre. Dans le cadre de certains paramètres, en utilisant la méthode spectrale, nous établissons la stabilité exponentielle du système. Cependant, lorsque le système n'est pas uniformément stable, nous établissons le taux optimal de la décroissance polynomiale de l'énergie du système. Dans la troisième partie, nous étudions la contrôlabilité exacte indirecte d'un système de Timoshenko mono-dimensionnel. En effet, nous considérons les cas lorsque la vitesse de propagation des ondes sont égales ou différentes. Tout d'abord, nous utilisons des analyses non harmoniques pour établir une inégalité d'observabilité faible, qui dépend du rapport des vitesses de propagation des ondes. Ensuite, en utilisant la méthode HUM, nous prouvons que le Système est parfaitement contrôlable et que le temps de contrôle peut être faible. / In this work, we study the stabilization and the exact controllability of some distributed problems. In the first part, we study the stability of a one-dimensional Bresse System with infinite memory type control and/or with heat conduction given by Cattaneo's law acting in the shear angle displacement, where we consider the interesting case of fully Dirichlet boundary conditions. Indeed, under a equal speed of propagation condition, we establish the exponential stability of the System. However, in the natural physical case when the speeds of propagation are different, using a spectrum method, we show that the Bresse System is not uniformly exponentially stable. In this case, we establish a polynomial energy decay rate. Our study is valid for all other mixed boundary conditions. In the second part, we study the stabilization of a weakly damped elastic System of an abstract second order equation. Indeed, under some condition on the parameters, using a spectrum method, we establish the exponential stability of the System. However, when the System is not uniformly stable, using a spectrum method, we establish the optimal polynomial decay rate of the energy of the System. In the third part, we study the indirect boundary exact controllability of a one-dimensional Timoshenko System. Indeed, we consider the cases when the speed waves propagate with equal or different speeds. We use non harmonic analysis to establish weak observability inequality, which depends on the ratio of the waves propagation speeds. Next, using the HUM method, we prove that the System is exactly controllable, and that the control time can be small.