Cette thèse s’intéresse au calcul de solutions globales de problèmes de commande optimaleen boucle ouverte. La méthodologie générale se base sur l’approche par les moments, oùun problème d’optimisation est relâché en un problème généralisé des moments, dont unehiérarchie de relaxations semi-définies peut être résolue numériquement. L’approche esttout d’abord appliquée aux problèmes impulsionnels linéaires à temps variant, en modélisantle contrôle par une mesure. Les conditions semi-définies qui en résultent permettentde s’affranchir complètement des difficultés liées à la discrétisation temporelle. Ensuite, ense basant sur le formalisme des mesures d’occupations, la méthode peut être étendue auxsystèmes impulsionnels non-linéaires, et fournit une suite monotone de bornes inférieuresau coût optimal. Enfin, les résultats précédents peuvent être transposés aux systèmes àcommutation, en modélisant chaque mode par une mesure d’occupation associée. Ceci permetd’obtenir des gains substantiels en charge de calcul par rapport à l’approche classiqueoù l’espace de contrôle est mesuré / This thesis details a global method for optimal control of open-loop systems. This is doneby relaxing the control problem as a generalized moment problem, which can be solvednumerically by a hierarchy of semi-definite relaxations. The approach is first applied tothe impulsive control of linear time varying systems, by modeling the controls by a measure.The resulting semi-definite conditions circumvent time discretiziation and relateddifficulties. By the use of occupation measures, the method is then extended to a classof impulsive non-linear problems. This results in a monotone sequence of lower boundsto the original control problem. Finally, those results are transposed to switched system,by modeling each mode by a corresponding occupation measure. This allows for largecomputational gains with respect to the classical approach, where the control space ismeasured

The main result of this thesis is the development of a theory of semidefinite facial reduction for the Euclidean distance matrix completion problem. Our key result shows a close connection between cliques in the graph of the partial Euclidean distance matrix and faces of the semidefinite cone containing the feasible set of the semidefinite relaxation. We show how using semidefinite facial reduction allows us to dramatically reduce the number of variables and constraints required to represent the semidefinite feasible set. We have used this theory to develop a highly efficient algorithm capable of solving many very large Euclidean distance matrix completion problems exactly, without the need for a semidefinite optimization solver. For problems with a low level of noise, our SNLSDPclique algorithm outperforms existing algorithms in terms of both CPU time and accuracy. Using only a laptop, problems of size up to 40,000 nodes can be solved in under a minute and problems with 100,000 nodes require only a few minutes to solve.

The main result of this thesis is the development of a theory of semidefinite facial reduction for the Euclidean distance matrix completion problem. Our key result shows a close connection between cliques in the graph of the partial Euclidean distance matrix and faces of the semidefinite cone containing the feasible set of the semidefinite relaxation. We show how using semidefinite facial reduction allows us to dramatically reduce the number of variables and constraints required to represent the semidefinite feasible set. We have used this theory to develop a highly efficient algorithm capable of solving many very large Euclidean distance matrix completion problems exactly, without the need for a semidefinite optimization solver. For problems with a low level of noise, our SNLSDPclique algorithm outperforms existing algorithms in terms of both CPU time and accuracy. Using only a laptop, problems of size up to 40,000 nodes can be solved in under a minute and problems with 100,000 nodes require only a few minutes to solve.

In this thesis, we develop tractable relaxations and efficient algorithms for large-scale optimization. Our developments are motivated by a recent paradigm, Compressed Sensing (CS), which consists of acquiring directly low-dimensional linear projections of signals, possibly corrupted with noise, and then using sophisticated recovery procedures for signal reconstruction. We start by analyzing how to utilize a priori information given in the form of sign restrictions on part of the entries. We propose necessary and sufficient on the sensing matrix for exact recovery of sparse signals, utilize them in deriving error bounds under imperfect conditions, suggest verifiable sufficient conditions and establish their limits of performance. In the second part of this thesis, we study the CS synthesis problem -selecting the minimum number of rows from a given matrix, so that the resulting submatrix possesses certifiably good recovery properties. We express the synthesis problem as the problem of approximating a given matrix by a matrix of specified low rank in the uniform norm and develop a randomized algorithm for this problem. The third part is dedicated to efficient First-Order Methods (FOMs) for large-scale, well-structured convex optimization problems. We propose FOMs with stochastic oracles that come with exact guarantees on solution quality, achieve sublinear time behavior, and through extensive simulations, show considerable improvement over the state-of-the-art deterministic FOMs. In the last part, we examine a general sparse estimation problem -estimating a block sparse linear transform of a signal from the undersampled observations of the signal corrupted with nuisance and stochastic noise. We show that an extension of the earlier results to this more general framework is possible. In particular, we suggest estimators that have efficiently verifiable guaranties of performance and provide connections to well-known results in CS theory.

abstract: This work presents research on practices in the day-ahead electric energy market, including replication practices and reliability coordinators used by some market operators to demonstrate the impact these practices have on market outcomes. The practice of constraint relaxations similar to those an Independent System Operator (ISO) might perform in day-ahead market models is implemented. The benefits of these practices are well understood by the industry; however, the implications these practices have on market outcomes and system security have not been thoroughly investigated. By solving a day-ahead market model with and without select constraint relaxations and comparing the resulting market outcomes and possible effects on system security, the effect of these constraint relaxation practices is demonstrated. Proposed market solutions are often infeasible because constraint relaxation practices and approximations that are incorporated into market models. Therefore, the dispatch solution must be corrected to ensure its feasibility. The practice of correcting the proposed dispatch solution after the market is solved is known as out-of-market corrections (OMCs), defined as any action an operator takes that modifies a proposed day-ahead dispatch solution to ensure operating and reliability requirements. The way in which OMCs affect market outcomes is illustrated through the use of different corrective procedures. The objective of the work presented is to demonstrate the implications of these industry practices and assess the impact these practices have on market outcomes. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2016

abstract: Constraint relaxation by definition means that certain security, operational, or financial constraints are allowed to be violated in the energy market model for a predetermined penalty price. System operators utilize this mechanism in an effort to impose a price-cap on shadow prices throughout the market. In addition, constraint relaxations can serve as corrective approximations that help in reducing the occurrence of infeasible or extreme solutions in the day-ahead markets. This work aims to capture the impact constraint relaxations have on system operational security. Moreover, this analysis also provides a better understanding of the correlation between DC market models and AC real-time systems and analyzes how relaxations in market models propagate to real-time systems. This information can be used not only to assess the criticality of constraint relaxations, but also as a basis for determining penalty prices more accurately. Constraint relaxations practice was replicated in this work using a test case and a real-life large-scale system, while capturing both energy market aspects and AC real-time system performance. System performance investigation included static and dynamic security analysis for base-case and post-contingency operating conditions. PJM peak hour loads were dynamically modeled in order to capture delayed voltage recovery and sustained depressed voltage profiles as a result of reactive power deficiency caused by constraint relaxations. Moreover, impacts of constraint relaxations on operational system security were investigated when risk based penalty prices are used. Transmission lines in the PJM system were categorized according to their risk index and each category was as-signed a different penalty price accordingly in order to avoid real-time overloads on high risk lines. This work also extends the investigation of constraint relaxations to post-contingency relaxations, where emergency limits are allowed to be relaxed in energy market models. Various scenarios were investigated to capture and compare between the impacts of base-case and post-contingency relaxations on real-time system performance, including the presence of both relaxations simultaneously. The effect of penalty prices on the number and magnitude of relaxations was investigated as well. / Dissertation/Thesis / Doctoral Dissertation Engineering 2016

Les Pérovskites hybrides organique-inorganique (PHOIs) ont suscité d’intenses recherches au coursdes dernières années. Dans cette thèse, nous avons dans un premier temps mis au point les différentsprocessus de préparation des échantillons et réalisé une caractérisation complète des films parmicroscopie à force atomique, spectroscopie photo-électronique par rayons X, mesure du potentiel desurface par sonde de Kelvin et mesure de la mobilité des charges par temps de vol. La distribution despièges à l'interface PHOI/Au a été étudiée via des mesure J-V-L en fonction de la températurecombinées avec des simulations numériques. Les relaxations diélectriques dans les PHOIs, tels que lamigration des ions et l’orientation du dipôle du cation organique, ont été étudiés par spectroscopied’impédance en fonction de la température. Dans la dernière partie de cette thèse, nous présentons uneétude originale qui démontre un mouvement des protons du groupement ammonium des cationsorganiques à l’interface avec le PEDOT : PSS. / Hybrid-organic-inorganic perovskites (HOIPs) have provoked intense research over the recent years.In this thesis, we contribute to this investigation by first examining the results of different solutionpreparation processes, followed by characterizing the films using atomic force microscopy, X-raydiffraction, ultra-violet photoelectron spectroscopy, X-ray photoelectron spectroscopy, Kelvin probesurface potential measurement, and time-of-flight mobility measurement. The state distribution of theHOIP/Au interface was then studied by low temperature J–V–L measurement combined withnumerical simulation. In the process of these characterizations, it became clear that the dielectricrelaxations in HOIPs, such as ion migration and organic cation dipole orientation, play an importantrole in the material, and the next part of the thesis presents an analysis of these mechanisms with thehelp of temperature dependent impedance spectroscopy measurement. These studies built thefoundations for the final part of the thesis, where we investigated a so far elusive subject in HOIPs, themigration of protons

In this Thesis, structure and dynamics of paramagnetic complexes for medical application are studied by Nuclear Magnetic Resonance (NMR). It focuses mainly on development of contrast agents (CA) for Magnetic Resonance Imaging (MRI) which is one of the most effective radiodiagnostic method nowadays. Most of the MRI CAs contains paramagnetic complexes of d- and f-metal ions. The presence of unpaired electron in proximity of NMR active nuclei has two main effects: paramagnetically induced shift and paramagnetically induced relaxa- tion. Both processes can dramatically change the NMR spectrum and often make it unobservable at all. Nevertheless, in many cases, acquisition of such spectra is possible and sometimes even less time-consuming than observation of diamag- netic molecules. Enhanced T1 relaxation allows faster pulse sequence repetition and increased chemical shift dispersion may lead to resolution of originally over- lapped signals. Moreover, the analysis of paramagnetic effects can provide useful information about the structure and dynamics of the studied system. Theoretical background of these effects is described in the Introduction of the Thesis. In the first part of Discussion in the Thesis, a new class of contrast agents for 19F-MRI based on nickel(II) and cobalt(II/III) ions is introduced...

Le problème généralisé des moments (PGM) est un problème d'optimisation linéaire sur des espaces de mesures. Il permet de modéliser simplement un grand nombre d'applications. En toute généralité il est impossible à résoudre mais si ses données sont des polynômes et des ensembles semi-algébriques alors on peut définir une hiérarchie de relaxations semidéfinies (SDP) - la hiérarchie moments-sommes-de-carrés (moments-SOS) - qui permet en principe d'approcher la valeur optimale avec une précision arbitraire. Le travail contenu dans cette thèse adresse deux facettes concernants le PGM et la hiérarchie moments-SOS: Une première facette concerne l'évolution des relaxations SDP pour le PGM. Le degré des poids SOS dans la hiérarchie moments-SOS augmente avec l'ordre de relaxation. Lorsque le nombre de variables n'est pas modeste, on obtient rapidement des programmes SDP de taille trop grande pour les logiciels de programmation SDP actuels, sauf si l'on peut utiliser des symétries ou une parcimonie structurée souvent présente dans beaucoup d'applications de grande taille. On présente donc un nouveau certificat de positivité sur un compact semi-algébrique qui (i) exploite la parcimonie présente dans sa description, et (ii) dont les polynômes SOS ont un degré borné à l'avance. Grâce à ce nouveau certificat on peut définir une nouvelle hiérarchie de relaxations SDP pour le PGM qui exploite la parcimonie et évite l'explosion de la taille des matrices semidéfinies positives liée au degré des poids SOS dans la hiérarchie standard. Une deuxième facette concerne (i) la modélisation de nouvelles applications comme une instance particulière du PGM, et (ii) l'application de la méthodologie moments-SOS pour leur résolution. En particulier on propose des approximations déterministes de contraintes probabilistes, un problème difficile car le domaine des solutions admissibles associées est souvent non-convexe et même parfois non connecté. Dans notre approche moments-SOS le domaine admissible est remplacé par un ensemble plus petit qui est le sous-niveau d'un polynôme dont le vecteur des coefficients est une solution optimale d'un certain SDP. La qualité de l'approximation (interne) croît avec le degré du polynôme et la taille du SDP. On illustre cette approche dans le problème du calcul du flux de puissance optimal dans les réseaux d'énergie, une application stratégique où la prise en compte des contraintes probabilistes devient de plus en plus cruciale (e.g., pour modéliser l'incertitude liée á l'énergie éolienne et solaire). En outre on propose une extension des cette procedure qui est robuste à l'incertitude sur la distribution sous-jacente. Des garanties de convergence sont fournies. Une deuxième contribution concerne l'application de la méthodologie moments-SOS pour l'approximation de solutions généralisés en commande optimale. Elle permet de capturer le comportement limite d'une suite minimisante de commandes et de la suite de trajectoires associée. On peut traiter ainsi le cas de phénomènes simultanés de concentrations de la commande et de discontinuités de la trajectoire. Une troisième contribution concerne le calcul de solutions mesures pour les lois de conservation hyperboliques scalaires dont l'exemple typique est l'équation de Burgers. Cette classe d'EDP non linéaire peut avoir des solutions discontinues difficiles à approximer numériquement avec précision. Sous certaines hypothèses, la solution mesurepeut être identifiée avec la solution classique (faible) à la loi de conservation. Notre approche moment-SOS fournit alors une méthode alternative pour approcher des solutions qui contrairement aux méthodes existantes évite une discrétisation du domaine. / The generalized moment problem (GMP) is a linear optimization problem over spaces of measures. It allows to model many challenging mathematical problems. While in general it is impossible to solve the GMP, in the case where all data are polynomial and semialgebraic sets, one can define a hierarchy of semidefinite relaxations - the moment-sums-of-squares (moment-SOS) hierachy - which in principle allows to approximate the optimal value of the GMP to arbitrary precision. The work presented in this thesis addresses two facets concerning the GMP and the moment-SOS hierarchy: One facet is concerned with the scalability of relaxations for the GMP. The degree of the SOS weights in the moment-SOS hierarchy grows when augmenting the relaxation order. When the number of variables is not small, this leads quickly to semidefinite programs (SDPs) that are out of range for state of the art SDP solvers, unless one can use symmetries or some structured sparsity which is typically present in large scale applications. We provide a new certificate of positivity which (i) is able to exploit the structured sparsity and (ii) only involves SOS polynomials of fixed degree. From this, one can define a new hierarchy of SDP relaxations for the GMP which can take into account sparsity and at the same time prevents from explosion of the size of SDP variables related to the increasing degree of the SOS weights in the standard hierarchy. The second facet focusses on (i) modelling challenging problems as a particular instance of the GMP and (ii) solving these problems by applying the moment-SOS hierarchy. In particular we propose deterministic approximations of chance constraints a difficult problem as the associated set of feasible solutions is typically non-convex and sometimes not even connected. In our approach we replace this set by a (smaller) sub-level-set of a polynomial whose vector of coefficients is a by-product of the moment-SOS hierarchy when modeling the problem as an instance of the GMP. The quality of this inner approximation improves when increasing the degree of the SDP relaxation and asymptotic convergence is guaranteed. The procedure is illustrated by approximating the feasible set of an instance of the chance-constrained AC Optimal Power Flow problem (a nonlinear problem in the management of energy networks) which nowadays becomes more and more important as we rely increasingly on uncertain energy sources such as wind and solar power. Furthermore, we propose an extension of this framework to the case where the underlying distribution itself is uncertain and provide guarantees of convergence. Another application of the moment-SOS methodology discussed in this thesis consider measure valued solutions to optimal control problems. We show how this procedure can capture the limit behavior of an optimizing sequence of control and its corresponding sequence of trajectories. In particular we address the case of concentrations of control and discontinuities of the trajectory may occur simultaneously. In a final contribution, we compute measure valued solutions to scalar hyperbolic conservation laws, such as Burgers equation. It is known that this class of nonlinear partial differential equations has potentially discontinuous solutions which are difficult to approximate numerically with accuracy. Under some conditions the measure valued solution can be identified with the classical (weak) solution to the conservation law. In this case our moment-SOS approach provides an alternative numerical scheme to compute solutions which in contrast to existing methods, does not rely on discretization of the domain.

A produção e liberação de substâncias vasodilatadoras pelas células endoteliais requer uma elevação sustentada na concentração intracelular de cálcio; essa elevação é consequente a um influxo de cálcio. Porém, a identidade do (s) canal (is) envolvido (s) nesse influxo ainda não foi (ram) determinada (s) conclusivamente. Existem evidências de que o gene TRPV4 (que codifica uma proteína permeável a cátions, inclusive ao cálcio) é expresso em células endoteliais. Porém, a falta de agentes que modulem especificamente a função dessa proteína não permitiu que o papel do TRPV4 no controle da função endotelial pudesse ser elucidado. Recentemente foram descritos dois novos compostos, o GSK1016790A (GSK) e o HC-067047 (HC), com ação ativadora e bloqueadora seletiva desse canal, respectivamente. Consequentemente, nesta dissertação descrevemos e interpretamos os resultados obtidos em experimentos concebidos para caracterizar o efeito do GSK1016790A (e com fins comparativos o efeito do 4PDD) em artérias isoladas de várias espécies. Para isso, empregamos anéis de artérias suspensos em cubas para órgão isolado para registro da tensão desenvolvida por esses anéis durante a contração isométrica provocada pela adição de fenilefrina; todos os experimentos foram realizados com solução de Krebs contendo diclofenaco (10 M). Inicialmente verificamos mediante imunohistoquímica a presença de imunorreatividade para o TRPV4 no endotélio da aorta torácica de rato. A adição de concentrações isoladas ou cumulativas de GSK produziu relaxamentos dependentes da concentração na aorta torácica de rato (CE50=0,5 nM; IC95%=0,35-0,72 nM; n=7); o 4PDD (1-10 µM), em concentrações isoladas, também produziu relaxamentos na aorta torácica de rato. Resultados semelhantes foram observados para o GSK na aorta torácica de coelho (CE50= 4,3 nM; IC95%=3,58-5,14 nM; n=5), de camundongo (CE50=1,4 nM; IC95%=0,85-2,24 nM; n=3) e de cobaia (CE50=0,2 nM; IC95%=0,12-0,22 nM; n=4). GSK relaxou também a aorta abdominal (CE50=6,5 nM; IC95%=3,71-11,3 nM; n=3) e a artéria femoral de coelho (CE50=17 nM; IC95%=16,8-18,7 nM; n=4); Os relaxamentos produzidos por ambas as drogas apareceram 1-2 min após a adição e atingiram o máximo em 5-8 min, foram reversíveis e não apresentaram taquifilaxia. Em todas as artérias os relaxamentos foram estritamente dependentes de endotélio e da presença de cálcio no meio extracelular. Na aorta torácica de rato, a pré-incubação com HC (5 minutos) aboliu o efeito do GSK sem afetar os relaxamentos produzidos pela acetilcolina. Em todas as artérias testadas os efeitos do GSK e do 4PDD foram revertidos completamente pelo HC (1-3 µM) ou pelo vermelho de rutênio (aorta torácica de rato e artérias de coelho, 1µM, VR). Esses resultados demonstram que os canais TRPV4 estão presentes na célula endotelial e que a sua ativação leva à produção de fatores relaxantes. Como corolário, esses resultados constituem indícios de que os canais TRPV4 podem participar da regulação da função das células endoteliais em situações fisiológicas e/ ou fisiopatológicas. / Production and release of vasodilator substances by endothelial cells require a sustained elevation of intracellular calcium which depends on calcium influx. The identity of the channels involved in this influx remains to be established. There is evidence that the TRPV4 gene (which encodes for a cation permeable channel including calcium) is expressed in endothelial cells; the lack of pharmacologic agents that selectively modulate the activity of TRPV4 channels has hindered the elucidation of its function in endothelial cells. Recently two new compounds, GSK1016790A (GSK) and HC-067047 (HC), which selectively activate or block TRPV4 channels, respectively, were described. This dissertation consists in the description and interpretation of results from experiments conceived to characterize the effect of GSK (and of 4PDD for comparison) in isolated arterial rings from several animal species. To this aim we used arterial rings mounted in isolated organ chambers; we recorded continuously the tension developed by them during isometric contractions elicited by phenylephrine (Phe); all the experiments were conducted using Krebs solution containing diclofenac (10 µM). Initially, we confirmed by immunohistochemistry the presence of anti-TRPV4 immunoreactivity in the endothelium of rat thoracic aorta. In rat thoracic aortic rings pre-constricted with Phe (0.1 µM) the addition of different concentrations of GSK (either single or cumulative concentrations) caused concentration-dependent relaxations (EC50=0.5 nM, 95%CI=0.35-0.72 nM, n=7); 4PDD (in single concentrations) also caused relaxations of rat thoracic aortic rings. Similar results were observed for GSK in thoracic aortic rings from rabbit (EC50=4.3 nM, 95%CI=3.58-5.14 nM, n=5), mouse (EC50=1.4 nM, 95%CI=0.85-2.24 nM, n=3) and guinea-pig (EC50=0.2 nM, 95%CI=0.12-0.22 nM, n=4). GSK also produced relaxations of rings from rabbit abdominal aorta (EC50=6.5 nM, 95%CI=3.71-11.3 nM, n=3) and femoral artery (EC50=17 nM, 95%CI=16.8-18.7 nM, n=4). Relaxations caused by both GSK and 4PDD started 1-2 min after their addition and reached a steady-state in 5-8min; they were reversible after washing-out and did not exhibit tachyphylaxis. In all the studied arteries GSK or 4PDD induced- relaxations were strictly endothelium- and extracellular calcium- dependent. Pre-incubation of rat thoracic aortic rings with HC (1 µM for 5min) abolished the effect of GSK but did not affect relaxations elicited by Ach (1 µM). In all the arterial rings HC (1-3 µM) also completely reverted the relaxations caused by GSK or 4PDD; in rabbit and rat thoracic aortic rings ruthenium red (1 µM) also completely reverted the relaxations caused by GSK or 4PDD. The present findings showing that TRPV4 channels are present in endothelial cells and that their activation results in the production and release of relaxing factors constitute an indication that TRPV4 channels could be involved in the regulation of endothelial cell functions under physiological or patho-physiological conditions.