Le projet de cette thèse est double. Le premier concerne l’extension des résultats précédents sur les conditions nécessaires d’optimalité pour des problèmes avec contraintes d’état, dans le cadre du contrôle optimal ainsi que dans le cadre de calcul des variations. Le deuxième objectif consiste à travailler sur deux nouveaux aspects de recherche : dériver des résultats de viabilité pour une classe de systèmes de contrôle avec des contraintes d’état dans lesquels les conditions dites ‘standard inward pointing conditions’ sont violées; et établir les conditions nécessaires d’optimalité pour des problèmes de minimisation de coût moyen éventuellement perturbés par des paramètres inconnus.Dans la première partie, nous examinons les conditions nécessaires d’optimalité qui jouent un rôle important dans la recherche de candidats pour être des solutions optimales parmi toutes les solutions admissibles. Cependant, dans les problèmes d’optimisation dynamique avec contraintes d’état, certaines situations pathologiques pourraient survenir. Par exemple, il se peut que le multiplicateur associé à la fonction objective (à minimiser) disparaisse. Dans ce cas, la fonction objective à minimiser n’intervient pas dans les conditions nécessaires de premier ordre: il s’agit du cas dit anormal. Un phénomène pire, appelé le cas dégénéré montre que, dans certaines circonstances, l’ensemble des trajectoires admissibles coïncide avec l’ensemble des candidats minimiseurs. Par conséquent, les conditions nécessaires ne donnent aucune information sur les minimiseurs possibles.Pour surmonter ces difficultés, de nouvelles hypothèses supplémentaires doivent être imposées, appelées les qualifications de la contrainte. Nous étudions ces deux problèmes (normalité et non dégénérescence) pour des problèmes de contrôle optimal impliquant des contraintes dynamiques exprimées en termes d’inclusion différentielle, lorsque le minimiseur a son point de départ dans une région où la contrainte d’état est non lisse. Nous prouvons que sous une information supplémentaire impliquant principalement le cône tangent de Clarke, les conditions nécessaires sous la forme dite ‘Extended Euler-Lagrange condition’ sont satisfaites en forme normale et non dégénérée pour deux classes de problèmes de contrôle optimal avec contrainte d’état. Le résultat sur la normalité est également appliqué pour le problème de calcul des variations avec contrainte d’état.Dans la deuxième partie de la thèse, nous considérons d’abord une classe de systèmes de contrôle avec contrainte d’état pour lesquels les qualifications de la contrainte standard du ‘premier ordre’ ne sont pas satisfaites, mais une qualification de la contrainte d’ordre supérieure (ordre 2) est satisfaite.Nous proposons une nouvelle construction des trajectoires admissibles (dit un résultat de viabilité) et nous étudions des exemples (tels que l’intégrateur non holonomique de Brockett) fournissant en plus un résultat d’estimation non linéaire. L’autre sujet de la deuxième partie de la thèse concerne l’étude d’une classe de problèmes de contrôle optimal dans lesquels des incertitudes apparaissent dans les données en termes de paramètres inconnus. En tenant compte d’un critère de performance sous la forme de coût moyen, une question cruciale est clairement de pouvoir caractériser les contrôles optimaux indépendamment de l’action du paramètre inconnu: cela permet de trouver une sorte de ‘meilleur compromis’ parmi toutes les réalisations possibles du système de contrôle tant que le paramètre varie. Pour ce type de problèmes, nous obtenons des conditions nécessaires d’optimalité sous la forme du Principe du Maximum (éventuellement pour le cas non lisse). / The project of this thesis is twofold. The first concerns the extension of previous results on necessary optimality conditions for state constrained problems in optimal control and in calculus of variations. The second aim consists in working along two new research lines: derive viability results for a class of control systems with state constraints in which ‘standard inward pointing conditions’ are violated; and establish necessary optimality conditions for average cost minimization problems possibly perturbed by unknown parameters.In the first part, we examine necessary optimality conditions which play an important role in finding candidates to be optimal solutions among all admissible solutions. However, in dynamic optimization problems with state constraints, some pathological situations might arise. For instance, it might occur that the multiplier associated with the objective function (to minimize) vanishes. In this case, the objective function to minimize does not intervene in first order necessary conditions: this is referred to as the abnormal case. A worse phenomenon, called the degenerate case shows that in some circumstances the set of admissible trajectories coincides with the set of candidates to be minimizers. Therefore the necessary conditions give no information on the possible minimizers.To overcome these difficulties, new additional hypotheses have to be imposed, known as constraint qualifications. We investigate these two issues (normality and non-degeneracy) for optimal control problems involving state constraints and dynamics expressed as a differential inclusion, when the minimizer has its left end-point in a region where the state constraint set in nonsmooth. We prove that under an additional information involving mainly the Clarke tangent cone, necessary conditions in the form of the Extended Euler-Lagrange condition are derived in the normal and non-degenerate form for two different classes of state constrained optimal control problems. Application of the normality result is shown also for the calculus of variations problem subject to a state constraint.In the second part of the thesis, we consider first a class of state constrained control systems for which standard ‘first order’ constraint qualifications are not satisfied, but a higher (second) order constraint qualification is satisfied. We propose a new construction for feasible trajectories (a viability result) and we investigate examples (such as the Brockett nonholonomic integrator) providing in addition a non-linear stimate result. The other topic of the second part of the thesis concerns the study of a class of optimal control problems in which uncertainties appear in the data in terms of unknown parameters. Taking into consideration an average cost criterion, a crucial issue is clearly to be able to characterize optimal controls independently of the unknown parameter action: this allows to find a sort of ‘best compromise’ among all the possible realizations of the control system as the parameter varies. For this type of problems, we derive necessary optimality conditions in the form of Maximum Principle (possibly nonsmooth).

L’objectif de cette étude est de développer une alimentation multisources exploitant la complémentarité batterie/supercondensateurs pour gagner en masse sur le stockage de l’énergie électrique embarquée à bord des aéronefs et des véhicules spatiaux. L’étude se déroule en trois parties :Dans la première partie, un outil d’aide à la décision permettant développer une alimentation hybride pour une application donnée est présenté. Cet outil a pour but d’estimer la masse optimale d’une alimentation hybride à partir des seules informations d’énergies spécifiques et puissances spécifiques des sources candidatesLa deuxième partie de l’étude s’appuie sur la complémentarité d’une étude bibliographique sur le comportement interne des supercondensateurs, couplée avec une campagne expérimentale de caractérisation et de vieillissement des supercondensateurs, pour construire et identifier les modèles multiphysiques de références commerciales de supercondensateurs nécessaires à l’optimisation fine du dimensionnement de l’alimentation hybride.À partir du modèle des sources, la troisième et dernière partie de cette étude a pour objectif de présenter la conception d’une architecture électrique répondant au besoin. En particulier, l’alimentation hybride proposée dans cette partie exploite dynamiquement et au maximum de leur capacité chacune des deux sources, tout en prenant soin de ne pas les contraindre excessivement. De par cette manière de faire, on se prémunit contre d’éventuelles défaillances des sources liées à leur utilisation abusive / The aim of this study is to develop an hybrid power supply using the complementarities between batteries and supercapacitors in order to improve the mass of electrical storage systems on aircrafts and spacecrafts.The study is divided into three parts: In the first part, a decision-making tool to develop a hybrid power supply given a mission profile is presented. Thanks to this tool, an estimation of the optimal mass of the hybrid power supply is done based only on the specific energy and the specific power of the sources.The second part is firstly composed of a synthesis of bibliography results on the internal behavior of supercapacitors; secondly an experimental test campaign is described. Its aim is characterizing, modeling and identifying the multiphysics behavior and ageing of supercapacitors on several commercial references. Those models are required for the fine sizing optimization of the hybrid power supply. Basing on the internal model of the sources, the aim of the third part of this study is to present the development of an hybrid architecture battery/supercapacitors which fulfills the electrical need for a specific application. This hybrid power supply takes dynamically advantage of the electrical sources at the maximum of their possibilities, but without overstressing them at the same time. Thanks to that, the aging rate of the sources and the failure rate of the system are limited

Parmi les outils les plus classiques de l'Analyse Multivariée, les Composantes Principales sont aussi un des plus anciens puisqu'elles furent introduites il y a plus d'un siècle par Pearson (1901) et redécouvertes ensuite par Hotelling (1933). Aujourd'hui, cette méthode est abondamment utilisée en Sciences Sociales, en Economie, en Biologie et en Géographie pour ne citer que quelques disciplines. Elle a pour but de réduire de façon optimale (dans un certain sens) le nombre de variables contenues dans un jeu de données.<p>A ce jour, les méthodes d'inférence utilisées en Analyse en Composantes Principales par les praticiens sont généralement fondées sur l'hypothèse de normalité des observations. Hypothèse qui peut, dans bien des situations, être remise en question.<p><p>Le but de ce travail est de construire des procédures de test pour l'Analyse en Composantes Principales qui soient valides sous une famille plus importante de lois de probabilité, la famille des lois elliptiques. Pour ce faire, nous utilisons la méthodologie de Le Cam combinée au principe d'invariance. Ce dernier stipule que si une hypothèse nulle reste invariante sous l'action d'un groupe de transformations, alors, il faut se restreindre à des statistiques de test également invariantes sous l'action de ce groupe. Toutes les hypothèses nulles associées aux problèmes considérés dans ce travail sont invariantes sous l'action d'un groupe de transformations appellées monotones radiales. L'invariant maximal associé à ce groupe est le vecteur des signes multivariés et des rangs des distances de Mahalanobis entre les observations et l'origine. <p><p>Les paramètres d'intérêt en Analyse en composantes Principales sont les vecteurs propres et valeurs propres de matrices définies positives. Ce qui implique que l'espace des paramètres n'est pas linéaire. Nous développons donc une manière d'obtenir des procédures optimales pour des suite d'experiences locales courbées. <p>Les statistiques de test introduites sont optimales au sens de Le Cam et mesurables en l'invariant maximal décrit ci-dessus.<p>Les procédures de test basées sur ces statistiques possèdent de nombreuses propriétés attractives: elles sont valides sous la famille des lois elliptiques, elles sont efficaces sous une densité spécifiée et possèdent de très bonnes efficacités asymptotiques relatives par rapport à leurs concurrentes. En particulier, lorsqu'elles sont basées sur des scores Gaussiens, elles sont aussi efficaces que les procédures Gaussiennes habituelles et sont bien plus efficaces que ces dernières si l'hypothèse de normalité des observations n'est pas remplie. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

This thesis presents the mixed integer bilevel programming problems where some optimality conditions and solution algorithms are derived. Bilevel programming problems are optimization problems which are partly constrained by another optimization problem. The theoretical part of this dissertation is mainly based on the investigation of optimality conditions of mixed integer bilevel program. Taking into account both approaches (optimistic and pessimistic) which have been developed in the literature to deal with this type of problem, we derive some conditions for the existence of solutions. After that, we are able to discuss local optimality conditions using tools of variational analysis for each different approach. Moreover, bilevel optimization problems with semidefinite programming in the lower level are considered in order to formulate more optimality conditions for the mixed integer bilevel program. We end the thesis by developing some algorithms based on the theory presented

We investigate optimal partnership of rearrangement-invariant Banach func- tion spaces for the Hilbert transform and the Riesz potential. We establish sharp theorems which characterize optimal action of these operators on such spaces. These results enable us to construct optimal domain (i.e. the largest) and op- timal range (i.e. the smallest) partner spaces when the other space is given. We illustrate the obtained results by non-trivial examples involving Generalized Lorentz-Zygmund spaces with broken logarithmic functions. The method is pre- sented in such a way that it should be easily adaptable to other appropriate operators. 1

This study describes the verse design of Old English poetry in terms of modern phonological theory, developing an analysis which allows all OE verse lines to be described in terms of single metrical design. Old English poetry is typified by a single type of line of variable length, characterised by four metrical peaks. The variation evident in the lengths of OE metrical units has caused previous models to overgenerate acceptable verse forms or to develop complex typologies of dozens of acceptable forms. In this study, Metrical phonology and Optimality theory are used to highlight some aspects of the relationship between syntax, phonology and verse metrics in determining how sentences and phrases interact with the verse structure to create variation. The main part of the study is a metrical model based on the results of a corpus analysis. The corpus is centred on the OE poems Genesis and Andreas, complemented by selected shorter poems. A template of a prototypical line is described based on a verse foot which contains three vocalic moras, and which can vary between 2 and 4 vocalic moras distributed across 1 to 4 syllables. Each standard line is shown to consist of four of these verse feet, leading to a line length which can vary between 8 and 16 vocalic moras. It is shown that the limited variation within the length of the verse foot causes the greater variation in the length of lines. The rare, longer ‘hypermetric’ line is also accounted for with a modified analysis. The study disentangles the verse foot, which is an abstract metrical structure, from the prosodic word, which is a phonological object upon which the verse foot is based, and with which it is often congruent. Separate sets of constraints are elaborated for creating prosodic words in OE, and for fitting them into verse feet and lines. The metrical model developed as a result of this analysis is supported by three smaller focused studies. The constraints for creating prosodic words are defended with reference to compounds and derivational nouns, and are supported by a smaller study focusing on the metrical realisation of non-Germanic personal names in OE verse. Names of biblical origin are often longer than the OE prosodic word can accommodate. The supporting study on non-Germanic names demonstrates how long words with no obvious internal morphology in OE are adapted first to OE prosody and then to the verse structure. The solution for the metrical realisation of these names is shown to be patterned on derivational nouns. The supporting study on compound numerals describes how phrases longer than a verse are accommodated by the verse design. It is shown that compound numerals, which consist of two or more numeral words (e.g. 777 – seofonhund and seofon and hundseofontig) are habitually rearranged within the text to meet the requirements of verse length and alliteration. A further supporting study discusses the difference between the line length constraints controlling OE verse design and those for Old Norse and Old Saxon verse. Previous studies have often conflated these three closely related traditions into a single system. It is shown that despite their common characteristics, the verse design described in this study applies to all OE verse, but not to ON or OS.

Esta tese investiga por meio da Teoria da Otimidade Estocástica (BOERSMA; HAYES, 2001) o processo de harmonia vocálica de altura (HVA), que envolve as vogais médias pretônicas /e, o/ e as torna [i, u] quando há uma vogal alta na sílaba seguinte, como em menino~minino, fortuna~furtuna. O estudo tem como motivação o fato de que a maior parte das pesquisas realizadas sobre HV em português brasileiro no dialeto gaúcho tiveram como foco uma análise na linha Laboviana da sociolinguística quantitativa (BISOL, 1981, SCHWINDT, 1995, 2002, CASAGRANDE, 2004, FERNANDES, 2014). Os dados empíricos desta pesquisa provêm da fala coletada por meio de entrevistas sociolinguísticas utilizadas no estudo de Fernandes (2014), que fazem parte do banco de dados VARSUL – Variação Linguística no Sul do Brasil, e pertencem a amostra chamada Jovens Escolarizados, com estudantes de 16 a 23 anos, de Porto Alegre. Os dados foram metodologicamente separados em 3 diferentes categorias, correspondentes ao tipo de vocábulo, devido à possibilidade da influência de fatores morfológicos na aplicação e/ou restrição da regra de HVA: Formas Nominais Não- Derivadas (FNND), Formas Nominais Derivadas (FND), e Formas Verbais (FV). Buscamos propor restrições de marcação ou fidelidade para tratar a HV como um processo envolvendo o traço de altura [+alto], com espraiamento regressivo, a fim de explicar propriedades que bloqueiem ou permitam o alçamento das vogais, com base nas proporções de pesquisas quantitativas que foram realizadas anteriormente.O estudo visou propor uma análise da harmonia vocálica com restrições universais para poder explanar padrões em foco nos dados, como homorganicidade e heterorganicidade da vogal-alvo e vogal-gatilho A análise também tornou possível uma observação analítica e particular dos dados, diferentemente dos estudos variacionistas prévios. As restrições universais e requisitos fonotáticos foram buscados no espírito da Teoria da Otimidade Clássica (TO, PRINCE; SMOLENSKY, [1993] 2004, MCCARTHY; PRINCE, 1995). Esta análise também se apoiou em restrições e traços de pesquisas anteriores de caráter similar sobre o tema (MATZENAUER; MIRANDA, 2003, LEE; OLIVEIRA, 2003, ALVES, 2011, BOHN, 2014, BATTISTI; FERNANDES 2017). Para representar e modelar a gramática da HVA variável utilizou-se o Gradual Learning Algorithm (GLA), de Boersma e Hayes (2001). A análise da HVA com ranking contínuo demonstrou a dominância das restrições License, Agree e de fidelidade. Arestrição que exige a homorganicidade está ranqueada com valores mais baixos na escala contínua para as FNND. A variabilidade está presente em todas as formas, sendo menos presente nas FV, e representa a existência de mais de um mapeamento inputoutput. Os resultados evidenciam que os falantes do dialeto gaúcho realizam HVA com mais frequência em uma sequência vocálica heterorgânica com uma vogal alta tônica contígua para formas nominais em geral, e com mais frequência em uma sequência vocálica homorgânica com vogal alta contígua para as formas verbais. A exigência de que a vogal-alvo deve ser seguida por uma vogal alta tônica é mais importante para formas nominais do que para verbos em geral.As análises estocásticas realizadas, que representam a gramática dos falantes do dialeto em questão, atestaram a natureza variável da HV, com proporções baixas de realização. A dominância de restrições foi demonstrada no ranking contínuo da TO Estocástica. Também foi possível realizar reflexões e direcionamentos para futuros estudos sobre o tema, como a influência de consoantes adjacentes à vogal alvo da harmonia. / This thesis investigates through Stochastic Optimality Theory the Height Vowel Harmony phenomenon (HVH), which raises the pretonic mid vowels /e, o/ to [i, u] when there is a high vowel in the next syllable, as in m[e]nino~minino ‘boy’, f[o]rtuna~f[u]rtuna ‘fortune’. The study is motivated by the fact that most research done on VH in Brazilian Portuguese in the Gaucho dialect focused on an analysis of the Labovian line of quantitative sociolinguistics (BISOL, 1981, SCHWINDT, 1995, 2002, CASAGRANDE, 2004, FERNANDES, 2014). The empirical data of this research are from naturally occurring speech collected through interviews used in the study of Fernandes (2014) and are part of the database VARSUL - Linguistic Variation in the South of Brazil, specifically the sample called Jovens Escolarizados, with students from 16 to 23 years old. The words of the sample were methodologically separated into 3 different categories, corresponding to the type of word, due to the possibility of the influence of morphological factors in the realization and/or restriction of the VH rule: Non-Derivational Nominal Words (NDNW), Derivational Nominal Words (DNW), Verb Class (VC). We sought to propose markedness and faithfulness constraints to treat VH as an analysis with the [+High] feature and regressive spreading, in order to explain properties that block or allow vowels to be raised or acquire the [high] feature, based on the proportions of previous quantitative researches. The objectives of the study aimed to propose an analysis of VH with universal constraints to be able to explain patterns in focus in the data, such as homorganicity and heterorganicity of the target-vowel and trigger-vowel The universal constraints and phonotatic requirements were chosen in the spirit of Classic Optimality Theory (OT, PRINCE; SMOLENSKY, 1993, 2004, MCCARTHY; PRINCE, 1995). This analysis is also based on constraints and features of previous similar studies on Brazilian Portuguese VH (MATZENAUER; MIRANDA, 2003, LEE; OLIVEIRA, 2003, ALVES, 2011, BOHN, 2014, BATTISTI; FERNANDES 2017). To represent and model the variable HVA grammar we used the Gradual Learning Algorithm (GLA), by Boersma and Hayes (2001). The HVA analysis with continuous ranking demonstrated the dominance of the License, Agree and faithfulness constraints families. The constraint that requires homorganicity is ranked with lower values in the continuous scale for the NDNW. The variability is present in all categories, being less present in the Verb Class, and represents the existence of more than one input-output mapping. The results show that speakers of the Gaucho dialect perform HVH more frequently in a heterorganic vowel sequence with a contiguous high tonic vowel for nominal words in general, and HVH is more frequent in a homorganic vowel sequence with contiguous high vowel for verbal words. The requirement that the targetvowel must be followed by a high tonic vowel is more important for nominal words than for verbs in general. The stochastic analyzes carried out, which represent the grammar of the speakers of the dialect in question, attested the variable nature of the HVH, which, with low proportions, demonstrated in the continuous ranking of the Stochastic OT the dominance of constraint families, and also provided reflections and directions for future studies on the subject, such as analysis of speech data using ultrasound and the role of consonants adjacent to the harmony target.

This thesis explores the perceived enjoyability of Deep Reinforcement learning AI agents (DeepRL agent) that strives towards optimality within the First Person Shooter game Unreal Tournament 2004 (UT2004). The DeepRL agent used in the experiments was created and then trained within this game against the AI agent which comes with the UT2004 game (known here as a trivial UT2004 agent). Through testing the opinions of participants who have played UT2004 deathmatches against both the DeepRL agent and the trivial UT2004 agent, the data collected in two participant surveys shows that the DeepRL agent is more enjoyable to face than a trivial UT2004 agent. By striving towards optimality the DeepRL agent developed a behaviour which despite making the DeepRL agent a great deal worse at UT2004 than the trivial UT2004 agent was more enjoyable to face than the trivial UT2004 agent. Considering this outcome the data suggests that DeepRL agents in UT2004 which are encouraged to strive towards optimality during training are “enjoyable enough” in order to be considered by game developers to be “good enough” when developing non-trivial opponents for games similar to UT2004. If the development time of a DeepRL agent is reduced or equal in comparison with the development time of a trivial agent then the DeepRL agent could hypothetically be preferable.

This document aims on aplication of sophisticated software programs to accomplish hydraulic analysis of real water supply, design and optimization measures for improvement of pressure conditions in water network. In this work is stated a list and description of software enabling to accomplish static or longterm hydraulic analysis of water supply when the most world used program EPANET 2.0 is described more deeply. There is described working of a EPANET and his algorithm also there are explain principles on which EPANET is based. During the hydraulic analysis of real system was used sophisticated software EPANET 2.0. With this program was processed hydraulic analysis of chosen water supply system of small consumption area. Based on the results of analysis pressure conditions has been designed and optimized measure to improve pressure conditions in the water network.

L’objet de cette thèse est l’étude des jeux champs moyen déterministes avec contrainte sur l’état. La théorie des jeux à champ moyen (mean field games (MFG)), initiée par Lasry et Lions en 2006, étudie des problèmes d’optimisation pour grandes populations d'agents dans un milieu dynamique. L'analyse mathématique de tels problèmes s'est jusqu'à présent concentrée sur des situations dans lequel les agents évoluent dans tout l’espace. En pratique, cependant, les agents ont des contraintes sur l'état. Le but de la thèse est celle d'étudier l'impact de ces contraintes sur l'analyse des systèmes de jeux à champ moyen. Nous montrons que les équilibres de Nash peuvent être décrits en termes de point fixe sur un espace de mesure sur des courbes contraintes (notion d’équilibre généralisé). Afin d’obtenir des résultats plus fins sur de tels équilibres, nous montrons un principe d’optimalité lisse pour les courbes optimales avec contraintes sur l’état. Nous en déduisons que les équilibres généralisés satisfont un système MFG, où les équations de Hamiton-Jacobi et les équations de transport doivent être entendues dans un sens spécifique. / The aim of this Thesis is to study deterministic mean field games with state constraints. Mean field games (MFG) is a recent theory invented by Lasry and Lions which studies optimization problems with large populations of agents in a dynamical framework. The mathematical analysis of such problems has so far focused on situations where the agents can evolve in the whole space. In practice, however, the agents often have constraints on their state. The aim of this Thesis is to understand the consequence of such constraints on the analysis of mean field games. We first show that the Nash MFG equilibria can be described as fixed points on the space of measures on constrained trajectories (generalized MFG equilibria). In order to obtain more precise results on these equilibria, we show a smooth optimality principle for the optimal trajectories of control problem with state constraints. We derive from this that the generalized equilibria satisfy a MFG system in which the Hamilton-Jacobi equation and the continuity equation have to be understand in a specific sense.