<div>Optimal control theory (OCT) exists since the 1950s. However, with the advent of modern computers, the design community delegated the task of solving the optimal control problems (OCPs) largely to computationally intensive direct methods instead of methods that use OCT. Some recent work showed that solvers using OCT could leverage parallel computing resources for faster execution. The need for near real-time, high quality solutions for OCPs has therefore renewed interest in OCT in the design community. However, certain challenges still exist that prohibits its use for solving complex practical aerospace problems, such as landing human-class payloads safely on Mars.</div><div><br></div><div>In order to advance OCT, this thesis introduces Epsilon-Trig regularization method to simply and efficiently solve bang-bang and singular control problems. The Epsilon-Trig method resolves the issues pertaining to the traditional smoothing regularization method. Some benchmark problems from the literature including the Van Der Pol oscillator, the boat problem, and the Goddard rocket problem verified and validated the Epsilon-Trig regularization method using GPOPS-II.</div><div><br></div><div>This study also presents and develops the usage of trigonometry for incorporating control bounds and mixed state-control constraints into OCPs and terms it as Trigonometrization. Results from literature and GPOPS-II verified and validated the Trigonometrization technique using certain benchmark OCPs. Unlike traditional OCT, Trigonometrization converts the constrained OCP into a two-point boundary value problem rather than a multi-point boundary value problem, significantly reducing the computational effort required to formulate and solve it. This work uses Trigonometrization to solve some complex aerospace problems including prompt global strike, noise-minimization for general aviation, shuttle re-entry problem, and the g-load constraint problem for an impactor. Future work for this thesis includes the development of the Trigonometrization technique for OCPs with pure state constraints.</div>

本篇論文旨在從優選理論（Optimality Theory）之框架背景來探討國、台語夾碼（Mandarin-Taiwanese Code-Mixing）時的連讀變調現象。由於此現象之探討涉及國語及台語之變調，本篇論文亦從優選理論之觀點來探討國語三聲變調（Mandarin Tone Sandhi）以及台語的變調（Taiwanese Tone Sandhi）。 在國語三聲變調方面，由於傳統派生（derivational）模式在處理國語三聲變調時，仍遺留了些許的問題。例如，無法以一致的方式來處理non-PP和PP的變調現象。本文主要針對這個問題，重新以優選理論的角度提出解決之道。文中分別提出了一組韻律制約（Prosodic Constraint）及一組聲調制約（Tonal Constraint）；根據這兩組制約，傳統派生模式所遺留下的缺失則得以獲得妥善的處理。 在台語變調方面，台語變調在傳統派生模式的探討中亦遺留下些許問題。例如，無法以一致的方式來處理non-adjunct和adjunct以及non-clitic和clitic的變調問題。本文根據優選理論，重新分析台語變調。文中分別提出了一組韻律制約及一組聲調制約；根據此兩組制約，則可以成功的免除傳統派生分析模式下的缺失。 國、台語夾碼時的變調是未曾被探討過的問題。本文先就國、台語夾碼時的變調，提出一個派生模式的分析。不過，以派生模式來處理國、台語夾碼變調時，遺留下必須限定國語變調規則和台語變調規則的運作次序這項缺點。因此，本文根據優選理論，重新分析了這個變調現象，並提出了一組聲調制約；這組聲調制約，配合國語及台語的韻律制約，得以成功的處理傳統派生模式所遺留下的問題。 / The present thesis is mainly devoted to the research issue of tone sandhi in Mandarin-Taiwanese code-mixing using an Optimality Theoretic (OT) Approach. Since the study of this code-mixed tone sandhi necessarily involves the tone sandhi rules of Mandarin and of Taiwanese, the tone sandhi phenomena in Mandarin and in Taiwanese are carefully discussed under OT as well. Tone sandhi in Mandarin has been widely studied by many Chinese linguistics under the derivational approach. This thesis argues that the previous analyses to Mandarin tone sandhi are inadequate and that an Optimality Theoretic approach is needed to account for tone sandhi in Mandarin. The inadequacy of the previous analyses comes from the common failure of offering a uniform solution to account for non-PP and PP word stings in Mandarin. Based on the Optimality Theory, this thesis proposes two sets of constraints to account for Mandarin tone sandhi; one is the prosodic constraints set and the other is the tonal constraints set. This thesis proves that these two constraints can successfully get rid of the problem left by the derivational tradition. Tone sandhi in Taiwanese is also widely studied by many Chinese linguistics under the derivational approach. This thesis argues that the previous analyses to Taiwanese tone sandhi are inadequate and that an Optimality Theoretic approach is needed to account for tone sandhi in Taiwanese. The inadequacy of the previous analyses comes from the fact that Taiwanese word strings with non-adjunct and adjunct structures as well as with non-clitic and clitic structures fail to be accounted for using a uniform solution. Based on the Optimality Theory, this thesis proposes two sets of constraints to account for Taiwanese tone sandhi; one is the prosodic constraints set and the other is the tonal constraints set. This thesis proves that these two constraints can successfully get rid of the problem left by the derivational tradition. Tone sandhi in Mandarin-Taiwanese code-mixing is a phenomenon that is very interesting but has not been studied before. This thesis thus offers a derivational analysis to this tone sandhi phenomenon first, where it is found that (1) in Mandarin-Taiwanese code-mixing, a Mandarin base tone can trigger Taiwanese tone sandhi and a Taiwanese low tone can trigger Mandarin tone sandhi, (2) in Mandarin-Taiwanese code-mixing, the Mandarin tone sandhi rule is sensitive to all and only the Mandarin tone sandhi domain and the Taiwanese tone sandhi rule is sensitive to all and only the Taiwanese tone sandhi domain, and (3) in Mandarin-Taiwanese code-mixing, the Taiwanese tone sandhi rule must apply before the Mandarin tone sandhi rule to derive the tonal output. However, since the demand for an extrinsic rule order between the tone sandhi rules of Mandarin and Taiwanese is inadequate, the tone sandhi phenomenon is reanalyzed under the framework of the Optimality Theory. A set of tonal constraints is proposed. According to the tonal constraints set, the inadequacy left by the derivational approach is successfully avoided.

This thesis deals with several statistical and probabilistic aspects of symmetry and asymmetry, both in a univariate and multivariate context, and is divided into three distinct parts. The first part, composed of Chapters 1, 2 and 3 of the thesis, solves two conjectures associated with multivariate skew-symmetric distributions. Since the introduction in 1985 by Adelchi Azzalini of the most famous representative of that class of distributions, namely the skew-normal distribution, it is well-known that, in the vicinity of symmetry, the Fisher information matrix is singular and the profile log-likelihood function for skewness admits a stationary point whatever the sample under consideration. Since that moment, researchers have tried to determine the subclasses of skew-symmetric distributions who suffer from each of those problems, which has led to the aforementioned two conjectures. This thesis completely solves these two problems. The second part of the thesis, namely Chapters 4 and 5, aims at applying and constructing extremely general skewing mechanisms. As such, in Chapter 4, we make use of the univariate mechanism of Ferreira and Steel (2006) to build optimal (in the Le Cam sense) tests for univariate symmetry which are very flexible. Actually, their mechanism allowing to turn a given symmetric distribution into any asymmetric distribution, the alternatives to the null hypothesis of symmetry can take any possible shape. These univariate mechanisms, besides that surjectivity property, enjoy numerous good properties, but cannot be extended to higher dimensions in a satisfactory way. For this reason, we propose in Chapter 5 different general mechanisms, sharing all the nice properties of their competitors in Ferreira and Steel (2006), but which moreover can be extended to any dimension. We formally prove that the surjectivity property holds in dimensions k>1 and we study the principal characteristics of these new multivariate mechanisms. Finally, the third part of this thesis, composed of Chapter 6, proposes a test for multivariate central symmetry by having recourse to the concepts of statistical depth and runs. This test extends the celebrated univariate runs test of McWilliams (1990) to higher dimensions. We analyze its asymptotic behavior (especially in dimension k=2) under the null hypothesis and its invariance and robustness properties. We conclude by an overview of possible modifications of these new tests./ Cette thèse traite de différents aspects statistiques et probabilistes de symétrie et asymétrie univariées et multivariées, et est subdivisée en trois parties distinctes. La première partie, qui comprend les chapitres 1, 2 et 3 de la thèse, est destinée à la résolution de deux conjectures associées aux lois skew-symétriques multivariées. Depuis l'introduction en 1985 par Adelchi Azzalini du plus célèbre représentant de cette classe de lois, à savoir la loi skew-normale, il est bien connu qu'en un voisinage de la situation symétrique la matrice d'information de Fisher est singulière et la fonction de vraisemblance profile pour le paramètre d'asymétrie admet un point stationnaire quel que soit l'échantillon considéré. Dès lors, des chercheurs ont essayé de déterminer les sous-classes de lois skew-symétriques qui souffrent de chacune de ces problématiques, ce qui a mené aux deux conjectures précitées. Cette thèse résoud complètement ces deux problèmes. La deuxième partie, constituée des chapitres 4 et 5, poursuit le but d'appliquer et de proposer des méchanismes d'asymétrisation très généraux. Ainsi, au chapitre 4, nous utilisons le méchanisme univarié de Ferreira and Steel (2006) pour construire des tests de symétrie univariée optimaux (au sens de Le Cam) qui sont très flexibles. En effet, leur méchanisme permettant de transformer une loi symétrique donnée en n'importe quelle loi asymétrique, les contre-hypothèses à la symétrie peuvent prendre toute forme imaginable. Ces méchanismes univariés, outre cette propriété de surjectivité, possèdent de nombreux autres attraits, mais ne permettent pas une extension satisfaisante aux dimensions supérieures. Pour cette raison, nous proposons au chapitre 5 des méchanismes généraux alternatifs, qui partagent toutes les propriétés de leurs compétiteurs de Ferreira and Steel (2006), mais qui en plus sont généralisables à n'importe quelle dimension. Nous démontrons formellement que la surjectivité tient en dimension k > 1 et étudions les caractéristiques principales de ces nouveaux méchanismes multivariés. Finalement, la troisième partie de cette thèse, composée du chapitre 6, propose un test de symétrie centrale multivariée en ayant recours aux concepts de profondeur statistique et de runs. Ce test étend le célèbre test de runs univarié de McWilliams (1990) aux dimensions supérieures. Nous en analysons le comportement asymptotique (surtout en dimension k = 2) sous l'hypothèse nulle et les propriétés d'invariance et de robustesse. Nous concluons par un aperçu sur des modifications possibles de ces nouveaux tests.

本論文以優選理論分析六家饒平客語和寧都田頭客語雙音節詞之連讀變調，並藉由聲調內部結構說明變調的動機。在六家饒平客語方面，主要是呈現位置變調(positional tone sandhi)，較有標(more marked)的聲調位於前字時發生變調。另外，此方言的陽平和陽去因歷史演變，兩者的本調(citation tone)同為HH，但兩者因不同的變調形式而產生不同的變調(sandhi tone)。陽去的變調形式為位置變調，而陽平的變調形式為環境變調(contextual tone sandhi)。本文採用聯合制約(Local Constraint Conjunction)捕捉環境變調制約運作的環境。另外，運用「詞素特定音韻」(morpheme-specific phonology)標記聯合制約，解釋陽平和陽去不同的變調規則。在寧都田頭客語方面，變調受詞法結構影響，且兩個音節皆有可能發生變調。本文利用標記制約理論(indexed constraints approach)解釋不同結構的變調情形。另藉由位置信實制約不同的排序，嘗試說明聲調的保留屬於類型差異(typological differences)。而此方言的變調類型包含位置變調和環境變調，同樣要求較有標的聲調改變，並使用聯合制約說明在環境變調的情況下制約運作的環境。 / This thesis investigates the tone sandhi in Liujia Raoping Hakka and Ningdu Tiantou Hakka under the framework of Optimality Theory. The internal structure of the tone reveals the motivation and the mechanism of tone sandhi. In terms of the tone sandhi in Liujia Raoping Hakka, the universal tonal markedness tendency could be regarded as the motivation triggering the positional tone sandhi in the left syllable. Moreover, the morpheme-specific phonology is adapted to account for the tone sandhi of historical merged tones, Yangping and Yangqu. Yangping and Yangqu are both high level tones; however, they display different tone sandhi patterns. Yangping displays the contextual tone sandhi whereas Yangqu displays the positional tone sandhi. Local conjunction constraints are posited to restrict markedness constraints to specific contexts in order to account for the mechanism of contextual tone sandhi. On the other hand, in terms of the tone sandhi in Ningdu Tiantou Hakka, the tone sandhi is construction sensitive and takes place in both syllables. The indexed constraint approach is adopted to explain the tone sandhi in different constructions. In addition, the preservation of tone is argued to be the typological difference according to different rankings of the positional faithfulness constraints. Finally, the tonal markedness tendency motivates the positional tone sandhi and the conjoined constraints are posited to govern the contextual tone sandhi in this dialect.

本論文觀察台灣地區國語閩南口音，也就是俗稱的「台灣國語」中展現的單元音化以及擦音卸解現象，建立「台灣國語語料庫」作為本論文分析的基礎，並且從優選理論的觀點探討這些台灣國語音韻現象。 根據「台灣國語語料庫」的數據顯示，韻核後介音 /j/ 以及 /w/ 容易被語者刪除，韻核前介音 /j/ 以及 /w/ 則傾向被語者保留。輕擦音 /f/ 在台灣國語中常被卸解為 /hw/。 本文的分析認為，國語閩南口音是一種方言的變異，反映了閩南語以及國語的部份制約排序。當語者表現出明顯的閩南語口音時，反映出閩南語的部份制約排序；而語者的閩南語口音較不明顯時，則反映了國語的部份制約排序。 / This thesis investigates monophthongization and fricative reconfiguration in the Taiwanese Accent of Mandarin (TM), and establishes the TM corpus as the base of phonological analysis. The Optimality Theory approach is adopted to account for the phonological phenomenon of TM. As indicated by the TM corpus, the postnuclear glides /j/ and /w/ tend to be deleted in TM; the prenuclear glides /j/ and /w/ tend to be preserved in TM; and the fricative /f/ tend to reconfigurate as /hw/ in TM. Our analysis considers that TM is a dialectal variation which reflects the subgrammars of Taiwanese and Mandarin. When the speaker shows a clear Taiwanese accent, the partially ordered ranking of Taiwanese is reflected; and when the speaker shows no obvious Taiwanese accent, the partially ordered ranking of Mandarin is reflected.

Nous considérons des processus de diffusion, définis par des équations différentielles stochastiques, et puis nous nous intéressons à des problèmes de premier passage pour les chaînes de Markov en temps discret correspon- dant à ces processus de diffusion. Comme il est connu dans la littérature, ces chaînes convergent en loi vers la solution des équations différentielles stochas- tiques considérées. Notre contribution consiste à trouver des formules expli- cites pour la probabilité de premier passage et la durée de la partie pour ces chaînes de Markov à temps discret. Nous montrons aussi que les résultats ob- tenus convergent selon la métrique euclidienne (i.e topologie euclidienne) vers les quantités correspondantes pour les processus de diffusion. En dernier lieu, nous étudions un problème de commande optimale pour des chaînes de Markov en temps discret. L’objectif est de trouver la valeur qui mi- nimise l’espérance mathématique d’une certaine fonction de coût. Contraire- ment au cas continu, il n’existe pas de formule explicite pour cette valeur op- timale dans le cas discret. Ainsi, nous avons étudié dans cette thèse quelques cas particuliers pour lesquels nous avons trouvé cette valeur optimale. / We consider diffusion processes, defined by stochastic differential equa- tions, and then we focus on first passage problems for Markov chains in dis- crete time that correspond to these diffusion processes. As it is known in the literature, these Markov chains converge in distribution to the solution of the stochastic differential equations considered. Our contribution is to obtain ex- plicit formulas for the first passage probability and the duration of the game for the discrete-time Markov chains. We also show that the results obtained converge in the Euclidean metric to the corresponding quantities for the diffu- sion processes. Finally we study an optimal control problem for Markov chains in discrete time. The objective is to find the value which minimizes the expected value of a certain cost function. Unlike the continuous case, an explicit formula for this optimal value does not exist in the discrete case. Thus we study in this thesis some particular cases for which we found this optimal value.

Thesis submitted for the joint institutional requirements for the double-badged degree of Doctor of Philosophy and Docteur de l'Université de Provence, Spécialité : Informatique. / Thesis (PhD)--Macquarie University, Division of Information and Communication Sciences, Department of Computing, 2008. / Includes bibliography (p. 229-240) and index. / Introduction -- Background -- A model-theoretic framework for PG -- Loose constraint-based parsing -- A computational model for gradience -- Conclusion. / The grammaticality of a sentence has conventionally been treated in a binary way: either a sentence is grammatical or not. A growing body of work, however, focuses on studying intermediate levels of acceptability, sometimes referred to as gradience. To date, the bulk of this work has concerned itself with the exploration of human assessments of syntactic gradience. This dissertation explores the possibility to build a robust computational model that accords with these human judgements. -- We suggest that the concepts of Intersective Gradience and Subsective Gradience introduced by Aarts for modelling graded judgements be extended to cover deviant language. Under such a new model, the problem then raised by gradience is to classify an utterance as a member of a specific category according to its syntactic characteristics. More specifically, we extend Intersective Gradience (IG) so that it is concerned with choosing the most suitable syntactic structure for an utterance among a set of candidates, while Subsective Gradience (SG) is extended to be concerned with calculating to what extent the chosen syntactic structure is typical from the category at stake. IG is addressed in relying on a criterion of optimality, while SG is addressed in rating an utterance according to its grammatical acceptability. As for the required syntactic characteristics, which serve as features for classifying an utterance, our investigation of different frameworks for representing the syntax of natural language shows that they can easily be represented in Model-Theoretic Syntax; we choose to use Property Grammars (PG), which offers to model the characterisation of an utterance. We present here a fully automated solution for modelling syntactic gradience, which characterises any well formed or ill formed input sentence, generates an optimal parse for it, then rates the utterance according to its grammatical acceptability. -- Through the development of such a new model of gradience, the main contribution of this work is three-fold. -- First, we specify a model-theoretic logical framework for PG, which bridges the gap observed in the existing formalisation regarding the constraint satisfaction and constraint relaxation mechanisms, and how they relate to the projection of a category during the parsing process. This new framework introduces the notion of loose satisfaction, along with a formulation in first-order logic, which enables reasoning about the characterisation of an utterance. -- Second, we present our implementation of Loose Satisfaction Chart Parsing (LSCP), a dynamic programming approach based on the above mechanisms, which is proven to always find the full parse of optimal merit. Although it shows a high theoretical worst time complexity, it performs sufficiently well with the help of heuristics to let us experiment with our model of gradience. -- And third, after postulating that human acceptability judgements can be predicted by factors derivable from LSCP, we present a numeric model for rating an utterance according to its syntactic gradience. We measure a good correlation with grammatical acceptability by human judgements. Moreover, the model turns out to outperform an existing one discussed in the literature, which was experimented with parses generated manually. / Mode of access: World Wide Web. / xxviii, 283 p. ill

Made available in DSpace on 2014-12-17T15:47:46Z (GMT). No. of bitstreams: 1 FrederikoSLNA.pdf: 5281687 bytes, checksum: 9fe12b6bcc355f7c67cf2f2c3ad9812b (MD5) Previous issue date: 2006-02-16 / This work performs an algorithmic study of optimization of a conformal radiotherapy plan treatment. Initially we show: an overview about cancer, radiotherapy and the physics of interaction of ionizing radiation with matery. A proposal for optimization of a plan of treatment in radiotherapy is developed in a systematic way. We show the paradigm of multicriteria problem, the concept of Pareto optimum and Pareto dominance. A generic optimization model for radioterapic treatment is proposed. We construct the input of the model, estimate the dose given by the radiation using the dose matrix, and show the objective function for the model. The complexity of optimization models in radiotherapy treatment is typically NP which justifyis the use of heuristic methods. We propose three distinct methods: MOGA, MOSA e MOTS. The project of these three metaheuristic procedures is shown. For each procedures follows: a brief motivation, the algorithm itself and the method for tuning its parameters. The three method are applied to a concrete case and we confront their performances. Finally it is analyzed for each method: the quality of the Pareto sets, some solutions and the respective Pareto curves / O presente trabalho realiza um Estudo Algor?tmico para Otimiza??o do Plano de Tratamento da Radioterapia Conformal. Inicialmente s?o apresentadas: uma vis?o geral sobre o c?ncer, o tratamento com radioterapia e no??es sobre a intera??o do feixe de radia??es ionizantes com a mat?ria. Uma proposta para Otimiza??o do Plano de Tratamento Radioter?pico ? desenvolvida de modo sistem?tico. ? apresentado o paradigma de problemas multicrit?rio, os conceitos de Pareto otimalidade e Pareto Domin?ncia. Um modelo Gen?rico de Otimiza??o para o Plano de Tratamento Radioter?pico ? proposto. S?o constru?das suas entradas, ? calculada a dose depositada no corpo do paciente atrav?s do conceito de matriz de dose, e ? apresentada a fun??o objetivo deste modelo. A complexidade dos problemas de otimiza??o do tratamento radioter?pico s?o classificados como de complexidade NP, este resultado justifica o desenvolvimento de m?todos heur?sticos para a sua resolu??o. S?o propostas tr?s metaheur?sticas para a Otimiza??o do Plano de Tratamento Radioter?pico: MOGA, MOSA e MOTS de acordo como o modelo gen?rico de otimiza??o proposto. Os projetos desses procedimentos metaheur?sticos s?o devidamente apresentados. Para cada m?todo se faz uma introdu??o liter?ria, dos seus algoritmos e a da metodologia usada para a afina??o dos par?metros. Os m?todos s?o aplicados a um caso concreto e confrontados atrav?s de medidas de performance. Finalmente ? analisado a qualidade dos conjuntos de Pareto produzidos por cada m?todo, s?o exibidas algumas solu??es geradas e as respectivas curvas de Pareto associadas

Al hoe meer organisasies in Suid-Afrika gaan tans deur 'n herstruktureringsfase wat meebring dat die totale werksmilieu verander. Die werknemer verkeer onder druk om aan die nuwe eise in die wereld van werk te voldoen. Druk om te presteer en werksuitset te !ewer mag disfunksionele stres en antler psigiese probleme meebring. Organisasies speel 'n belangrike rol in die dinamiese groeiproses van die individuele werknemer en raak toenemend bewus van die werknemer se fisiese en psigiese gesondheid. Talle organisasies het reeds korporatiewe gimnasiums opgerig en sommige bied subsidiering van lidmaatskap aan gesondheidsklubs aan hul werknemers. Sekere mediese skemas begin self gesondheidsplanne ontwerp met behulp van gesondheidsklubs om die gesondheid van die werknemer te bevorder. / M.A. (Bedryfsielkunde)

Les terres agricoles ont été durablement contaminées à la fois par les pesticides mis à la disposition des agriculteurs pour lutter contre les charançons et autres insectes nuisibles, et par les engrais azotées pour augmenter la productivité chez les plantes.Des recherches récentes concernent des cultures alternatives écologiques utilisant les plantes de service qui fournissent les nutriments aux plantes principales. Ce travail de thèse s'inscrit dans cette perspective, d'un point de vue modélisation.L'accent est mis sur la résolution de problèmes de contrôle du phénomène d'absorption de nutriments, par les racines dans la rhizosphère (partie proche des racines), en considérant les deux cas de sols : sol sain et sol pollué.Ces phénomènes d'absorption sont modélisés par des systèmes d'advection-diffusion de type Nye-Tinker-Barber (NTB). La concentration de nutriments absorbée, solution du problème, est une fonction du temps et de l'espace.On étudie l'existence de solution du système NTB dans les deux cas où la fonction d'absorption de nutriments à la frontière (surface de la racine) appelée fonction de Michealis-Menten, est linéaire et/ou non linéaire, à l’aide des outils d’analyse fonctionnelle. On étudie ensuite les problèmes de contrôle optimal associés au système NTB, en considérant les deux cas linéaire et non linéaire, en application pour les deux cas d’absorption de nutriments en sol non pollué puis en sol pollué. Pour le premier cas, on utilise les techniques classiques de recherche d'un contrôle pour les systèmes distribués, tandis que, pour le second cas, on fait appel aux notions de contrôle sans regret et contrôle à moindres regrets de J.-L. Lions. Les contrôles obtenus pour les différents problèmes sont caractérisés chacun par un système d'optimalité (SO) cas sans pollution, et système d’optimalité singulier (SOS) dans le cas avec pollution.= / Agriculture soils were highly contaminated for a long time by pesticides which were widely used by producers to fight against weevils. Soils where also contaminated by the use of fertilizers to increase the plant development. An ecological alternative using service plants is encouraged following recent research. The aim of this work is to give a mathematical and a modelling point of view as we study the mecha- nisms of nutrient transfer to plants using the mathematical analysis and optimal control theories. The two cases of polluted and non-polluted soils are considered. The nutrient transfer and uptake processes are modeled by an advection-diffusion system derived from the Nye-Tinker-Barber (NTB) model. The absorbed nutrient concentration represented by the Michaelis-Mention function at the root surface of the principal plant, depends on time and space. We study the existence of a solution for the linear and nonlinear NTB systems, then we characterize the opti- mal control which corresponds to the added nutrients from the service plant. For the pollution case, we use the concept of low-regret and no-regret control of J.-L. Lions.