Résumé : Depuis la fin du XXème siècle, l’augmentation du prix du pétrole brut et les problématiques environnementales poussent l’industrie automobile à développer des technologies plus économes en carburant et générant moins d’émissions de gaz à effet de serre. Parmi ces technologies, les véhicules électriques hybrides constituent une solution viable et performante. En alliant un moteur électrique et un moteur à combustion, ces véhicules possèdent un fort potentiel de réduction de la consommation de carburant sans sacrifier son autonomie. La présence de deux moteurs et de deux sources d’énergie requiert un contrôleur, appelé système de gestion d’énergie, responsable de la commande simultanée des deux moteurs. Les performances du véhicule en matière de consommation dépendent en partie de la conception de ce contrôleur. Les véhicules électriques hybrides rechargeables, plus récents que leur équivalent non rechargeable, se distinguent par l’ajout d’un chargeur interne permettant la recharge de la batterie pendant l’arrêt du véhicule et par conséquent la décharge de celle-ci au cours d’un trajet. Cette particularité ajoute un degré de complexité pour ce qui est de la conception du système de gestion d’énergie. Dans cette thèse, nous proposons un modèle complet du véhicule dédié à la conception du contrôleur. Nous étudions ensuite la dépendance de la commande optimale des deux moteurs par rapport au profil de vitesse suivi au cours d’un trajet ainsi qu’à la quantité d’énergie électrique disponible au début d’un trajet. Cela nous amène à proposer une technique d’auto-apprentissage visant l’amélioration de la stratégie de gestion d’énergie en exploitant un certain nombre de données enregistrées sur les trajets antérieurs. La technique proposée permet l’adaptation de la stratégie de contrôle vis-à-vis du trajet en cours en se basant sur une pseudo-prédiction de la totalité du profil de vitesse. Nous évaluerons les performances de la technique proposée en matière de consommation de carburant en la comparant avec une stratégie optimale bénéficiant de la connaissance exacte du profil de vitesse ainsi qu’avec une stratégie de base utilisée couramment dans l’industrie. // Abstract : Since the end of the XXth century, the increase in crude oil price and the environmental concerns lead the automotive industry to develop technologies that can improve fuel savings and decrease greenhouse gases emissions. Among these technologies, the hybrid electric vehicles stand as a reliable and efficient solution. By combining an electrical motor and an internal combustion engine, these vehicles can bring a noticeable improvement in terms of fuel consumption without sacrificing the vehicle autonomy. The two motors and the two energy storage systems require a control unit, called energy management system, which is responsible for the command decision of both motors. The vehicle performances in terms of fuel consumption greatly depend on this control unit. The plug-in hybrid electric vehicles are a more recent technology compared to their non plug-in counterparts. They have an extra internal battery charger that allows the battery to be charged during OFF state, implying a possible discharge during a trip. This particularity adds complexity when it comes to the design of the energy management system. In this thesis, a complete vehicle model is proposed and used for the design of the controller. A study is then carried out to show the dependence between the optimal control of the motors and the speed profile followed during a trip as well as the available electrical energy at the beginning of a trip. According to this study, a self-learning optimization technique that aims at improving the energy management strategy by exploiting some driving data recorded on previous trips is proposed. The technique allows the adaptation of the control strategy to the current trip based on a pseudo-prediction of the total speed profile. Fuel consumption performances for the proposed technique will be evaluated by comparing it with an optimal control strategy that benefits from the exact a priori knowledge of the speed profile as well as a basic strategy commonly used in industry.

Achieving robust and reliable autonomous operation even in complex unstructured environments is a central goal of field robotics. As the environments and scenarios to which robots are applied have continued to grow in complexity, so has the challenge of properly defining preferences and tradeoffs between various actions and the terrains they result in traversing. These definitions and parameters encode the desired behavior of the robot; therefore their correctness is of the utmost importance. Current manual approaches to creating and adjusting these preference models and cost functions have proven to be incredibly tedious and time-consuming, while typically not producing optimal results except in the simplest of circumstances. This thesis presents the development and application of machine learning techniques that automate the construction and tuning of preference models within complex mobile robotic systems. Utilizing the framework of inverse optimal control, expert examples of robot behavior can be used to construct models that generalize demonstrated preferences and reproduce similar behavior. Novel learning from demonstration approaches are developed that offer the possibility of significantly reducing the amount of human interaction necessary to tune a system, while also improving its final performance. Techniques to account for the inevitability of noisy and imperfect demonstration are presented, along with additional methods for improving the efficiency of expert demonstration and feedback. The effectiveness of these approaches is confirmed through application to several real world domains, such as the interpretation of static and dynamic perceptual data in unstructured environments and the learning of human driving styles and maneuver preferences. Extensive testing and experimentation both in simulation and in the field with multiple mobile robotic systems provides empirical confirmation of superior autonomous performance, with less expert interaction and no hand tuning. These experiments validate the potential applicability of the developed algorithms to a large variety of future mobile robotic systems.

In this thesis, we develop preconditioned iterative methods for the solution of matrix systems arising from PDE-constrained optimization problems. In order to do this, we exploit saddle point theory, as this is the form of the matrix systems we wish to solve. We utilize well-known results on saddle point systems to motivate preconditioners based on effective approximations of the (1,1)-block and Schur complement of the matrices involved. These preconditioners are used in conjunction with suitable iterative solvers, which include MINRES, non-standard Conjugate Gradients, GMRES and BiCG. The solvers we use are selected based on the particular problem and preconditioning strategy employed. We consider the numerical solution of a range of PDE-constrained optimization problems, namely the distributed control, Neumann boundary control and subdomain control of Poisson's equation, convection-diffusion control, Stokes and Navier-Stokes control, the optimal control of the heat equation, and the optimal control of reaction-diffusion problems arising in chemical processes. Each of these problems has a special structure which we make use of when developing our preconditioners, and specific techniques and approximations are required for each problem. In each case, we motivate and derive our preconditioners, obtain eigenvalue bounds for the preconditioners where relevant, and demonstrate the effectiveness of our strategies through numerical experiments. The goal throughout this work is for our iterative solvers to be feasible and reliable, but also robust with respect to the parameters involved in the problems we consider.

This dissertation progressively addresses research problems related to the trajectory optimization for fuel cell powered UAVs, from propulsion system model development, to optimal trajectory analyses and optimal trajectory applications. A dynamic model of a fuel cell powered UAV propulsion system is derived by combining a fuel cell system dynamic model, an electric motor dynamic model, and a propeller performance model. The influence of the fuel cell system dynamics on the optimal trajectories of a fuel cell powered UAV is investigated in two phases. In the first phase, the optimal trajectories of a fuel cell powered configuration and that of a conventional gas powered configuration are compared for point-to-point trajectory optimization problems with different performance index functions. In the second phase, the influence of the fuel cell system parameters on the optimal fuel consumption cost of the minimum fuel point-to-point optimal trajectories is investigated. This dissertation also presents two applications for the minimum fuel point-to-point optimal trajectories of a fuel cell powered UAV: three-dimensional minimum fuel route planning and path generation, and fuel cell system size optimization with respect to a UAV mission.

Asymptotic stability is a key notion of system stability for controlled dynamical systems as it guarantees that the system trajectories are bounded in a neighborhood of a given isolated equilibrium point and converge to this equilibrium over the infinite horizon. In some applications, however, asymptotic stability is not the appropriate notion of stability. For example, for systems with a continuum of equilibria, every neighborhood of an equilibrium contains another equilibrium and a nonisolated equilibrium cannot be asymptotically stable. Alternatively, in stabilization of spacecraft dynamics via gimballed gyroscopes, it is desirable to find state- and output-feedback control laws that guarantee partial-state stability of the closed-loop system, that is, stability with respect to part of the system state. Furthermore, we may additionally require finite-time stability of the closed-loop system, that is, convergence of the system's trajectories to a Lyapunov stable equilibrium in finite time. The Hamilton-Jacobi-Bellman optimal control framework provides necessary and sufficient conditions for the existence of state-feedback controllers that minimize a given performance measure and guarantee asymptotic stability of the closed-loop system. In this research, we provide extensions of the Hamilton-Jacobi-Bellman optimal control theory to develop state-feedback control laws that minimize nonlinear-nonquadratic performance criteria and guarantee semistability, partial-state stability, finite-time stability, and finite-time partial state stability of the closed-loop system.

The Earth harbors around 300 000 plant species. The rich and complex environment provided by plants is considered a key factor for the extraordinary diversity of the terrestrial fauna by, for example, providing food and shelter. This thesis contributes to the understanding of these questions by investigating how the interplay of physiology, demography, and evolution gives rise to variation and diversity in fundamental plant traits. This will help us answer questions such as: How has this amazing diversity of plant species emerged? Which mechanisms maintain diversity? How are plant strategies and plant diversity influenced by variations in the environment? A plant faces multiple problems to survive and reproduce successfully. These problems can be modeled by considering traits, trade-offs and a fitness measure. For example: How to maximize growth rate, while maximizing structural stability? I will investigate four plant models in order to understand the function of plants, and mechanisms promoting diversity.  Paper I: We study how annual plants with and without growth constraints should optimize their flowering time when productivity or season length changes. With a dynamic ontogenetic growth model and optimal control theory we prove that a bang-bang reproductive control is optimal under constrained growth and constant mortality rate. We find that growth constraints can flip the direction of optimal phenological response for increasing productivity. The reason is that the growth rate of vegetative mass saturates at high productivity and therefore it is better to flower earlier and take advantage of a longer reproductive period. If season length extends equally both in the beginning and the end of the season, growth constraints control the direction of the optimal response as well. Our theory can help explaining phenological patterns along productivity gradients, and can be linked to empirical observations made on a calendar scale. Paper II: We introduce a new measure of tree crown-rise efficiency based on the loss of biomass of the tree during growth. The more mass the tree looses during growth, the less crown-rise efficient it is. Top-heavy shapes loose more biomass than bottom-heavy shapes. Light-use efficiency is defined as the mean light assimilation of the leaves in the crown times the ratio of leaf mass and total mass. We then study the trade-off between light-use efficiency to crown-rise efficiency for tree crown shapes. We assume that the total tree mass is constant, and a constant vertical light gradient represent the shading from a surrounding forest. We find large differences in crown shapes at intermediate vertical light gradient, when both self-shading and mean-field shading are important, suggesting light-use vs crown-rise efficiency as a new trade-off that can explain tree diversity. Our crown-rise efficiency measure could easily be integrated into existing forest models. Paper III: We extend an evolutionary tree crown model, where trees with different heights compete for light, with drought-induced mortality rates depending on ground-water availability and the depth of an optional taproot. The model does not include competition for ground water. Our model explains how ground-water availability can shape plant communities, when taproot and non-taproot strategies can coexist, and when only one of these strategies can persist. We investigate how emerging plant diversity varies with water table depth, soil water gradient and drought-induced mortality rate. The taproot enables plants to reach deep water, thus reducing mortality, but also carries a construction cost, thus inducing a trade-off. We find that taproots maintain plant diversity under increasing drought mortality, and that taproots evolve when groundwater is accessible at low depths. There are no viable strategies at high drought mortality and deep water table. Red Queen evolutionary dynamics appear at intermediate drought mortality in mixed communities with and without taproots, as the community never reaches a final evolutionarily stable composition. Paper IV: We extend a size-structured plant model, with self-shading and two evolving traits, crown top-heaviness and crown width-to-height ratio. The model allows us to identify salient trade-offs for the crown shape. The most important trade-off for top-heaviness is light-use efficiency vs crownrise efficiency, and the most important trade-off for width-to-height ratio is self-shading vs branch costs. We find that when the two traits coevolve; the outcome is a single common evolutionarily stable strategy (ESS), far away from the highest net primary production (NPP). When only sun angle is decreasing with increasing latitude both the crown width-to-height ratio and crown top-heaviness decrease. However, when light response in addition to the sun angle decreases with increasing latitude, the crown width-to-height ratio is nearly invariant of latitude except at low site productivity when the ratio decreases with latitude. Top-heaviness is always decreasing with increasing latitude. Finally, we find that crown top-heaviness increases with the NPP or leaf-area index (LAI) at ESS, but crown width-to-height ratio is maximal at an intermediate NPP or LAI. / Artikel I: Arters reproduktionsframgång (fitness), till exempel antal avkommor eller frön som produceras under livet, är ofta avgörande för huruvida de är evolutionärt framgångsrika eller inte. Här undersöker vi hur ettåriga växter med eller utan tillväxtbegränsningar ska optimera sin blomningstid när produktivitet eller säsongslängd ändras. Det är optimalt att gå direkt från tillväxt till blomning när tillväxten är begränsad och dödligheten är konstant. Vid ökad produktivitet sker blomningen tidigare med tillväxtbegränsningar men senare utan tillväxtbegränsningar, vilket beror på att med tillväxtbegränsningar ökar den vegetativa massan långsamt. Därför är det bättre att blomma tidigare och ta tillvara på en längre reproduktionsperiod. Vi får samma resultat om säsongslängden ökar lika mycket i början och slutet av säsongen. Vår teori kan bidra till att förutsäga blomningstider vid produktivitetsförändringar och säsongsförändringar. Artikel II: Tillväxten hos träd kan begränsas av brist på ljus, vatten, och näring, men också genom förlust av grenar. Vi introducerar ett nytt mått på tillväxteffektiviteten hos trädkronor baserat på förlust av biomassa under trädets tillväxt. Ju mer massa trädet förlorar under tillväxt, desto mindre tillväxteffektiva är de. Topptunga former förlorar mer biomassa än bottentunga former. Vi studerar avvägningar mellan ljuseffektivitet och tillväxteffektivitet för trädformer, där ljuseffektiviteten definieras som medelljusupptaget för löven i kronan. Vi antar en konstant totalmassa, och en statisk vertikal skuggning som representerar skuggningen från en omgivande skog. Vi hittar stora skillnader i kronformer vid en medelhög skuggning, då både självskuggningen och medelskuggningen har betydelse. Vårt mått för tillväxteffektivitet kan enkelt integreras i existerande skogsmodeller. Studien visar att avvägningar mellan tillväxteffektivitet och ljuseffektivitetet kan vara viktig för mångfalden av trädformer i en skog. En överraskande upptäckt är att konformade eller sfäriska trädkronor aldrig är effektiva, men däremot timglasformade kronor. Artikel III: Växter kan försvara sig på olika sätt mot torka, till exempel genom att rulla ihop bladen eller genom att reproducera tidigare och därigenom undvika uttdragen torka. Här undersöker vi fördelarna med en pålrot vid torka. En pålrot är en rot som växer nedåt för att nå djupliggande grundvatten. Vi utvidgar en evolutionär modell av trädkronor med grundvatten och en pålrot, där träd med olika höjd konkurrerar om ljus. Det finns ingen konkurrens om vatten. Vi undersöker hur mångfalden hos träden beror på vattendjup, vattengradient och dödlighet orsakad av torka. Med hjälp av pålroten kan träden nå djupt vatten och därigenom minska dödligheten, men den medför också en kostnad, så en avvägning måste göras. Vi ser att pålrötter upprätthåller mångfalden hos växterna vid ökad mortalitet, och att pålrötter uppstår när grundvattnet är grunt. Det finns inga strategier som kan överleva om grundvattnet är djupt och dödligheten är hög. Vår modell kan förklara hur grundvatten kan förändra sammansättningen på trädsamhällen, när träd med och utan pålrot kan samexistera, och under vilka förutsättningar endast en av strategierna förväntas dominera. Artikel IV: Träd som växer upp i en skog måste konkurrera med andra träd om ljus, framförallt större träd. Detta ger upphov till en asymmetrisk ljuskonkurrens, där de små träden hämmas av större träd. Små träd har därmed små chanser att överleva utom då skogen nyligen störts och det öppnas upp en glänta. Vid denna ljuskonkurrens kan man anta att trädkronans form har stor betydelse för trädets framgång. Frågan är hur de evolutionärt fördelaktiga kronformerna beror på latituden och produktiviteten. Vi antar att latituden påverkar solens genomsnittliga vinkel och ljusrespons. Vi utvidgar en storleksstrukturerad trädmodell med självskuggning där två evolverande egenskaper beskriver kronans topptyngd och bredd. Med modellen kan vi undersöka vilka strategiska avvägningar som bestämmer om kronans form blir konkurrenskraftig. En topptung krona har högt ljusupptag eftersom det finns mest ljus högt upp i grenverket. Å andra sidan har den en låg tillväxteffektivitet eftersom topptunga kronor måste tappa mycket grenar för att behålla sin form. En bred krona har en låg självskuggning eftersom bladen är utspridda. Å andra sidan har den höga kostnader för de långa grenar som krävs. Vi finner att när dessa egenskaper evolverar tillsammans så finns endast en evolutionärt stabil strategi (ESS), långt från den högsta nettoproduktionen. När endast solvinkeln minskar med ökande latitud minskar både kronans bredd och topptyngd, men när både solvinkel och ljusrespons minskar med ökande latitud så är bredden nästan oförändrad utom vid låg produktivitet då den minskar med latituden. Kronans topptyngd minskar alltid med latituden. Slutligen ser vi hur kronans topptyngd alltid ökar med nettoproduktionen vid ESS, medan kronans bredd har ett maxium för ett mellanvärde hos nettoproduktionen vid ESS.

Renewable energy is key to a sustainable future. However, the intermittency of most renewable sources and lack of sufficient storage in the current power grid means that reliable integration of significantly more renewables will be a challenging task. Moreover, increased integration of renewables not only increases uncertainty, but also reduces the fraction of traditional controllable generation capacity that is available to cope with supply-demand imbalances and uncertainties. Less traditional generation also means less rotating mass that provides very short term, yet very important, kinetic energy storage to the system and enables mitigation of the frequency drop subsequent to major contingencies but before controllable generation can increase production. Demand, on the other side, has been largely regarded as non-controllable and inelastic in the current setting. However, there is strong evidence that a considerable portion of the current and future demand, such as electric vehicle load, is flexible. That is, the instantaneous power delivered to it needs not to be bound to a specific trajectory. In this thesis, we focus on harnessing demand flexibility as a key to enabling more renewable integration and cost reduction. We start with a data driven analysis of the potential of flexible demands, particularly plug-in electric vehicle (PEV) load. We first show that, if left unmanaged, these loads can jeopardize grid reliability by exacerbating the peaks in the load profile and increasing the negative correlation of demand with wind energy production. Then, we propose a simple local policy with very limited information and minimal coordination that besides avoiding undesired effects, has the positive side-effect of substantially increasing the correlation of flexible demand with wind energy production. Such local policies could be readily implemented as modifications to existing "grid friendly" charging modes of plug-in electric vehicles. We then propose improved localized charging policies that counter balance intermittency by autonomously responding to frequency deviations from the nominal frequency and show that PEV load can offer a substantial amount of such ancillary services. Next, we consider the case where real-time prices are employed to provide incentives for demand response. We consider a flexible load under such a pricing scheme and obtain the optimal policy for responding to stochastic price signals to minimize the expected cost of energy. We show that this optimal policy follows a multi-threshold form and propose a recursive method to obtain these thresholds. We then extend our results to obtain optimal policies for simultaneous energy consumption and ancillary service provision by flexible loads as well as optimal policies for operation of storage assets under similar real-time stochastic prices. We prove that the optimal policy in all these cases admits a computationally efficient form. Moreover, we show that while optimal response to prices reduces energy costs, it will result in increased volatility in the aggregate demand which is undesirable. We then discuss how aggregation of flexible loads can take us a step further by transforming the loads to controllable assets that help maintain grid reliability by counterbalancing the intermittency due to renewables. We explore the value of load flexibility in the context of a restructured electricity market. To this end, we introduce a model that economically incentivizes the load to reveal its flexibility and provides cost-comfort trade-offs to the consumers. We establish the performance of our proposed model through evaluation of the price reductions that can be provided to the users compared to uncontrolled and uncoordinated consumption. We show that a key advantage of aggregation and coordination is provision of "regulation" to the system by load, which can account for a considerable price reduction. The proposed scheme is also capable of preventing distribution network overloads. Finally, we extend our flexible load coordination problem to a multi-settlement market setup and propose a stochastic programming approach in obtaining day-ahead market energy purchases and ancillary service sales. Our work demonstrates the potential of flexible loads in harnessing renewables by affecting the load patterns and providing mechanisms to mitigate the inherent intermittency of renewables in an economically efficient manner. / text

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本文以最適控制理論證明，獎勵再生能源產出之政策，應以再生能源淨能源產出做為獎勵的基礎，而非現行以再生能源總能源產出做為獎勵基礎之模式。這裡的淨能源產出，指的是再生能源廠商生產出之再生能源，減去生產再生能源時所用的能源投入。本文首先將社會最適情況下的總能源產出分別與以淨能源產出和總能源產出為獎勵政策基礎之價格與數量政策下之總能源產出作比較，提出獎勵再生能源產出的政策，需以淨能源產出做為獎勵的基礎，而非現行以總能源產出作為基礎的政策，接著，在以淨能源產出為基礎的政策下，探討環境外部性與防治成本以及研究發展的議題。 / By the optimal control theory, this paper proves that policies on encouraging the production of renewable energy should be based on its net output or net energy instead of on its gross output or gross energy. Here net energy is defined as the surplus of renewable energy output minus energy input from its production. This paper first compares the optimal gross output of the renewable energy under the social optimal condition with the gross outputs under the price-based policy instrument and the quantity-based policy instrument based on net energy output and gross energy output, respectively, suggesting that policy instruments used to encourage the production of renewable energy should be based on its net output instead of on its gross output. Finally, it probes the cases of environmental externality and R&D based on the net output of renewable energy.

The problem addressed in this research is the in-flight generation of trajectories for autonomous unmanned aircraft, which requires a method of generating pseudo-optimal trajectories in near-real-time, on-board the aircraft, and without external intervention. The focus of this research is the enhancement of a particular inverse dynamics direct method that is a candidate solution to the problem. This research introduces the following contributions to the method. A quaternion-based inverse dynamics model is introduced that represents all orientations without singularities, permits smooth interpolation of orientations, and generates more accurate controls than the previous Euler-angle model. Algorithmic modifications are introduced that: overcome singularities arising from parameterization and discretization; combine analytic and finite difference expressions to improve the accuracy of controls and constraints; remove roll ill-conditioning when the normal load factor is near zero, and extend the method to handle negative-g orientations. It is also shown in this research that quadratic interpolation improves the accuracy and speed of constraint evaluation. The method is known to lead to a multimodal constrained nonlinear optimization problem. The performance of the method with four nonlinear programming algorithms was investigated: a differential evolution algorithm was found to be capable of over 99% successful convergence, to generate solutions with better optimality than the quasi- Newton and derivative-free algorithms against which it was tested, but to be up to an order of magnitude slower than those algorithms. The effects of the degree and form of polynomial airspeed parameterization on optimization performance were investigated, and results were obtained that quantify the achievable optimality as a function of the parameterization degree. Overall, it was found that the method is a potentially viable method of on-board near- real-time trajectory generation for unmanned aircraft but for this potential to be realized in practice further improvements in computational speed are desirable. Candidate optimization strategies are identified for future research.