<p>Forest management involves numerous stochastic elements. To sustainably manage forest resources, it is crucial to acknowledge these sources as uncertainty or risk, and incorporate them in adaptive decision-making. Here, I developed several stochastic programming models in the form of passive or active adaptive management for natural mixed-species hardwood forests in Indiana. I demonstrated how to use these tools to deal with time-invariant and time-variant natural disturbances in optimal planning of harvests.</p> <p> Markov decision process (MDP) models were first constructed based upon stochastic simulations of an empirical forest growth model for the forest type of interest. Then, they were optimized to seek the optimal or near-optimal harvesting decisions while considering risk and uncertainty in natural disturbances. In particular, a classic expected-criterion infinite-horizon MDP model was first used as a passive adaptive management tool to determine the optimal action for a specific forest state when the probabilities of forest transition remained constant over time. Next, a two-stage non-stationary MDP model combined with a rolling-horizon heuristic was developed, which allowed information update and then adjustments of decisions accordingly. It was used to determine active adaptive harvesting decisions for a three-decade planning horizon during which natural disturbance probabilities may be altered by climate change.</p> <p> The empirical results can be used to make some useful quantitative management recommendations, and shed light on the impacts of decision-making on the forests and timber yield when some stochastic elements in forest management changed. In general, the increase in the likelihood of damages by natural disturbance to forests would cause more aggressive decisions if timber production was the management objective. When windthrow did not pose a threat to mixed hardwood forests, the average optimal yield of sawtimber was estimated to be 1,376 ft³/ac/acre, while the residual basal area was 88 ft²/ac. Assuming a 10 percent per decade probability of windthrow that would reduce the stand basal area considerably, the optimal sawtimber yield per decade would decline by 17%, but the residual basal area would be lowered only by 5%. Assuming that the frequency of windthrow increased in the magnitude of 5% every decade under climate change, the average sawtimber yield would be reduced by 31%, with an average residual basal area slightly around 76 ft²/ac. For validation purpose, I compared the total sawtimber yield in three decades obtained from the heuristic approach to that of a three-decade MDP model making <i>ex post</i> decisions. The heuristic approach was proved to provide a satisfactory result which was only about 18% lower than the actual optimum.</p> These findings highlight the need for landowners, both private and public, to monitor forests frequently and use flexible planning approaches in order to anticipate for climate change impacts. They also suggest that climate change may considerably lower sawtimber yield, causing a concerning decline in the timber supply in Indiana. Future improvements of the approaches used here are recommended, including addressing the changing stumpage market condition and developing a more flexible rolling-horizon heuristic approach.

Early diagnosis is a promising strategy to reduce premature mortalities and for optimal use of resources. But the absence of mathematical models specific to the data settings in LMIC’s impedes the construction of economic analysis necessary for decision-makers in the development of cancer control programs. This thesis presents a new methodology for parameterizing the natural history model of breast cancer based on data availabilities in low and middle income countries, and formulation of a control optimization problem to find the optimal screening schedule for mammography screening, solved using dynamic programming. As harms and benefits are known to increase with the increase in the number of lifetime screens, the trade-off was modeled by formulating the immediate reward as a function of false positives and life-years saved. The method presented in thesis will provide optimal screening schedules for multiple scenarios of Willingness to Pay (numeric value assigned for each life-year lived), including the resulting total number of lifetime screens per person, which can help decision-makers evaluate current resource availabilities or plan future resource needs for implementation.

In this thesis we focus on new methods for probabilistic model checking (PMC) with linear temporal logic (LTL). The standard approach translates an LTL formula into a deterministic ω-automaton with a double-exponential blow up. There are approaches for Markov chain analysis against LTL with exponential runtime, which motivates the search for non-deterministic automata with restricted forms of non-determinism that make them suitable for PMC. For MDPs, the approach via deterministic automata matches the double-exponential lower bound, but a practical application might benefit from approaches via non-deterministic automata. We first investigate good-for-games (GFG) automata. In GFG automata one can resolve the non-determinism for a finite prefix without knowing the infinite suffix and still obtain an accepting run for an accepted word. We explain that GFG automata are well-suited for MDP analysis on a theoretic level, but our experiments show that GFG automata cannot compete with deterministic automata. We have also researched another form of pseudo-determinism, namely unambiguity, where for every accepted word there is exactly one accepting run. We present a polynomial-time approach for PMC of Markov chains against specifications given by an unambiguous Büchi automaton (UBA). Its two key elements are the identification whether the induced probability is positive, and if so, the identification of a state set inducing probability 1. Additionally, we examine the new symbolic Muller acceptance described in the Hanoi Omega Automata Format, which we call Emerson-Lei acceptance. It is a positive Boolean formula over unconditional fairness constraints. We present a construction of small deterministic automata using Emerson-Lei acceptance. Deciding, whether an MDP has a positive maximal probability to satisfy an Emerson-Lei acceptance, is NP-complete. This fact has triggered a DPLL-based algorithm for deciding positiveness.

Probabilistic model checking mainly concentrates on techniques for reasoning about the probabilities of certain path properties or expected values of certain random variables. For the quantitative system analysis, however, there is also another type of interesting performance measure, namely quantiles. A typical quantile query takes as input a lower probability bound p ∈ ]0,1] and a reachability property. The task is then to compute the minimal reward bound r such that with probability at least p the target set will be reached before the accumulated reward exceeds r. Quantiles are well-known from mathematical statistics, but to the best of our knowledge they have not been addressed by the model checking community so far. In this paper, we study the complexity of quantile queries for until properties in discrete-time finite-state Markov decision processes with nonnegative rewards on states. We show that qualitative quantile queries can be evaluated in polynomial time and present an exponential algorithm for the evaluation of quantitative quantile queries. For the special case of Markov chains, we show that quantitative quantile queries can be evaluated in pseudo-polynomial time.

Cette étude s’inscrit dans le domaine de l’intelligence artificielle, plus précisément au croisement des deux domaines que sont la planification autonome en environnement probabiliste et la vérification formelle probabiliste. Dans ce contexte, elle pose la question de la maîtrise de la complexité face à l’intégration de nouvelles technologies dans les systèmes critiques : comment garantir que l’ajout d’une intelligence à un système, sous la forme d’une autonomie, ne se fasse pas au détriment de la sécurité ? Pour répondre à cette problématique, cette étude a pour enjeu de développer un processus outillé, permettant de concevoir des systèmes auto-adaptatifs critiques, ce qui met en œuvre à la fois des méthodes de modélisation formelle des connaissances d’ingénierie, ainsi que des algorithmes de planification sûre et optimale des décisions du système. / This study takes place in the broad field of Artificial Intelligence, specifically at the intersection of two domains : Automated Planning and Formal Verification in probabilistic environment. In this context, it raises the question of the integration of new technologies in critical systems, and the complexity it entails : How to ensure that adding intelligence to a system, in the form of autonomy, is not done at the expense of safety ? To address this issue, this study aims to develop a tool-supported process for designing critical, self-adaptive systems. Throughout this document, innovations are therefore proposed in methods of formal modeling and in algorithms for safe and optimal planning.

Cette thèse aborde différents aspects de la modélisation de la microstructure du marché et des problèmes de Market Making, avec un accent particulier du point de vue du praticien. Le carnet d’ordres, au cœur du marché financier, est un système de files d’attente complexe à haute dimension. Nous souhaitons améliorer la connaissance du LOB pour la communauté de la recherche, proposer de nouvelles idées de modélisation et développer des applications pour les Market Makers. Nous remercions en particuler l’équipe Automated Market Making d’avoir fourni la base de données haute-fréquence de très bonne qualité et une grille de calculs puissante, sans laquelle ces recherches n’auraient pas été possible. Le Chapitre 1 présente la motivation de cette recherche et reprend les principaux résultats des différents travaux. Le Chapitre 2 se concentre entièrement sur le LOB et vise à proposer un nouveau modèle qui reproduit mieux certains faits stylisés. A travers cette recherche, non seulement nous confirmons l’influence des flux d’ordres historiques sur l’arrivée de nouveaux, mais un nouveau modèle est également fourni qui réplique beaucoup mieux la dynamique du LOB, notamment la volatilité réalisée en haute et basse fréquence. Dans le Chapitre 3, l’objectif est d’étudier les stratégies de Market Making dans un contexte plus réaliste. Cette recherche contribueà deux aspects : d’une part le nouveau modèle proposé est plus réaliste mais reste simple à appliquer pour la conception de stratégies, d’autre part la stratégie pratique de Market Making est beaucoup améliorée par rapport à une stratégie naive et est prometteuse pour l’application pratique. La prédiction à haute fréquence avec la méthode d’apprentissage profond est étudiée dans le Chapitre 4. De nombreux résultats de la prédiction en 1- étape et en plusieurs étapes ont retrouvé la non-linéarité, stationarité et universalité de la relation entre les indicateurs microstructure et le changement du prix, ainsi que la limitation de cette approche en pratique. / This thesis addresses different aspects around the market microstructure modelling and market making problems, with a special accent from the practitioner’s viewpoint. The limit order book (LOB), at the heart of financial market, is a complex continuous high-dimensional queueing system. We wish to improve the knowledge of LOB for the research community, propose new modelling ideas and develop concrete applications to the interest of Market Makers. We would like to specifically thank the Automated Market Making team for providing a large high frequency database of very high quality as well as a powerful computational grid, without whom these researches would not have been possible. The first chapter introduces the incentive of this research and resumes the main results of the different works. Chapter 2 fully focuses on the LOB and aims to propose a new model that better reproduces some stylized facts. Through this research, not only do we confirm the influence of historical order flows to the arrival of new ones, but a new model is also provided that captures much better the LOB dynamic, notably the realized volatility in high and low frequency. In chapter 3, the objective is to study Market Making strategies in a more realistic context. This research contributes in two aspects : from one hand the newly proposed model is more realistic but still simple enough to be applied for strategy design, on the other hand the practical Market Making strategy is of large improvement compared to the naive one and is promising for practical use. High-frequency prediction with deep learning method is studied in chapter 4. Many results of the 1-step and multi-step prediction have found the non-linearity, stationarity and universality of the relationship between microstructural indicators and price change, as well as the limitation of this approach in practice.

Energy management systems (EMSs), implemented in the electronic control unit (ECU) of an actual vehicle with electri ed powertrain, is a much simpler version of the theoretically developed EMS. Such simpli cation is done to accommodate the EMS within the given memory constraint and computational capacity of the ECU. The simpli cation should ensure reasonable performance compared to theoretical EMS under real-life driving scenarios. The process of simpli cation must be effective to create a versatile and utilitarian EMS. The reinforcement learning-based controllers feature pro table characteristics in optimizing the performance of controllable physical systems as they do not mandatorily require a mathematical model of system dynamics (i.e. they are model-free). Quite naturally, it can aspired to testify such prowess of reinforcement learning-based controllers in achieving near-global optimal performance for energy management system (supervisory) of electri ed powertrains. Before deployment of any supervisory controller as a mainstream controller, they should be essentially scrutinized through various levels of virtual simulation platforms with an ascending order of physical system emulating-capability. The controller evolves from a mathematical concept to an utilitarian embedded system through a series of these levels where it undergoes gradual transformation to finally become apposite for a real physical system. Implementation of the control strategy in a Simulink-based forward simulation model could be the first stage of the aforementioned evolution process. This brief will delineate all the steps required for implementing an reinforcement learning-based supervisory controller in a forward simulation model of a hybrid electric vehicle. A novel framework of loss-minimization based instantaneous optimal strategy is introduced for the energy management system of a multi-mode hybrid electric powertrain in this brief. The loss-minimization strategy is flexible enough to be implemented in any architecture of electrified powertrains. It is mathematically proven that the overall system loss minimization is equivalent to the minimization of fuel consumption. An online simulation framework is developed in this article to evaluate the performance of a multi-mode electrified powertrain equipped with more than one power source. An electrically variable transmission with two planetary gear-set has been chosen as the centerpiece of the powertrain considering the versatility and future prospects of such transmissions. It is noteworthy to mention that a novel architecture topology selected for this dissertation is engendered through a series of rigorous screening process whose workflow is presented here with brevity. One of the legitimate concern of multi-mode transmission is it's proclivity to contribute discontinuity of power-flow in the downstream of the powertrain. Mode-shift events can be predominantly held responsible for engendering such discontinuity. Advent of dynamic coordinated control as a technique for ameliorating such discontinuity has been substantiated by many scholars in literature. Hence, a system-level coordinated control is employed within the energy management system which governs the mode schedule of the multi-mode powertrain in real-time simulation. / Thesis / Doctor of Philosophy (PhD)

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La raréfaction des sources de production conventionnelles et leurs émissions nocives ont favorisé l’essor notable de la production renouvelable, plus durable et mieux répartie géographiquement. Toutefois, son intégration au système électrique est problématique. En effet, la production renouvelable est peu prédictible et issue de sources majoritairement incontrôlables, ce qui compromet la stabilité du réseau, la viabilité économique des producteurs et rend nécessaire la définition de solutions adaptées pour leur participation au marché de l’électricité. Dans ce contexte, le projet scientifique Winpower propose de relier par un réseau à courant continu les ressources de plusieurs acteurs possédant respectivement des fermes éoliennes offshore (acteurs EnR) et des centrales de stockage de masse (acteurs CSM). Cette configuration impose aux acteurs d’assurer conjointement la gestion du réseau électrique.Nous supposons que les acteurs participent au marché comme une entité unique : cette hypothèse permet aux acteurs EnR de tirer profit de la flexibilité des ressources contrôlables pour minimiser le risque de pénalités sur le marché de l’électricité, aux acteurs CSM de valoriser leurs ressources auprès des acteurs EnR et/ou auprès du marché et à la coalition de faciliter la gestion des déséquilibres sur le réseau électrique, en agrégeant les ressources disponibles. Dans ce cadre, notre travail s’attaque à la problématique de la participation au marché EPEX SPOT Day-Ahead de la coalition comme une centrale électrique virtuelle ou CVPP (Cooperative Virtual Power Plant). Nous proposons une architecture de pilotage multi-acteurs basée sur les systèmes multi-agents (SMA) : elle permet d’allier les objectifs et contraintes locaux des acteurs et les objectifs globaux de la coalition.Nous formalisons alors l’agrégation et la planification de l’utilisation des ressources comme un processus décisionnel de Markov (MDP), un modèle formel adapté à la décision séquentielle en environnement incertain, pour déterminer la séquence d’actions sur les ressources contrôlables qui maximise l’espérance des revenus effectifs de la coalition. Toutefois, au moment de la planification des ressources de la coalition, l’état de la production renouvelable n’est pas connue et le MDP n’est pas résoluble en l’état : on parle de MDP partiellement observable (POMDP). Nous décomposons le POMDP en un MDP classique et un état d’information (la distribution de probabilités des erreurs de prévision de la production renouvelable) ; en extrayant cet état d’information de l’expression du POMDP, nous obtenons un MDP à état d’information (IS-MDP), pour la résolution duquel nous proposons une adaptation d’un algorithme de résolution classique des MDP, le Backwards Induction.Nous décrivons alors un cadre de simulation commun pour comparer dans les mêmes conditions nos propositions et quelques autres stratégies de participation au marché dont l’état de l’art dans la gestion des ressources renouvelables et contrôlables. Les résultats obtenus confortent l’hypothèse de la minimisation du risque associé à la production renouvelable, grâce à l’agrégation des ressources et confirment l’intérêt de la coopération des acteurs EnR et CSM dans leur participation au marché de l’électricité. Enfin, l’architecture proposée offre la possibilité de distribuer le processus de décision optimale entre les différents acteurs de la coalition : nous proposons quelques pistes de solution dans cette direction. / Renewable Energy Sources (RES) has grown remarkably in last few decades. Compared to conventional energy sources, renewable generation is more available, sustainable and environment-friendly - for example, there is no greenhouse gases emission during the energy generation. However, while electrical network stability requires production and consumption equality and the electricity market constrains producers to contract future production a priori and respect their furniture commitments or pay substantial penalties, RES are mainly uncontrollable and their behavior is difficult to forecast accurately. De facto, they jeopardize the stability of the physical network and renewable producers competitiveness in the market. The Winpower project aims to design realistic, robust and stable control strategies for offshore networks connecting to the main electricity system renewable sources and controllable storage devices owned by different autonomous actors. Each actor must embed its own local physical device control strategy but a global network management mechanism, jointly decided between connected actors, should be designed as well.We assume a market participation of the actors as an unique entity (the coalition of actors connected by the Winpower network) allowing the coalition to facilitate the network management through resources aggregation, renewable producers to take advantage of controllable sources flexibility to handle market penalties risks, as well as storage devices owners to leverage their resources on the market and/or with the management of renewable imbalances. This work tackles the market participation of the coalition as a Cooperative Virtual Power Plant. For this purpose, we describe a multi-agent architecture trough the definition of intelligent agents managing and operating actors resources and the description of these agents interactions; it allows the alliance of local constraints and objectives and the global network management objective.We formalize the aggregation and planning of resources utilization as a Markov Decision Process (MDP), a formal model suited for sequential decision making in uncertain environments. Its aim is to define the sequence of actions which maximize expected actual incomes of the market participation, while decisions over controllable resources have uncertain outcomes. However, market participation decision is prior to the actual operation when renewable generation still is uncertain. Thus, the Markov Decision Process is intractable as its state in each decision time-slot is not fully observable. To solve such a Partially Observable MDP (POMDP), we decompose it into a classical MDP and an information state (a probability distribution over renewable generation errors). The Information State MDP (IS-MDP) obtained is solved with an adaptation of the Backwards Induction, a classical MDP resolution algorithm.Then, we describe a common simulation framework to compare our proposed methodology to some other strategies, including the state of the art in renewable generation market participation. Simulations results validate the resources aggregation strategy and confirm that cooperation is beneficial to renewable producers and storage devices owners when they participate in electricity market. The proposed architecture is designed to allow the distribution of the decision making between the coalition’s actors, through the implementation of a suitable coordination mechanism. We propose some distribution methodologies, to this end.