Cette thèse porte sur l'optimisation et la commande prédictive des centrales de production d'énergie en utilisant des modèles physiques des installations. Les modèles sont réalisés à l'aide du langage Modelica, un langage équationnel adapté à la modélisation de systèmes multi-physiques. La modélisation de systèmes physiques dans ce langage est présentée dans une première partie, ainsi que les traitements symboliques réalisés par les compilateurs Modelica pour mettre les modèles sous une forme adaptée à l'optimisation. On présente dans une seconde partie le développement d'une méthode d'optimisation dynamique hybride pour les centrales de production d'énergie, qui fournit une trajectoire optimisée de l'installation sur un horizon long. Les trajectoires calculées incluent les trajectoires des commandes continues ainsi que les décisions d'engagement des différents équipements. L'algorithme d'optimisation combine la méthode de collocation et une méthode nommée Sum Up Rounding (SUR) pour la prise en compte des décisions d'engagement. Un algorithme de commande prédictive (MPC) est enfin introduit afin de garantir le suivi des trajectoires optimales et de prendre en compte en temps réel la présence de perturbations et les erreurs du modèle d'optimisation. L'algorithme MPC utilise des modèles linéarisés tangents générés automatiquement à partir du modèle non linéaire. / This thesis deals with hybrid optimal control and Model Predictive Control (MPC) of power plants by use of physical models. Models of the facilities are developped with Modelica, an equation based language tailored for modelling multi-physics systems. Modeling of physical systems with Modelica is introduced in a first part, as well as some of the symbolic processing done by Modelica compilers that transform the original model to a form suited for optimization. Then, a method to solve optimal control problems on hybrid systems (such as power plants) is presented. This methods provides an optimal trajectory for the power plant on a long horizon. The optimal trajectory computed by the method includes the trajectories of continuous inputs as well as switching decisions for components in the plant. The optimization algorithm combines the collocation method and a method named Sum Up Rounding (SUR) for dealing with switches. Finally, a Model Predictive Controller is developped in order to follow this optimal trajectory in real time, and to cope with disturbances on the actual system and modelling errors. The proposed MPC uses tangent linear models of the plant that are derived automatically from the nonlinear model.

Support for this work from Praxair; the McMaster Advanced Control Consortium; and the Natural Sciences and Engineering Research Council of Canada (NSERC), Grant CRDPJ 445717, is gratefully acknowledged. / In the air separation industry, cryogenic distillation is the dominant technology for separating large quantities of air into individual high purity component products. Due to the complexity of the process, in addition to significant energy input, air separation units (ASUs) also have high degrees of material and thermal integration and low process agility. As markets become more competitive and dynamic, especially after electricity market deregulation, ASUs can no longer practice mostly stationary operations, and are in need for design and control strategies to achieve high adaptability. In this study, we address such issues through a dynamic optimization framework. The use of rigorous dynamic models is important for developing economically beneficial designs and operating practices. The first part of this study focuses on the modeling aspect. For the column section of the plant, a full-order stage-wise model and a collocation based reduced order model are proposed. Model size, simulation time and predication accuracy are compared. For the primary heat exchanger, a novel moving boundary model is derived to handle the phase change in such a multi-stream heat exchanger. Simulation results demonstrate the capability of the proposed model in tracking the boundary points of the phase change occurrence, as well as the potential pinch point, along the length of the heat exchanger. The second part of the study addresses the operation aspects of ASUs through conducting dynamic optimization studies with collocation based dynamic models. We first performed a comprehensive analysis for a storage-then-utilization strategy on a nitrogen plant, following a two-tier multi-period formulation. As the parameter varies with time, the plant collects liquid, either directly from liquid product or by liquefaction of overproduced gas product, and then redistributes it for meeting gas product demand or as additional reflux. Effects of electricity price and demand profiles, additional operation costs, as well as product specifications are explored. Then we investigated the economic incentive for employing preemptive actions on a super-staged argon system, which allows the plant to take actions before external changes arrive. In the evaluation, changes are in the gas oxygen product demand. During the preemptive period, the plant takes either a single set or multiple sets of control actions. In the demand increase case, operation degrees of freedom are introduced to or removed from the set of decision variables. The demand decrease scenarios are explored with an under-supplied or saturated liquid oxygen market. / Dissertation / Doctor of Philosophy (PhD)

<p>Efficient global dynamic optimization (GDO) using spatial branch-and-bound (SBB) requires the ability to construct tight bounds for the dynamic model. This thesis works toward efficient GDO by developing effective convex relaxation techniques for models with ordinary differential equations (ODEs). In particular, a novel algorithm, based upon a verified interval ODE method and the McCormick relaxation technique, is developed for constructing convex and concave relaxations of solutions of nonlinear parametric ODEs. In addition to better convergence properties, the relaxations so obtained are guaranteed to be no looser than their underlying interval bounds, and are typically tighter in practice. Moreover, they are rigorous in the sense of accounting for truncation errors. Nonetheless, the tightness of the relaxations is affected by the overestimation from the dependency problem of interval arithmetic that is not addressed systematically in the underlying interval ODE method. To handle this issue, the relaxation algorithm is extended to a Taylor model ODE method, which can provide generally tighter enclosures with better convergence properties than the interval ODE method. This way, an improved version of the algorithm is achieved where the relaxations are generally tighter than those computed with the interval ODE method, and offer better convergence. Moreover, they are guaranteed to be no looser than the interval bounds obtained from Taylor models, and are usually tighter in practice. However, the nonlinearity and (potentially) nonsmoothness of the relaxations impedes their fast and reliable solution. Therefore, the algorithm is finally modified by incorporating polyhedral relaxations in order to generate relatively tight and computationally cheap linear relaxations for the dynamic model. The resulting relaxation algorithm along with a SBB procedure is implemented in the MC++ software package. GDO utilizing the proposed relaxation algorithm is demonstrated to have significantly reduced computational expense, up to orders of magnitude, compared to existing GDO methods.</p> / Doctor of Philosophy (PhD)

This research effort develops a comprehensive computational framework to support the parametric optimal design of uncertain dynamical systems. Uncertainty comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it; not accounting for uncertainty may result in poor robustness, sub-optimal performance and higher manufacturing costs. Contemporary methods for the quantification of uncertainty in dynamical systems are computationally intensive which, so far, have made a robust design optimization methodology prohibitive. Some existing algorithms address uncertainty in sensors and actuators during an optimal design; however, a comprehensive design framework that can treat all kinds of uncertainty with diverse distribution characteristics in a unified way is currently unavailable. The computational framework uses Generalized Polynomial Chaos methodology to quantify the effects of various sources of uncertainty found in dynamical systems; a Least-Squares Collocation Method is used to solve the corresponding uncertain differential equations. This technique is significantly faster computationally than traditional sampling methods and makes the construction of a parametric optimal design framework for uncertain systems feasible. The novel framework allows to directly treat uncertainty in the parametric optimal design process. Specifically, the following design problems are addressed: motion planning of fully-actuated and under-actuated systems; multi-objective robust design optimization; and optimal uncertainty apportionment concurrently with robust design optimization. The framework advances the state-of-the-art and enables engineers to produce more robust and optimally performing designs at an optimal manufacturing cost. / Ph. D.

Simulation has been used to model combat for a long time. Recently, it has been accepted that combat is a complex adaptive system (CAS). Multi-agent systems (MAS) are also considered as a powerful modelling and development environment to simulate combat. Agent-based distillations (ABD) - proposed by the US Marine Corp - are a type of MAS used mainly by the military for exploring large scenario spaces. ABDs that facilitated the analysis and understanding of combat include: ISAAC, EINSTein, MANA, CROCADILE and BactoWars. With new concepts such as networked forces, previous ABDs can implicitly simulate a networked force. However, the architectures of these systems limit the potential advantages gained from the use of networks. In this thesis, a novel network centric multi-agent architecture (NCMAA) is pro-posed, based purely on network theory and CAS. In NCMAA, each relationship and interaction is modelled as a network, with the entities or agents as the nodes. NCMAA offers the following advantages: 1. An explicit model of interactions/relationships: it facilitates the analysis of the role of interactions/relationships in simulations; 2. A mechanism to capture the interaction or influence between networks; 3. A formal real-time reasoning framework at the network level in ABDs: it interprets the emergent behaviours online. For a long time, it has been believed that it is hard in CAS to reason about emerging phenomena. In this thesis, I show that despite being almost impossible to reason about the behaviour of the system by looking at the components alone because of high nonlinearity, it is possible to reason about emerging phenomena by looking at the network level. This is undertaken through analysing network dynamics, where I provide an English-like reasoning log to explain the simulation. Two implementations of a new land-combat system called the Warfare Intelligent System for Dynamic Optimization of Missions (WISDOM) are presented. WISDOM-I is built based on the same principles as those in existing ABDs while WISDOM-II is built based on NCMAA. The unique features of WISDOM-II include: 1. A real-time network analysis toolbox: it captures patterns while interaction is evolving during the simulation; 2. Flexible C3 (command, control and communication) models; I 3. Integration of tactics with strategies: the tactical decisions are guided by the strategic planning; 4. A model of recovery: it allows users to study the role of recovery capability and resources; 5. Real-time visualization of all possible information: it allows users to intervene during the simulation to steer it differently in human-in-the-loop simulations. A comparison between the fitness landscapes of WISDOM-I and II reveals similarities and differences, which emphasise the importance and role of the networked architecture and the addition of strategic planning. Lastly but not least, WISDOM-II is used in an experiment with two setups, with and without strategic planning in different urban terrains. When the strategic planning was removed, conclusions were similar to traditional ABDs but were very different when the system ran with strategic planning. As such, I show that results obtained from traditional ABDs - where rational group planning is not considered - can be misleading. Finally, the thesis tests and demonstrates the role of communication in urban ter-rains. As future warfighting concepts tend to focus on asymmetric warfare in urban environments, it was vital to test the role of networked forces in these environments. I demonstrate that there is a phase transition in a number of situations where highly dense urban terrains may lead to similar outcomes as open terrains, while medium to light dense urban terrains have different dynamics

In this thesis we investigate single and multi-player stochastic dynamic optimization prob-lems. We consider both discrete and continuous time processes. In the multi-player setup we investigate zero-sum games with both complete and partial information. We study partially observable stochastic games with average cost criterion and the state process be-ing discrete time controlled Markov chain. The idea involved in studying this problem is to replace the original unobservable state variable with a suitable completely observable state variable. We establish the existence of the value of the game and also obtain optimal strategies for both players. We also study a continuous time zero-sum stochastic game with complete observation. In this case the state is a pure jump Markov process. We investigate the nite horizon total cost criterion. We characterise the value function via appropriate Isaacs equations. This also yields optimal Markov strategies for both players. In the single player setup we investigate risk-sensitive control of continuous time Markov chains. We consider both nite and in nite horizon problems. For the nite horizon total cost problem and the in nite horizon discounted cost problem we characterise the value function as the unique solution of appropriate Hamilton Jacobi Bellman equations. We also derive optimal Markov controls in both the cases. For the in nite horizon average cost case we shown the existence of an optimal stationary control. we also give a value iteration scheme for computing the optimal control in the case of nite state and action spaces. Further we introduce a new class of stochastic processes which we call stochastic processes with \age-dependent transition rates". We give a rigorous construction of the process. We prove that under certain assunptions the process is Feller. We also compute the limiting probabilities for our process. We then study the controlled version of the above process. In this case we take the risk-neutral cost criterion. We solve the in nite horizon discounted cost problem and the average cost problem for this process. The crucial step in analysing these problems is to prove that the original control problem is equivalent to an appropriate semi-Markov decision problem. Then the value functions and optimal controls are characterised using this equivalence and the theory of semi-Markov decision processes (SMDP). The analysis of nite horizon problems becomes di erent from that of in nite horizon problems because of the fact that in this case the idea of converting into an equivalent SMDP does not seem to work. So we deal with the nite horizon total cost problem by showing that our problem is equivalent to another appropriately de ned discrete time Markov decision problem. This allows us to characterise the value function and to nd an optimal Markov control.

Die Dissertation beschäftigt sich mit der gekoppelten Simulation von Klimaanlage, Regelung und Gebäude mit Hilfe des Simulationssystems TRNSYS. Während für das Gebäude ein vorhandenes TRNSYS Modul verwendet wird, wurden für Klimaanlage und Regelung neue Simulationsmodule entwickelt. Der Klimaanlagensimulator ist seinerseits modular aufgebaut enthält sowohl geometrisch physikalische und empirische als auch kombinierte Modelle für die Simulation von Ventilatoren, Lufterhitzern, Feuchtluftkühlern, Befeuchtern, Regeneratoren, Plattenwärmeüberträgern, Kreislaufwärmerückgewinnern, Ventilen, hydraulischen Schaltungen usw., die für die Simulation sehr variabel miteinander verschaltet werden können. Es wurden optimierte Regelstrategien für konventionelle und DEC-Anlagen entwickelt und entsprechende TRNSYS-Module zur Umsetzung in die Simulation programmiert. Für die Sequenzregelung mehrerer Größen (z.B. Temperatur, Feuchte) wurde ein frei programmierbarer Mehrsequenzregler entwickelt, der den scheinbaren Reglerstillstand über Verknüpfungen blockierter Stellglieder einer Regelsequenz verhindert. Die Qualität der Regelsequenzen wurde mit Hilfe eines über das Rosenbrockverfahren und der dynamischen Optimierung ermittelten optimalen Vergleichsprozesses bewertet.

Cette thèse étudie comment le taux de change effectif réel (TCER) et ses mesures associées (volatilité du TCER et désalignement du TCER) affectent la croissance de la productivité totale des facteurs (CPTF). Elle analyse également les canaux par lesquels le TCER et ses mesures associées agissent sur la productivité totale des facteurs (PTF). La première partie étudie comment le TCER lui-Même, d'une part, et la volatilité du TCER, d'autre part, influencent la productivité. Une analyse du lien entre le niveau du TCER et la PTF dans le chapitre 1 indique qu'une appréciation de taux de change cause une augmentation de la PTF. Mais cet impact est également non- inéaire: en-Dessous du seuil, le TCER influence négativement la productivité tandis qu'au-Dessus du seuil il agit positivement. Les résultats du chapitre 2 illustrent que la volatilité du TCER affecte négativement la CPTF. Nous avons également constaté que la volatilité du TCER agit sur PTF selon le niveau du développement financier. Pour les pays modérément financièrement développés, la volatilité du TCER réagit négativement sur la productivité et n'a aucun effet sur la productivité pour les niveaux très bas et très élevés du développement financier. La deuxième partie examine les canaux par lesquels le TCER et ses mesures associées influencent la productivité. Les résultats du chapitre 3 illustrent que la volatilité du TCER a un impact négatif élevé sur l'investissement. Ces résultats sont robustes dans les pays à faible revenu et les pays à revenu moyens, et en employant une mesure alternative de volatilité du TCER. Le chapitre 4 montre que le désalignement du taux de change réel et la volatilité du taux de change réel affectent négativement les exportations. Il démontre également que la volatilité du taux de change réel est plus nocive aux exportations que le désalignement. Ces résultats sont corroborés par des résultats sur des sous-Échantillons de pays à bas revenu et à revenu moyen. / This dissertation investigates how the real effective exchange rate (REER) and its associated asurements (REER volatility and REER misalignment) affect total factor productivity growth (TFPG). It also analyzes the channels through which the REER and its associated measurements act on total factor productivity (TFP). The first part studies how the REER itself, on the one hand, and the REER volatility, on the other hand, influence productivity. An analysis of the link between the level of REER and TFP in chapter 1 reveals that an exchange rate appreciation causes an increase of TFP. But this impact is also nonlinear: below the threshold, real exchange rate influences negatively productivity while above the threshold it acts positively. The results of chapter 2 illustrate that REER volatility affects negatively TFPG. We also found that REER volatility acts on TFP according to the level of financial development. For moderately financially developed countries, REER volatility reacts negatively on productivity and has no effect on productivity for very low and very high levels of financial development. The second part examines the channels through which the REER and its associated measurements influence productivity. The results of chapter 3 illustrate that the exchange rate volatility has a strong negative impact on investment. This outcome is robust in low income and middle income countries, and by using an alternative measurement of exchange rate volatility. Chapter 4 show that both real exchange rate misalignment and real exchange rate volatility affect negatively exports. It also demonstrates that real exchange rate volatility is more harmful to exports than misalignment. These outcomes are corroborated by estimations on subsamples of Low- ncome and Middle-Income countries