Orientador: Daniela Renata Cantane / Resumo: Este trabalho utiliza um modelo epidemiológico para analisar o comportamento de crises bancárias que possuem origem em um determinado país e são propagadas para outros países atingindo proporções mundiais. O modelo matemático epidemiológico Suscetíveis, Infectados e Recuperados (SIR) empregado permite simular a dinâmica da crise separando os países em três estados: suscetíveis, infectados e recuperados, em cada instante de tempo, além de prever a extensão da crise. Os parâmetros do modelo são obtidos da literatura para cada país envolvido e a crise segue uma dinâmica diferente dependendo do país de origem. Uma breve descrição da importância dos bancos em nível macroeconônico e suas funções básicas são apresentadas. Também são apresentadas algumas definições desta crise, denominada crise sistêmica, bem como os canais de transmissão de como um banco com problemas financeiros, denominado infectado, transmite esta condição para outro. Considerada a possibilidade de uma crise sistêmica, o Banco Central deve intervir nos bancos com problemas. Esta tarefa pode ser modelada como um problema de controle ótimo inserindo uma variável de controle no modelo SIR, que representa a intervenção do Banco Central, e uma função objetivo, em que o custo dessa intervenção deve ser minimizado. O objetivo deste trabalho é investigar um modelo de otimização aplicado ao risco bancário e propor o método heurístico \textit{Variable Neighbourhood Search} (VNS) para resolução do problema de controle ótimo... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This work uses an epidemiological model to analyze the behavior of bank crises that originate in a given country and are propagated to other countries reaching worldwide proportions. The epidemiological mathematical model Susceptible, Infected and Recovered (SIR) used allows to simulate the dynamics of the crisis separating the countries in three states: susceptible, infected and recovered, in each instant of time, in addition to predicting the extent of the crisis. The model parameters are obtained from the literature for each country involved and the crisis follows a different dynamic depending on the country of origin. A brief description of the importance of banks at the macroeconomic level and their basic functions is presented. Some definitions of this crisis, called systemic crisis, are also presented, as well as the transmission channels of how a bank with financial problems, called infected, transmits this condition to another. Considering the possibility of a systemic crisis, the Central Bank must intervene in troubled banks. This task can be xiv modeled as an optimal control problem by inserting a control variable in the SIR model, which represents Central Bank intervention, and an objective function involving the cost of this intervention and must be minimized. The objective of this work is to investigate an optimization model applied to banking risk and propose the Variable Neighborhood Search (VNS) heuristic method to solve the proposed optimal control problem. ... (Complete abstract click electronic access below) / Mestre

This thesis develops a calibrated model of the Cal Poly Central Chilled Water Plant with Thermal Energy Storage for use in determining an optimal operating control strategy. The model was developed using a transient systems simulation program (TRNSYS) that includes plant performance and manufacturer data for the primary system components, which are comprised of pumps, chillers, cooling towers, and a thermal energy storage tank. The model is calibrated to the actual measured performance of the plant using the current control strategy as a baseline. By observing and quantifying areas for potential improvement in plant performance under conditions of high campus cooling load demands, alternative control strategies for the plant are proposed. Operation of the plant under each of these control strategies is simulated in the model and evaluated for overall energy and demand-usage cost savings. These results are used to recommend improvements in the plant’s current control strategy, as well as to propose an optimal control strategy that may be applied to reduce plant operating costs. The results of the model identify that the plant can perform more economically by employing more chiller power to charge the Thermal Energy Storage tank to higher capacities during overnight periods when the utility rates are lower. Staging the operation of the different chillers to more precisely follow the tank charges during these off-peak periods can ensure faster tank charging when its capacity may not be sufficient to meet the peak and part-peak cooling load demands. A proposed control strategy to accomplish this breaks the overnight Off-Peak rate period into three periods with separate control setpoints, which are designed to maintain the tank charge capacity at the minimum levels to be able to accommodate the daily campus cooling demands during peak and part-peak hours.

In Canada, more than 1.11 TWh of energy per year is generated by diesel generators in off-grid remote areas. Delivering energy to these territories always has a high cost for the local and federal governments both financially and environmentally. Substituting fossil fuels with clean energies is the solution. However, the unreliability and intermittency of renewable energies (RE) are always challenging issues that need to be solved. Zinc air flow battery (ZAFB) with decoupled power and energy capacity can bring sustainability and reliability for microgrids. In this study, an efficient model was developed for ZAFB, which is applicable for large-scale modeling, and incorporated in microgrid modeling. A bilevel optimization approach was implemented in the microgrid model to find the optimal size and control of the microgrid simultaneously over the project lifetime. Using model predictive control (MPC) and based on user-defined foresight horizon and known information like energy demand and RE resources, the control model decides the future changes in microgrid components. This tool is used to propose the best microgrid design for these communities to reduce or eliminate their dependency on fossil fuels. The functionality of this tool was evaluated by three case studies in British Columbia: Blind Channel, Hot Springs Cove and Moresby Island. Zero CO2 emission and zero fuel consumption were achieved by a 100% RE microgrid consisting of wind and tidal turbines and large ZAFB. The net present cost (NPC) of this system and cost of energy are 39 – 46 % and 55 – 60 % less than the base case costs in which diesel is the main energy source. ZAFB with a longer storage duration (50 – 60 hours) satisfies 17 – 23% of annual energy demand in these case studies. / Graduate

Membrane Distillation (MD) is an emerging sustainable desalination technique. While MD has many advantages and can be powered by solar thermal energy, its main drawback is the low water production rate. However, the MD process has not been fully optimized in terms of its manipulated and controlled variables. This is largely due to the lack of adequate dynamic models to study and simulate the process. In addition, MD is prone to membrane fouling, which is a fault that degrades the performance of the MD process. This work has three contributions to address these challenges. First, we derive a mathematical model of Direct Contact Membrane Distillation (DCMD), which is the building block for the next parts. Then, the proposed model is extended to account for membrane fouling and an observer-based fouling detection method is developed. Finally, various control strategies are implemented to optimize the performance of the DCMD solar-powered process. In part one, a reduced-order dynamic model of DCMD is developed based on lumped capacitance method and electrical analogy to thermal systems. The result is an electrical equivalent thermal network to the DCMD process, which is modeled by a system of nonlinear differential algebraic equations (DAEs). This model predicts the water-vapor flux and the temperature distribution along the module length. Experimental data is collected to validate the steady-state and dynamic responses of the proposed model, with great agreement demonstrated in both. The second part proposes an extension of the model to account for membrane fouling. An adaptive observer for DAE systems is developed and convergence proof is presented. A method for membrane fouling detection is then proposed based on adaptive observers. Simulation results demonstrate the performance of the membrane fouling detection method. Finally, an optimization problem is formulated to maximize the process efficiency of a solar-powered DCMD. The adapted method is known as Extremum Seeking (ES). A Newton-based ES is designed and the proposed model is used to accurately forecast the distilled water flux. Although good results are obtained with this method, a practical modification to the ES scheme is proposed to enhance the practical stability.

Master‘s thesis contains the issue of positional control of the separate exciting DC motor. In the work is the creation of mathematical model. Next theme of document are questions of optimal control and method of solution LQ controler. The work is also a proposal state observer.

Les actionneurs piézoélectriques sont très utilisés pour les systèmes de positionnement pour des tâches à l'échelle micro/nanométrique en raison de leur haute résolution (sub-micrométrique), leur grande bande passante, et une densité de force élevée. Cependant, ils sont caractérisés par des non-linéarités telles que l'hystérésis et la dérive lente, par une grande sensibilité à l’environnement, et pour certains par des comportements oscillatoires. Ces caractéristiques ont un impact considérable sur les tâches que ces actionneurs doivent effectuer et leur contrôle reste souvent difficile. Différents correcteurs robustes ont été développés pour contrôler les actionneurs piézoélectriques. Il s'agit notamment de l'approche grand gain, des approches H-inf, des approches de contrôle basée sur l'observation des perturbations, ...etc. Ces techniques ont démontré une amélioration significative des performances mais mènent souvent à des correcteurs d'ordre élevé qui sont difficiles à mettre en œuvre. Cette thèse consiste à développer des correcteurs pour des actionneurs piézoélectriques en combinant l'analyse d'intervalle et les techniques classiques de commande.Les avantages principaux d’utiliser des intervalles est qu'ils permettent de modéliser facilement les incertitudes paramétriques en les limitant par des bornes. Par ailleurs, les travaux existants démontrent qu’il est possible de synthétiser de manière plus simplifiée des correcteurs robustes d’ordre faible, c-à-d ordre inférieur à celui du modèle. L'état de l'art sur l'utilisation des techniques par intervalle pour la synthèse de correcteurs peut être présenté en deux catégories : les techniques par intervalle basées sur des fonctions de transfert, et les techniques par intervalle basées sur la représentation d’état. Les techniques par intervalle basées sur les fonctions de transfert sont actuellement limitées pour modéliser et synthétiser des correcteurs pour des systèmes monovariables incertains tandis que les techniques basées sur la représentation d'état sont bien adaptées pour des systèmes multivariables incertains. Néanmoins, ces travaux existants pour des systèmes multivariables sont limités aux modèles avec des matrices d'état et d'entrée de structures spéciales. En outre, elles ne portent que sur le degré de stabilité du système en boucle fermée et ne prennent pas donc en compte des spécifications sur les performances. Cette thèse développe des outils de synthèse de correcteurs robustes pour des systèmes multivariables à incertitudes paramétriques dans l’approche d’état par intervalle sans structure particulière et en considérant à priori des performances. Des validations expérimentales sur différents actionneurs piézoélectriques, et ce en commande en position et en force, sont efféctuées. Enfin, la thèse propose également l’extension des observateurs à entrée inconnue pour les systèmes par intervalle afin de compléter les techniques de commande proposées. / Piezoelectric actuators are widely used at micro/nanoscale because of their simpleconfiguration, high resolution (sub-nanometric), high speed (large bandwidth upto 1kHz), and high force density. However, they are characterized by some nonlinearitiessuch as hysteresis, internal friction and creep,...etc. These characteristicsconsiderably impact the dynamics of the piezoactuators which makes the controlof these systems not a trivial task. Various robust controllers have been developedto control piezoelectric actuators. These include high gain feedback approach, H1approach, disturbance observer based control approach,...etc. Those techniquesdemonstrated a significant improvement of the control performance, but they oftenderive controllers with high-order which are difficult for implementation. Tobypass this limitation, we focus on the thesis on combining interval analysis withclassical controller design techniques to obtain a low order controllers. The mainadvantage of intervals is that they permit to model parametric uncertainties easilyby bounding them. Furthermore, the process of modeling the system uncertaintiesby intervals makes the synthesis of robust controller with low order relatively easy.The state of the art on the use of interval techniques to design and derive robustcontrollers for uncertain system can be divided into two categories: intervaltransfer functions based approaches and interval state-space representation basedapproaches. Interval transfer functions based designs have been widely used tomodel and to control SISO (Single Input single Output) systems subjected to uncertainties.These approaches make the synthesis of robust controllers for suchsystems easy with providing good performance. However, the current work thatuse interval transfer functions are limited to systems in SISO case. In the otherside, the state-space based approaches have been shown to be well adapted tosynthesis robust controllers for multivariable systems. Nevertheless, the excitingworks are limited to systems with state and input matrices of special structures.Furthermore, they address only the degree of stability of the closed-loop systemwithout discussing performance specification. In order to make the design of robustcontroller using interval state-space approach possible for any interval state-spacestructure, this thesis will explore the interval state-space control design using robustpole assignment technique. This proposed approach will guarantee the stability and the desired performance of the closed-loop system also it allows to obtaina low order controller.For this matter, an algorithm based on Set Inversion Via Interval Analysis(SIVIA) combined with interval eigenvalues computation is proposed to seek for aset of robust gains. This recursive SIVIA-based algorithm allows to approximatewith subpaving the set solutions [K] that satisfy the inclusion of the eigenvaluesof the closed-loop system in a desired region in the complex plan. Furthermore,simple algorithms are proposed to find the optimal feedback gains among the rangeof robust gains [K] as well as the range of the gains that satisfy input constraints,all with the help of interval analysis. Finally, in order to improve the controllerperformance, we were directed our attention to nonlinear control approaches andespecially interval sliding mode control (ISMC) design using interval observers.The effectiveness of the proposed approaches are tested by a real experimentationon several platforms developed in our laboratory to achieve robust performance.

A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, sufficient conditions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the parameter in the L1-norm. It is shown that these conditions are also necessary, provided that the dependence of data on the parameter is sufficiently strong.

An optimal control problem governed by the heat equation with nonlinear boundary conditions is considered. The objective functional consists of a quadratic terminal part and a quadratic regularization term. It is known, that an SQP method converges quadratically to the optimal solution of the problem. To handle the quadratic optimal control subproblems with high precision, very large scale mathematical programming problems have to be treated. The constrained problem is reduced to an unconstrained one by a method due to Bertsekas. A multigrid approach developed by Hackbusch is applied to solve the unconstrained problems. Some numerical examples illustrate the behaviour of the method.

We discuss a parallel library of efficient algorithms for the solution of linear-quadratic optimal control problems involving largescale systems with state-space dimension up to $O(10^4)$. We survey the numerical algorithms underlying the implementation of the chosen optimal control methods. The approaches considered here are based on invariant and deflating subspace techniques, and avoid the explicit solution of the associated algebraic Riccati equations in case of possible ill-conditioning. Still, our algorithms can also optionally compute the Riccati solution. The major computational task of finding spectral projectors onto the required invariant or deflating subspaces is implemented using iterative schemes for the sign and disk functions. Experimental results report the numerical accuracy and the parallel performance of our approach on a cluster of Intel Itanium-2 processors.

The H_infinity control problem is studied for linear constant coefficient descriptor systems. Necessary and sufficient optimality conditions as well as controller formulas are derived in terms of deflating subspaces of even matrix pencils for problems of arbitrary index. A structure preserving method for computing these subspaces is introduced. In combination these results allow the derivation of a numerical algorithm with advantages over the classical methods.