The scheduling of the converter aisle of a nickel smelting plant is a non-trivial task with significant consequences to plant profitability and production. An optimization-based scheduling formulation is developed using a continuous-time paradigm to accurately represent event timings. The formulation accounts for environmental restrictions on sulfur dioxide emissions using event timing constraints. The formulation includes novel semi-continuous modeling to represent flash furnaces which operate with a continuous inlet flow and intermittent discrete material removal, as well as, a novel sequencing and symmetry-breaking scheme to account for identical units operating in parallel. A rolling horizon feature is included in the formulation to accommodate multi-period optimization. Tightening constraints are developed and used to improve the computational performance of the optimization and demonstrate the capacity of the proposed methodology to function as a real-time decision-support tool. A solution procedure is presented where an aggregate model is used to bound the objective function of the master problem in a two layer optimization scheme. Finally, a novel multi-tiered procedure is presented to enhance the optimization solution by re-optimizing for objectives of decreasing priority in order to minimize task start times and penalize deviations in the furnace flow rate. To address the closed-loop properties of scheduling, a reactive scheduling mechanism is included to allow for rescheduling to account the impact of process disturbances on the operating schedule. A methodology for reducing radical scheduling changes due to the optimization during reactive scheduling is presented. The reactive scheduling algorithm utilizes a tiered optimization approach that progressively increases the degrees of freedom available, as required, in order to achieve a feasible production schedule. The use of the reactive scheduling algorithm demonstrates the ability to reject disturbances and transition plant operation in an agile manner. / Thesis / Master of Applied Science (MASc)

This work presents novel continuous-time delta-sigma modulator architectures with low-power consumption and improved signal transfer functions which are suitable for wideband A/D conversion in wireless applications, e.g., 3G and 4G receivers. The research has explored two routes for improving the overall performance of continuous-time delta-sigma modulator. The first part of this work proposes the use of the power efficient Successive-Approximations (SAR) architecture, instead of the conventional Flash ADC, as the internal quantizer of the delta-sigma modulator. The SAR intrinsic latency has been addressed by means of a faster clock for the quantizer as well as full-period delay compensation. The use of SAR quantizer allows for increasing the resolution while reducing the total power consumption and complexity. A higher resolution quantizer, made feasible by the SAR, would allow implementing more aggressive noise shaping to facilitate wideband delta-sigma A/D conversion at lower over-sampling-rates. As proof of concept, a first-order CT delta-sigma modulator with a 5-bit SAR quantizer is designed and implemented in a 130 nm CMOS process which achieves 62 dB dynamic range over 1.92 MHz signal bandwidth meeting the requirements of the WCDMA standard. The prototype modulator draws 3.1 mW from a single 1.2 V supply and occupies 0.36 mm2 of die area. The second part of this research addresses the issue of out-of-band peaking in the signal-transfer-function (STF) of the widely used feedforward structure. The STF peaking is harmful to the performance of the modulator as it allows an interferer to saturate the quantizer and result in severe harmonic distortion and instability. As a remedy to this problem a general low-pass and peaking-free STF design methodology has been proposed which allows for implementing an all-pole filter in the input signal path for any given NTF. Based on the proposed method, the STF peaking of any feedforward modulator can be eliminated using extra feed-in paths to all the integrator inputs. A major drawback of the conventional feedforward topology having low-pass STF is the large sensitivity of the STF to the coefficients. In particular, component mismatch, due to random errors in the relative values of individual resistors or capacitors, can significantly degrade the anti-aliasing of the CT modulator and give rise to the unwanted STF peaking. To solve this problem two new architectures, namely dual-feedback and dual-feed-in are proposed which allow us to synthesize a low-pass STF with a smaller number of coefficients than the feedforward structure. The dual-feedback structure which shows significantly lower sensitivity to coefficient mismatch is extensively analyzed and simulated. Also for proof of concept a third-order modulator is implemented in a 130 nm CMOS process which achieves 76 dB dynamic-range over 5 MHz signal bandwidth meeting, for example, the requirements of a DVB-H receiver standard. In addition the modulator shows 77 dB anti-aliasing and less than 0.1 dB worst-case STF peaking. The measured power consumption of the modulator is 6 mW from a single 1.2 V and the die area is 0.56 mm2.

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No / An investigation is carried out on the nature of QoS measures for queues with correlated traffic in both discrete and continuous time domains. The study focuses on the single server GI(G)/M-[x]/1/N and GI(G)/Geo([x])/1/N queues with finite capacity, N, a general batch renewal arrival process (BRAP), GI(G) and either batch Poisson, M-[x] or batch geometric, Geo([x]) service times with general batch sizes, X. Closed form expressions for QoS measures, such as queue length and waiting time distributions and blocking probabilities are stochastically derived and showed to be, essentially, time domain invariant. Moreover, the sGGeo(sGGo)/Geo/l/N queue with a shifted generalised geometric (sGGeo) distribution is employed to assess the adverse impact of varying degrees of traffic correlations upon basic QoS measures and consequently, illustrative numerical results are presented. Finally, the global balance queue length distribution of the M-Geo/M-Geo/1/N queue is devised and reinterpreted in terms of information theoretic principle of entropy maximisation. (C) 2014 Elsevier Inc. All rights reserved.

Phylogenetics explores the evolutionary relationships among species and one of the main approaches is to construct phylogenetic trees through inference-based methods. Beyond the evolutionary insights these trees provide, the underlying tree structure can also be used to study geographical migration of species. These geographical models, reminiscent of models of DNA sequence evolution, have predominantly been discrete in their nature. However, this poses a multitude of challenges, especially with high-dimensional state-spaces. Previous work has explored the possibility of using continuous diffusion models for geographical migration, however these were not aiming to model non-local migration and large state-spaces. This paper presents and evaluates a scalable continuous phylogenetic migration model which aims to approximate conventional discrete migration models in the case of local and non-local migration.

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.

The performance modelling of large-scale systems using discrete-state approaches is fundamentally hampered by the well-known problem of state-space explosion, which causes exponential growth of the reachable state space as a function of the number of the components which constitute the model. Because they are mapped onto continuous-time Markov chains (CTMCs), models described in the stochastic process algebra PEPA are no exception. This thesis presents a deterministic continuous-state semantics of PEPA which employs ordinary differential equations (ODEs) as the underlying mathematics for the performance evaluation. This is suitable for models consisting of large numbers of replicated components, as the ODE problem size is insensitive to the actual population levels of the system under study. Furthermore, the ODE is given an interpretation as the fluid limit of a properly defined CTMC model when the initial population levels go to infinity. This framework allows the use of existing results which give error bounds to assess the quality of the differential approximation. The computation of performance indices such as throughput, utilisation, and average response time are interpreted deterministically as functions of the ODE solution and are related to corresponding reward structures in the Markovian setting. The differential interpretation of PEPA provides a framework that is conceptually analogous to established approximation methods in queueing networks based on meanvalue analysis, as both approaches aim at reducing the computational cost of the analysis by providing estimates for the expected values of the performance metrics of interest. The relationship between these two techniques is examined in more detail in a comparison between PEPA and the Layered Queueing Network (LQN) model. General patterns of translation of LQN elements into corresponding PEPA components are applied to a substantial case study of a distributed computer system. This model is analysed using stochastic simulation to gauge the soundness of the translation. Furthermore, it is subjected to a series of numerical tests to compare execution runtimes and accuracy of the PEPA differential analysis against the LQN mean-value approximation method. Finally, this thesis discusses the major elements concerning the development of a software toolkit, the PEPA Eclipse Plug-in, which offers a comprehensive modelling environment for PEPA, including modules for static analysis, explicit state-space exploration, numerical solution of the steady-state equilibrium of the Markov chain, stochastic simulation, the differential analysis approach herein presented, and a graphical framework for model editing and visualisation of performance evaluation results.

La chaîne de réception des téléphones mobiles de dernière génération utilisent au moins deux étages de transposition en fréquence avant d'effectuer la démodulation en quadrature. La transposition en fréquence augmente la complexité du système et engendre de nombreux problèmes tels que la limitation de l'échelle dynamique et l'introduction de bruit issu de l'oscillateur local. Il est alors nécessaire d'envisager une numérisation du signal le plus près possible de l'antenne. Cette dernière permet la conversion directe d'un signal analogique en un signal numérique à des fréquences intermédiaires. Elle simplifie ainsi la conception globale du système et limite les problèmes liés aux mélangeurs. Pour cela, des architectures moins conventionnelles doivent être développées, comme la conversion analogique-numérique utilisant la modulation Sigma-Delta à temps continu. La modélisation comportementale de ce convertisseur analogique-numérique, ainsi que la conception des principaux blocs ont donc été l'objet de cette thèse. L'application d'une méthodologie de conception avancée, permettant la simulation mixte des blocs fonctionnels à différents niveaux d'abstraction, a permis de valider aussi bien la conception des circuits que le système global de conversion. En utilisant une architecture à multiples boucles de retour avec un quantificateur multi-bit, le convertisseur Sigma-Delta passe bande à temps continu atteint un rapport signal sur bruit (SNR) d'environ 76 dB dans une large bande de 20MHz. / Wireless front-end receivers of last generation mobile devices operate at least two frequency translations before I/Q demodulation. Frequency translation increases the system complexity, introducing several problems associated with the mixers (dynamic range limitation, noise injection from the local oscillator, etc.). Herein, the position of the analog-to-digital interface in the receiver chain can play an important role. Moving the analog-to-digital converter (ADC) as near as possible to the antenna, permits to simplify the overall system design and to alleviate requirements associated with analog functions (filters, mixers). These currently requirements have led to a great effort in designing improved architectures as Continuous-Time Delta-Sigma ADCs. The behavioural modeling this converter, although the circuit design of the main blocks has been the subject of this thesis. The use of an advanced design methodology, allowing the mixed simulation at different levels of abstraction, allows to validate both the circuit design and the overall system conversion. Using a multi-feedback architecture associated with a multi-bit quantizer, the continuous-time Bandpass Delta-Sigma converter achieves a SNR of about 76 dB in a wide band of 20MHz.

Les travaux présentés dans ce mémoire traitent de l'identification des systèmes dynamiques représentés sous la forme de modèles linéaires continus à paramètres variant lentement au cours du temps. La complexité du problème d'identification provient d'une part du caractère inconnu de la loi de variation des paramètres et d'autre part de la présence de bruits de nature inconnue sur les signaux mesurés. Les solutions proposées s'appuient sur une combinaison judicieuse du filtre de Kalman en supposant que les variations des paramètres peuvent être représentées sous la forme d'une marche aléatoire et de la méthode de la variable instrumentale qui présente l'avantage d'être robuste vis à vis de la nature des bruits de mesure. Les algorithmes de type récursif sont développés dans un contexte d'identification en boucle ouverte et en boucle fermée. Les différentes variantes se distinguent par la manière dont est construit la variable instrumentale. Inspirée de la solution développée pour les systèmes linéaires à temps invariant, une construction adaptative de la variable instrumentale est suggérée pour pouvoir suivre au mieux l'évolution des paramètres. Les performances des méthodes développées sont évaluées à l'aide de simulations de Monte Carlo et montrent la suprématie des solutions proposées s'appuyant sur la variable instrumentale par rapport celles plus classiques des moindres carrés récursifs. Les aspects pratiques et d'implantation numérique sont d'une importance capitale pour obtenir de bonnes performances lorsque ces estimateurs sont embarqués. Ces aspects sont étudiés en détails et plusieurs solutions sont proposées non seulement pour robustifier les estimateurs vis à vis du choix des hyper-paramètres mais également vis à vis de leur implantation numérique. Les algorithmes développés sont venus enrichir les fonctions de la boîte à outils CONTSID pour Matlab. Enfin, les estimateurs développés sont exploités pour faire le suivi de paramètres de deux systèmes physiques : un benchmark disponible dans la littérature constitué d'un filtre électronique passe-bande et une vanne papillon équipant les moteurs de voiture. Les deux applications montrent le potentiel des approches proposées pour faire le suivi de paramètres physiques variant lentement dans le temps / The work presented in this thesis deals with the identification of dynamic systems represented through continuous-time linear models with slowly time-varying parameters. The complexity of the identification problem comes on the one hand from the unknown character of the parameter variations and on the other hand from the presence of noises of unknown nature on the measured signals. The proposed solutions rely on a judicious combination of the Kalman filter assuming that the variations of the parameters can be represented in the form of a random walk, and the method of the instrumental variable which has the advantage of being robust with respect to the nature of the measurement noises. The recursive algorithms are developed in an open-loop and closed-loop identification setting. The different variants are distinguished by the way in which the instrumental variable is built. Inspired by the solution developed for time-invariant linear systems, an adaptive construction of the instrumental variable is suggested in order to be able to follow the evolution of the parameters as well as possible. The performance of the developed methods are evaluated using Monte Carlo simulations and show the supremacy of the proposed solutions based on the instrumental variable compared with the more classical least squares based approaches. The practical aspects and implementation issues are of paramount importance to obtain a good performance when these estimators are used. These aspects are studied in detail and several solutions are proposed not only to robustify the estimators with respect to the choice of hyperparameters but also with respect to their numerical implementation. The algorithms developed have enhanced the functions of the CONTSID toolbox for Matlab. Finally, the developed estimators are considered in order to track parameters of two physical systems: a benchmark available in the literature consisting of a bandpass electronic filter and a throttle valve equipping the car engines. Both applications show the potential of the proposed approaches to track physical parameters that vary slowly over time

Neste trabalho estudamos as noções de alcançabilidade e controlabilidade para sistemas lineares a tempo contínuo com perturbações aditivas e saltos nos parâmetros sujeitos a uma cadeia de Markov geral. Definimos conceitos de alcançabilidade e controlabilidade médios de maneira natural exigindo que os valores esperados dos gramianos correspondentes sejam definidos positivos. Visando obter uma condição testável para ambos os conceitos, introduzimos conjuntos de matrizes de alcançabilidade e de controlabilidade para esta classe de sistemas e usamos certas propriedades de invariância para mostrar que: o sistema é alcançável em média, e, analogamente, controlável em média, se e somente se as matrizes respectivas, de alcançabilidade e de controlabilidade, têm posto completo. Usamos alcançabilidade média de sistemas para mostrar que a matriz de segundo momento do estado é definida positiva com uma margem uniforme. Uma consequência deste resultado no problema de estimação linear do estado é que a matriz de covariância do erro de estimação é positiva definida em média, no sentido que existe um nível mínimo de ruído nas estimativas. Na sequência, para estimadores lineares markovianos, estudamos a limitação do valor esperado da matriz de covariância do erro para mostrar que o filtro é estável num certo sentido, sendo esta uma propriedade desejável em aplicações reais. Quanto às aplicações da controlabilidade média, usamos este conceito para estabelecer condições necessárias e suficientes que garantem a existência de um processo de controle que leva a componente contínua do estado do sistema para a origem em tempo finito e com probabilidade positiva. / In this work we study the reachability and controllability notions for continuous-time linear systems with exogenous inputs and jump parameters driven by a quite general Markov chain. We define a rather natural average reachability and controllability concepts by requiring that the associated gramians are average positive definite, respectively. Aiming at testable conditions for each concept, we introduce certain sets of matrices linked with the gramians, and employ some invariance properties to find rank-based conditions. We show for average reachable systems that the state second moment is positive definite. One consequence of this result in the context of linear estimation for reachable systems is that the expectation of the error covariance matrix is positive definite. Moreover, for linear markovian filters we study the average boundedness of the error covariance matrix to show that the filter is stable in an appropriate sense, which consists in a property that is desirable in real applications. Regarding the average controllability concept, we show that it is a necessary and sufficient condition for the feasibility of the following control problem: find a control process that drives the continuous component of the state to zero in finite time with positive probability.