Cette thèse s'inscrit dans le cadre de la gestion d'énergie d'un Véhicule Hybride Électrique. Pour ce type de véhicule, l'optimisation énergétique est un enjeu majeur. Cela consiste à calculer les commandes optimales minimisant la consommation énergétique du véhicule sous un nombre fini de contraintes. Deux types de méthodes peuvent être utilisées pour résoudre ce problème d'optimisation. La première méthode et la plus utilisée, la méthode numérique, utilisant des modèles cartographiques basés sur des données. Elle présente deux inconvénients majeurs: temps de calcul et mémoire importants. La deuxième méthode, appelée analytique, qui permet de remédier à ces deux problèmes, a été utilisée dans cette thèse. Plus l'architecture du véhicule devient complexe (plusieurs machines électriques, moteur thermique, élévateur de tension), plus l'intérêt de cette approche sera important. La méthodologie analytique, proposée dans cette thèse, est composée principalement de trois étapes : la modélisation convexe, le calcul analytique des commandes et la validation des commandes analytiques sur un simulateur de véhicule. Cette méthodologie a été appliquée sur les trois configurations possibles du véhicule étudié : parallèle, bi-parallèle et série. Finalement, l'ajout de l'élévateur de tension dans la gestion d'énergie ainsi que l'étude de son impact sur la consommation énergétique du véhicule sont présentés dans le dernier chapitre. Les résultats obtenus en simulation montrent que la méthode analytique a permis de réduire considérablement le temps de calcul tout en ayant une sous-optimalité très faible. / This thesis focuses on the energy management of Hybrid Electric Vehicle. In this type of vehicle, energy optimization is a major challenge. It consists of calculating optimal commands that minimize the vehicle’s energy consumption under a finite number of constraints. The optimization issue could be solved using a digital method or an analytical method. This choice depends on the nature of energy models that monitor the optimization criteria: analytical or maps of experimental measurements. However, this method presents numerous disadvantages. Its calculation is extremely time-consuming for instance. Therefore, the works presented in this thesis were directed in order to develop an analytical solution where the calculation is lesstime consuming. The architecture of the vehicle is complex. In fact, the vehicle contains two electrical machines, a thermal engine and a step-up. These components have all a straight impact on the vehicle’s energy consumption so several optimization variables were defining. Consequently, working on an analytical solution was a natural choice. The proposed analytical methodology consists of three steps: convex modeling, the command analytical calculation as well as the analytical command validation on a vehicle simulator. This methodology was applied to three possible configurations of the studied vehicle: parallel, biparallel and in serial. Finally, the step-up addition to the energy management as well as the study of itsimpact on the vehicle’s energy consumption are presented in the last chapter. The simulation results show that the analytical method reduces considerably the computing time and has an extremely low suboptimality.

[pt] Diversos problemas em engenharia, aprendizado de máquina e economia podem ser resolvidos através de Programação Semidefinida (SDP). Potenciais aplicações podem ser encontradas em telecomunicações, fluxo de potência e teoria dos jogos. Além disso, como SDP é uma subclasse de otimização convexa, temos uma série de propriedades e garantias que fazem da SDP uma tecnologia muito poderosa. Entretanto, dentre as diferentes subclasses de otimização convexa, SDP ainda permanece como uma das mais desafiadoras. Instancias de larga escala ainda não podem ser resolvidas pelos atuais softwares disponíveis. Nesse sentido, esta tese porpõe um novo algoritmo para resolver problemas de SDP. A principal contribuição deste novo algoritmo é explorar a propriedade de posto baixo presente em diversas instancias. A convergência desta nova metodologia é provada ao mostrar que o algoritmo proposto é um caso particular do Approximate Proximal Point Algorithm. Adicionalmente, as variáveis ótimas duais são disponibilizadas como uma consequência do algoritmo proposto. Além disso, disponibilizamos um software para resolver problemas de SDP, chamado ProxSDP. Três estudos de caso são utilizados para avaliar a performance do algoritmo proposto. / [en] Many problems of interest can be solved by means of Semidefinite Programming (SDP). The potential applications range from telecommunications, electrical power systems, game theory and many more fields. Additionally, the fact that SDP is a subclass of convex optimization brings a set of theoretical guarantees that makes SDP very appealing. However, among all sub-classes of convex optimization, SDP remains one of the most challenging in practice. State-of-the-art semidefinite programming solvers still do not efficiently solve large scale instances. In this regard, this thesis proposes a novel algorithm for solving SDP problems. The main contribution of this novel algorithm is to achieve a substantial speedup by exploiting the low-rank property inherent to several SDP problems. The convergence of the new methodology is proved by showing that the novel algorithm reduces to a particular case of the Approximated Proximal Point Algorithm. Along with the theoretical contributions, an open source numerical solver, called ProxSDP, is made available with this work. The performance of ProxSDP in comparison to state-of-the-art SDP solvers is evaluated on three case studies.

In this thesis, we present some contributions to the Markov jump linear systems theory in a context of partial information on the Markov chain. We consider that the state of the Markov chain cannot be measured, but instead there is only an observed variable that could model an asynchronous phenomenon between the application and the plant, or a simple fault detection and isolation device. In this formulation, we investigate the problem of designing controllers and filters depending only on the observed variable in the context of H2, H?, and mixed H2/H? control theory. Numerical examples and academic applications are presented for active-fault tolerant control systems and networked control systems. / Nesta tese, apresentamos algumas contribuições para a teoria de sistemas lineares com saltos markovianos em um contexto de observação parcial da cadeia de Markov. Consideramos que o estado da cadeia de Markov não pode ser medido, porém existe uma variável observada que pode modelar um fenômeno assíncrono entre a aplicação e a planta, ou ainda um dispositivo de detecção de falhas simples. Através desse modelo, investigamos o problema da síntese de controladores e filtros que dependem somente da variável observada no contexto das teorias de controle H2, H?, e misto H2/H?. Exemplos numéricos e aplicações acadêmicas são apresentadas no âmbito dos sistemas de controle tolerantes a falhas e dos sistemas de controle através da rede.

In this thesis, we present some contributions to the Markov jump linear systems theory in a context of partial information on the Markov chain. We consider that the state of the Markov chain cannot be measured, but instead there is only an observed variable that could model an asynchronous phenomenon between the application and the plant, or a simple fault detection and isolation device. In this formulation, we investigate the problem of designing controllers and filters depending only on the observed variable in the context of H2, H?, and mixed H2/H? control theory. Numerical examples and academic applications are presented for active-fault tolerant control systems and networked control systems. / Nesta tese, apresentamos algumas contribuições para a teoria de sistemas lineares com saltos markovianos em um contexto de observação parcial da cadeia de Markov. Consideramos que o estado da cadeia de Markov não pode ser medido, porém existe uma variável observada que pode modelar um fenômeno assíncrono entre a aplicação e a planta, ou ainda um dispositivo de detecção de falhas simples. Através desse modelo, investigamos o problema da síntese de controladores e filtros que dependem somente da variável observada no contexto das teorias de controle H2, H?, e misto H2/H?. Exemplos numéricos e aplicações acadêmicas são apresentadas no âmbito dos sistemas de controle tolerantes a falhas e dos sistemas de controle através da rede.

Compressive sensing (CS) is a novel sampling methodology representing a paradigm shift from conventional data acquisition schemes. The theory of compressive sensing ensures that under suitable conditions compressible signals or images can be reconstructed from far fewer samples or measurements than what are required by the Nyquist rate. So far in the literature, most works on CS concentrate on one-dimensional or two-dimensional data. However, besides involving far more data, three-dimensional (3D) data processing does have particularities that require the development of new techniques in order to make successful transitions from theoretical feasibilities to practical capacities. This thesis studies several issues arising from the applications of the CS methodology to some 3D image processing tasks. Two specific applications are hyperspectral imaging and video compression where 3D images are either directly unmixed or recovered as a whole from CS samples. The main issues include CS decoding models, preprocessing techniques and reconstruction algorithms, as well as CS encoding matrices in the case of video compression. Our investigation involves three major parts. (1) Total variation (TV) regularization plays a central role in the decoding models studied in this thesis. To solve such models, we propose an efficient scheme to implement the classic augmented Lagrangian multiplier method and study its convergence properties. The resulting Matlab package TVAL3 is used to solve several models. Computational results show that, thanks to its low per-iteration complexity, the proposed algorithm is capable of handling realistic 3D image processing tasks. (2) Hyperspectral image processing typically demands heavy computational resources due to an enormous amount of data involved. We investigate low-complexity procedures to unmix, sometimes blindly, CS compressed hyperspectral data to directly obtain material signatures and their abundance fractions, bypassing the high-complexity task of reconstructing the image cube itself. (3) To overcome the "cliff effect" suffered by current video coding schemes, we explore a compressive video sampling framework to improve scalability with respect to channel capacities. We propose and study a novel multi-resolution CS encoding matrix, and a decoding model with a TV-DCT regularization function. Extensive numerical results are presented, obtained from experiments that use not only synthetic data, but also real data measured by hardware. The results establish feasibility and robustness, to various extent, of the proposed 3D data processing schemes, models and algorithms. There still remain many challenges to be further resolved in each area, but hopefully the progress made in this thesis will represent a useful first step towards meeting these challenges in the future.

We investigate the effects of quantized channel state information (CSI) on the performance of resource allocation algorithms in wireless networks. The thesis starts with a brief overview of a specific type of quantizer, referred to as a conservative quantizer where we propose the optimality and sufficiency conditions as well as practical methods to find such quantizers. We apply this theory to the quantization of transmitter CSI in point-to-point Gaussian channels and transmission under short-term power constraints. Next, we show that in a multiple-node decode-and-forward (DF) cooperative network, the same structure for quantizer is close to op- timal for the sum-rate objective function. Based on a proposed upper bound on the rate loss in such scenarios, we also argue that the quantizer should assign uneven numbers of quantization bits to different links in the network. The simulation results show that given a target rate loss level, through quantization and bit allocation, there is, on average, 0.5−1 bits per link savings in CSI feedback requirements compared to the uniform and equal bit allocation approaches. Given the many benefits in non-uniform allocation of CSI rate in the network, we formulate a generalized bit allocation scheme which is extensible to arbitrary classes of network resource allocation problems. In the last part of this thesis, we focus on power control in an interference network and then, investigate the effects of CSI imperfections on the performance of power control algorithms. First, we propose an iterative power control algorithm based on a fixed-point iteration and prove its local convergence. Then, we show that for a centralized implementation of the power control algorithm, a uniform in dB (geometric) quantizer of channel power is efficient. Based on this choice of channel quantizer, we propose a bound on rate loss in terms of the resolution of the ii deployed quantizer, where a 3 dB in quantization error is shown to contribute to a maximum of 1 bit rate loss at each user. Similarly to the previous scenario, the upper bound suggests that an uneven assignment of numbers of quantization levels leads to smaller distortion. Based on this bound, we develop the corresponding bit allocation laws. We also investigate the effects of CSI errors on the performance of distributed power control algorithms and show that, compared to the centralized case, the distributed algorithm could lead to a further SINR loss of up to 3 dB for one or more transmitters. This error is due to the fact that because of CSI errors, the estimated interference level at each receiver is different from the induced interference wireless transmitters expect.

We investigate the effects of quantized channel state information (CSI) on the performance of resource allocation algorithms in wireless networks. The thesis starts with a brief overview of a specific type of quantizer, referred to as a conservative quantizer where we propose the optimality and sufficiency conditions as well as practical methods to find such quantizers. We apply this theory to the quantization of transmitter CSI in point-to-point Gaussian channels and transmission under short-term power constraints. Next, we show that in a multiple-node decode-and-forward (DF) cooperative network, the same structure for quantizer is close to op- timal for the sum-rate objective function. Based on a proposed upper bound on the rate loss in such scenarios, we also argue that the quantizer should assign uneven numbers of quantization bits to different links in the network. The simulation results show that given a target rate loss level, through quantization and bit allocation, there is, on average, 0.5−1 bits per link savings in CSI feedback requirements compared to the uniform and equal bit allocation approaches. Given the many benefits in non-uniform allocation of CSI rate in the network, we formulate a generalized bit allocation scheme which is extensible to arbitrary classes of network resource allocation problems. In the last part of this thesis, we focus on power control in an interference network and then, investigate the effects of CSI imperfections on the performance of power control algorithms. First, we propose an iterative power control algorithm based on a fixed-point iteration and prove its local convergence. Then, we show that for a centralized implementation of the power control algorithm, a uniform in dB (geometric) quantizer of channel power is efficient. Based on this choice of channel quantizer, we propose a bound on rate loss in terms of the resolution of the ii deployed quantizer, where a 3 dB in quantization error is shown to contribute to a maximum of 1 bit rate loss at each user. Similarly to the previous scenario, the upper bound suggests that an uneven assignment of numbers of quantization levels leads to smaller distortion. Based on this bound, we develop the corresponding bit allocation laws. We also investigate the effects of CSI errors on the performance of distributed power control algorithms and show that, compared to the centralized case, the distributed algorithm could lead to a further SINR loss of up to 3 dB for one or more transmitters. This error is due to the fact that because of CSI errors, the estimated interference level at each receiver is different from the induced interference wireless transmitters expect.

In a series of work initiated by Nemirovsky and Yudin, and later extended by Nesterov, first-order algorithms for unconstrained minimization with optimal theoretical complexity bound have been proposed. On the other hand, conjugate gradient algorithms as one of the widely used first-order techniques suffer from the lack of a finite complexity bound. In fact their performance can possibly be quite poor. This dissertation is partially on tightening the gap between these two classes of algorithms, namely the traditional conjugate gradient methods and optimal first-order techniques. We derive conditions under which conjugate gradient methods attain the same complexity bound as in Nemirovsky-Yudin's and Nesterov's methods. Moreover, we propose a conjugate gradient-type algorithm named CGSO, for Conjugate Gradient with Subspace Optimization, achieving the optimal complexity bound with the payoff of a little extra computational cost. We extend the theory of CGSO to convex problems with linear constraints. In particular we focus on solving $l_1$-regularized least square problem, often referred to as Basis Pursuit Denoising (BPDN) problem in the optimization community. BPDN arises in many practical fields including sparse signal recovery, machine learning, and statistics. Solving BPDN is fairly challenging because the size of the involved signals can be quite large; therefore first order methods are of particular interest for these problems. We propose a quasi-Newton proximal method for solving BPDN. Our numerical results suggest that our technique is computationally effective, and can compete favourably with the other state-of-the-art solvers.

There is a prolific increase in the penetration of user devices such as smartphones and tablets. In addition, user expectations for higher Quality of Service (QoS), enhanced data rates and lower latencies are relentless. In this context, network densification through the dense deployment of small cell networks, underlaying the currently existing macrocell networks, is the most appealing approach to handle the aforementioned requirements. Small cell networks are capable of reusing the spectrum locally and providing most of the capacity while macrocell networks provide a blanket coverage for mobile user equipment (UEs). However, such setup imposes a lot of issues, among which, co-tier and cross-tier interference are the most challenging. To handle co-tier interference, I have proposed a semi-distributed (hierarchical) interference management scheme based on joint clustering and resource allocation (RA) for small cells. I have formulated the problem as a Mixed Integer Non-Linear Program (MINLP), whose solution was obtained by dividing the problem into two sub-problems, where the related tasks were shared between the Femto Gateway (FGW) and small cells. As for cross-tier interference, I have formulated RA problems for both the macrocell and small cells as optimization problems. In particular, I have introduced the idea of ``Tier-Awareness'' and studied the impact of the different RA policies in the macrocell tier on the small cells performance. I have shown that the RA policy in one tier should be carefully selected. In addition, I have formulated the RA problem for small cells as an optimization problem with an objective function that accounts for both RA and admission control (AC). Finally, I have studied cloud radio access network (C-RAN) of small cells which has been considered as a typical realization of a mobile network which is capable of supporting soft and green technologies in Fifth Generation (5G) networks, as well as a platform for the practical implementation of network multiple-input multiple-output (MIMO) and coordinated multi-point (CoMP) transmission concepts. / February 2016

abstract: In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems - in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) - whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers - machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers. We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors, and analyze systems with 100+ dimensional state-space. Furthermore, we extend our algorithms to analyze robust stability over more complicated geometries such as hypercubes and arbitrary convex polytopes. Our algorithms can be readily extended to address a wide variety of problems in control such as Hinfinity synthesis for systems with parametric uncertainty and computing control Lyapunov functions. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2016