This work describes a framework for simultaneous estimation and modeling (SEAM) of dynamic systems using non-Gaussian belief fusion by first presenting the relevant fundamental formulations, then building upon these formulations incrementally towards a more general and ubiquitous framework. Multi-Gaussian belief fusion (MBF) is introduced as a natural and effective method of fusing non-Gaussian probability distribution functions (PDFs) in arbitrary dimensions efficiently and with no loss of accuracy. Construction of some multi-Gaussian structures for potential use in MBF is addressed. Furthermore, recursive Bayesian estimation (RBE) is developed for linearized systems with uncertainty in model parameters, and a rudimentary motion model correction stage is introduced. A subsequent improvement to motion model correction for arbitrarily non-Gaussian belief is developed, followed by application to observation models. Finally, SEAM is generalized to fully nonlinear and non-Gaussian systems. Several parametric studies were performed on simulated experiments in order to assess the various dependencies of the SEAM framework and validate its effectiveness in both estimation and modeling. The results of these studies show that SEAM is capable of improving estimation when uncertainty is present in motion and observation models as compared to existing methods. Furthermore, uncertainty in model parameters is consistently reduced as these parameters are updated throughout the estimation process. SEAM and its constituents have potential uses in robotics, target tracking and localization, state estimation, and more. / Doctor of Philosophy / The simultaneous estimation and modeling (SEAM) framework and its constituents described in this dissertation aim to improve estimation of signals where significant uncertainty would normally introduce error. Such signals could be electrical (e.g. voltages, currents, etc.), mechanical (e.g. accelerations, forces, etc.), or the like. Estimation is accomplished by addressing the problem probabilistically through information fusion. The proposed techniques not only improve state estimation, but also effectively "learn" about the system of interest in order to further refine estimation. Potential uses of such methods could be found in search-and-rescue robotics, robust control algorithms, and the like. The proposed framework is well-suited for any context where traditional estimation methods have difficulty handling heightened uncertainty.

Um dos desafios que ainda precisa ser superado com o objetivo de melhorar o desempenho do controle preditivo (MPC) é a sua manutenção. Reidentificação do processo é uma das melhores opções disponíveis para atualizar o modelo interno do MPC, a fim de melhorar seu desempenho. No entanto, o processo de reidentificação é dispendioso. Pesquisadores propuseram dois métodos diferentes, capazes de detectar divergências entre o processo real e o seu modelo, através da análise de correlações parciais. Utilizando essas técnicas, ao invés de reidentificar todos os sub-modelos do processo, apenas algumas entradas com divergência significativas teriam que ser perturbadas e somente a parte degradada do modelo seria atualizada. Entretanto, não há informações suficientes e análises sobre a influência das estruturas de modelo nos resultados das correlações parciais. Além disso, apesar de ambas as abordagens serem eficientes na detecção de divergências significativas, elas não fornecem informações suficientes sobre a sua quantificação. Esta dissertação de mestrado demonstra que o método de Carlsson (2010) é uma solução particular do método de Badwe et al. (2009), quando os modelos utilizados no processo de identificação são estruturas FIR. Além disso, alguns outros tipos de estruturas serão estudados, de modo a verificar se eles são adequados para a análise da correlação parcial, com o objetivo de detectar esse tipo de divergência. Quanto à limitação da detecção do nível da divergência entre o modelo e a planta, este trabalho propõe um projeto inicial de um novo método para resolver este problema, através da adição de ruído branco off-line nos dados coletados do processo, com diferentes variações antes da análise da correlação parcial. Um estudo de caso simulado é mostrado, que confirma a eficácia desta nova técnica. Finalmente, são apresentadas as conclusões encontradas e as possibilidades para estudos futuros. / One of the challenges that still needs to be overcome in order to improve the performance of the model predictive control (MPC) is its maintenance. Re-identification of the process is one of the best options available to update the internal model of the MPC, in order to improve performance. However, re-identification is costly. Researchers have proposed two different methods able to detect plant mismatch through partial correlation analysis. Using these techniques, instead of re-identifying all the sub-models in the process, only a few inputs with significant mismatch would have to be perturbed and only the degraded portion of the model would be updated. Nevertheless, there is not enough information and analysis about the influence of the model structures for identification on partial correlation results. Besides, although both approaches are efficient in detecting significant mismatches, they do not provide enough information about its magnitude. This masters thesis demonstrates that the Carlssons method (2010) is a particular solution of the Badwe et al.s method, when the models used on the identification process are FIR structures. Moreover, some other types of structures will be analyzed in order to check if they are suitable for the partial correlation procedure to detect plant mismatches. Concerning the limitation of the detection the level of plant-mismatch, this thesis proposes a starting project of a new method to address this issue by adding offline white noise to the collected data from the process with different variances before analyzing the partial correlation. A simulation case study is shown that confirms the efficacy of this new technique. Finally, conclusions and possible future studies are presented.

Um dos desafios que ainda precisa ser superado com o objetivo de melhorar o desempenho do controle preditivo (MPC) é a sua manutenção. Reidentificação do processo é uma das melhores opções disponíveis para atualizar o modelo interno do MPC, a fim de melhorar seu desempenho. No entanto, o processo de reidentificação é dispendioso. Pesquisadores propuseram dois métodos diferentes, capazes de detectar divergências entre o processo real e o seu modelo, através da análise de correlações parciais. Utilizando essas técnicas, ao invés de reidentificar todos os sub-modelos do processo, apenas algumas entradas com divergência significativas teriam que ser perturbadas e somente a parte degradada do modelo seria atualizada. Entretanto, não há informações suficientes e análises sobre a influência das estruturas de modelo nos resultados das correlações parciais. Além disso, apesar de ambas as abordagens serem eficientes na detecção de divergências significativas, elas não fornecem informações suficientes sobre a sua quantificação. Esta dissertação de mestrado demonstra que o método de Carlsson (2010) é uma solução particular do método de Badwe et al. (2009), quando os modelos utilizados no processo de identificação são estruturas FIR. Além disso, alguns outros tipos de estruturas serão estudados, de modo a verificar se eles são adequados para a análise da correlação parcial, com o objetivo de detectar esse tipo de divergência. Quanto à limitação da detecção do nível da divergência entre o modelo e a planta, este trabalho propõe um projeto inicial de um novo método para resolver este problema, através da adição de ruído branco off-line nos dados coletados do processo, com diferentes variações antes da análise da correlação parcial. Um estudo de caso simulado é mostrado, que confirma a eficácia desta nova técnica. Finalmente, são apresentadas as conclusões encontradas e as possibilidades para estudos futuros. / One of the challenges that still needs to be overcome in order to improve the performance of the model predictive control (MPC) is its maintenance. Re-identification of the process is one of the best options available to update the internal model of the MPC, in order to improve performance. However, re-identification is costly. Researchers have proposed two different methods able to detect plant mismatch through partial correlation analysis. Using these techniques, instead of re-identifying all the sub-models in the process, only a few inputs with significant mismatch would have to be perturbed and only the degraded portion of the model would be updated. Nevertheless, there is not enough information and analysis about the influence of the model structures for identification on partial correlation results. Besides, although both approaches are efficient in detecting significant mismatches, they do not provide enough information about its magnitude. This masters thesis demonstrates that the Carlssons method (2010) is a particular solution of the Badwe et al.s method, when the models used on the identification process are FIR structures. Moreover, some other types of structures will be analyzed in order to check if they are suitable for the partial correlation procedure to detect plant mismatches. Concerning the limitation of the detection the level of plant-mismatch, this thesis proposes a starting project of a new method to address this issue by adding offline white noise to the collected data from the process with different variances before analyzing the partial correlation. A simulation case study is shown that confirms the efficacy of this new technique. Finally, conclusions and possible future studies are presented.

Le concept du radar MIMO est prometteur en raison des nombreux avantages qu'il apporte par rapport aux architectures radars actuelles : flexibilité pour la formation de faisceau à l'émission - large illumination de la scène et résolution fine après traitement - et allègement de la complexité des systèmes, via la réduction du nombre d'antennes et la possibilité de transférer des fonctions de contrôle et d'étalonnage du système dans le domaine numérique. Cependant, le radar MIMO reste au stade du concept théorique, avec une prise en compte insuffisante des impacts du manque d'orthogonalité des formes d'onde et des défauts matériels.Ce travail de thèse, dans son ambition de contribuer à ouvrir la voie vers le radar MIMO opérationnel, consiste à anticiper et compenser les défauts du monde réel par des traitements numériques. La première partie traite de l'élaboration des formes d'onde MIMO. Nous montrons que les codes de phase sont optimaux en termes de résolution spatiale. Nous présentons également leurs limites en termes d'apparition de lobes secondaires en sortie de filtre adapté. La seconde partie consiste à accepter les défauts intrinsèques des formes d'onde et proposer des traitements adaptés au modèle de signal permettant d'éliminer les lobes secondaires résiduels induits. Nous développons une extension de l'Orthogonal Matching Pursuit (OMP) qui satisfait les conditions opérationnelles, notamment par sa robustesse aux erreurs de localisation, sa faible complexité calculatoire et la non nécessité de données d'apprentissage. La troisième partie traite de la robustesse des traitements vis-à-vis des écarts au modèle de signal, et particulièrement la prévention et l'anticipation de ces phénomènes afin d'éviter des dégradations de performance. En particulier, nous proposons une méthode numérique d'étalonnage des phases des émetteurs. La dernière partie consiste à mener des expérimentations en conditions réelles avec la plateforme radar MIMO Hycam. Nous montrons que certaines distorsions subies non anticipées, même limitées en sortie de filtre adapté, peuvent impacter fortement les performances en détection des traitements dépendant du modèle de signal. / The MIMO radar concept promises numerous advantages compared to today's radar architectures: flexibility for the transmitting beampattern design - including wide scene illumination and fine resolution after processing - and system complexity reduction, through the use of less antennas and the possibility to transfer system control and calibration to the digital domain. However, the MIMO radar is still at the stage of theoretical concept, with insufficient consideration for the impacts of waveforms' lack of orthogonality and system hardware imperfections.The ambition of this thesis is to contribute to paving the way to the operational MIMO radar. In this perspective, this thesis work consists in anticipating and compensating the imperfections of the real world with processing techniques. The first part deals with MIMO waveform design and we show that phase code waveforms are optimal in terms of spatial resolution. We also exhibit their limits in terms of sidelobes appearance at matched filter output. The second part consists in taking on the waveform intrinsic imperfections and proposing data-dependent processing schemes for the rejection of the induced residual sidelobes. We develop an extension for the Orthogonal Matching Pursuit (OMP) that satisfies operational requirements, especially localization error robustness, low computation complexity, and nonnecessity of training data. The third part deals with processing robustness to signal model mismatch, especially how it can be prevented or anticipated to avoid performance degradation. In particular, we propose a digital method of transmitter phase calibration. The last part consists in carrying out experiments in real conditions with the Hycam MIMO radar testbed. We exhibit that some unanticipated encountered distortions, even when limited at the matched filter output, can greatly impact the performance in detection of the data-dependent processing methods.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Model predictive control (MPC) strategies have become the standard for advanced control applications in the process industry. Significant benefits are generated from the MPC's capacity to ensure that the plant operates within its constraints more profitably. However, like any controller, after some time under operation, MPCs rarely function as when they were initially designed. A large percentage of performance degradation of MPC is associated with the deterioration of model that controller uses to predict process outputs and calculate inputs. The objective of the present work is implementation of mathematical methods that can be used to detect model-plant mismatch in linear and nonlinear MPC systems. In this work, techniques based on cross correlation, partial correlation and mutual information are implemented and tested by numerical simulation in case studies characteristic of the petrochemical industry, represented by linear and nonlinear models, operating under MPC control. The results obtained through the applying the techniques are analyzed and compared as to their efficiency is not intended to offer their potential for real industrial applications. / Estratégias de controle preditivo (MPC) têm-se tornado o padrão para aplicações de controle avançado na indústria de processos. Os benefícios significativos são gerados a partir da habilidade do controlador MPC de assegurar que a planta opere dentro das restrições de forma mais lucrativa. Porém, como todo controlador, depois de algum tempo em operação, os MPCs raramente funcionam como quando foram inicialmente projetados. Uma grande porcentagem da degradação do desempenho dos controladores MPC está associada à deterioração do modelo que o controlador usa para fazer a predição das saídas do processo e calcular as entradas. O objetivo do presente trabalho é a implementação de métodos matemáticos que possam ser utilizados para a detecção de erros planta-modelo em sistemas de controle MPC lineares e não lineares. Neste trabalho, técnicas baseadas em correlação cruzada, correlação parcial e informação mútua são implementadas e testadas por simulação numérica em estudos de caso característicos da indústria petroquímica, representados por modelos lineares e não lineares, operando sob controle MPC. Os resultados obtidos através da aplicação das técnicas são analisados e comparados quanto à sua eficiência no objetivo proposto avaliando seu potencial para aplicações industriais reais.