<p>This thesis concerns modeling and control of bilinear systems (BLS). BLS are linear but not jointly linear in state and control. In the first part of the thesis, a background to BLS and their applications to modeling and control is given. The second part, and likewise the principal theme of this thesis, is dedicated to theoretical aspects of identification, modeling and control of mainly BLS, but also linear systems. In the last part of the thesis, applications of bilinear and linear modeling and control to the activated sludge process (ASP) are given.</p>

<p>The intention is to draw more specific connections between certain deconvolution methods and also to demonstrate the application of the statistical theory of estimation in the presence of measurement error. A parametric methodology for deconvolution when the underlying distribution is of the Pareto form is developed. Maximum likelihood estimation (MLE) of the parameters of the convolved distributions is considered. Standard errors of the estimated parameters are calculated from the inverse Fisher&rsquo / s information matrix and a jackknife method. Probability-probability (P-P) plots and Kolmogorov-Smirnov (K-S) goodnessof- fit tests are used to evaluate the fit of the posited distribution. A bootstrapping method is used to calculate the critical values of the K-S test statistic, which are not available.</p>

The scope of the thesis is to estimate the parameters of continuous-time models used within control and communication from sampled data with high accuracy and in a computationally efficient way.In the thesis, continuous-time models of systems controlled in a networked environment, errors-in-variables systems, stochastic closed-loop systems, and wireless channels are considered. The parameters of a transfer function based model for the process in a networked control system are estimated by a covariance function based approach relying upon the second order statistical properties of input and output signals. Some other approaches for estimating the parameters of continuous-time models for processes in networked environments are also considered. The multiple input multiple output errors-in-variables problem is solved by means of a covariance matching algorithm. An analysis of a covariance matching method for single input single output errors-in-variables system identification is also presented. The parameters of continuous-time autoregressive exogenous models are estimated from closed-loop filtered data, where the controllers in the closed-loop are of proportional and proportional integral type, and where the closed-loop also contains a time-delay. A stochastic differential equation is derived for Jakes's wireless channel model, describing the dynamics of a scattered electric field with the moving receiver incorporating a Doppler shift. / <p>The thesis consists of five main parts, where the first part is an introduction- Parts II-IV are based on the following articles:</p><p><strong>Part II</strong> - Networked Control Systems</p><p>1. Y. Irshad, M. Mossberg and T. Söderström. <em>System identification in a networkedenvironment using second order statistical properties</em>.</p><p>A versionwithout all appendices is published as Y. Irshad, M. Mossberg and T. Söderström. <em>System identification in a networked environment using second order statistical properties</em>. Automatica, 49(2), pages 652–659, 2013.</p><p>Some preliminary results are also published as M. Mossberg, Y. Irshad and T. Söderström. <em>A covariance function based approachto networked system identification.</em> In Proc. 2nd IFAC Workshop on Distributed Estimation and Control in Networked Systems, pages 127–132, Annecy,France, September 13–14, 2010</p><p>2. Y. Irshad and M. Mossberg. <em>Some parameters estimation methods applied tonetworked control systems</em>.A journal submission is made. Some preliminary results are published as Y. Irshad and M. Mossberg.<em> A comparison of estimation concepts applied to networked control systems</em>. In Proc. 19th Int. Conf. on Systems, Signals andImage Processing, pages 120–123, Vienna, Austria, April 11–13, 2012.</p><p><strong>Part III</strong> - Errors-in-variables Identification</p><p>3. Y. Irshad and M. Mossberg. <em>Continuous-time covariance matching for MIMOEIV system identification</em>. A journal submission is made.</p><p>4. T. Söderström, Y. Irshad, M. Mossberg and W. X. Zheng. <em>On the accuracy of acovariance matching method for continuous-time EIV identification. </em>Provisionally accepted for publication in Automatica.</p><p>Some preliminary results are published as T. Söderström, Y. Irshad, M. Mossberg, and W. X. Zheng. <em>Accuracy analysis of a covariance matching method for continuous-time errors-in-variables system identification</em>. In Proc. 16th IFAC Symp. System Identification, pages 1383–1388, Brussels, Belgium, July 11–13, 2012.</p><p><strong>Part IV</strong> - Wireless Channel Modeling</p><p>5. Y. Irshad and M. Mossberg.<em> Wireless channel modeling based on stochasticdifferential equations .</em>Some results are published as M. Mossberg and Y. Irshad.<em> A stochastic differential equation forwireless channelsbased on Jakes’s model with time-varying phases,</em> In Proc. 13th IEEEDigitalSignal Processing Workshop, pages 602–605, Marco Island, FL, January4–7, 2009.</p><p><strong>Part V</strong> - Closed-loop Identification</p><p>6. Y. Irshad and M. Mossberg. Closed-loop identification of P- and PI-controlledtime-delayed stochastic systems.Some results are published as M. Mossberg and Y. Irshad. <em>Closed-loop identific ation of stochastic models from filtered data</em>, In Proc. IEEE Multi-conference on Systems and Control,San Antonio, TX, September 3–5, 2008</p>

<p>The intention is to draw more specific connections between certain deconvolution methods and also to demonstrate the application of the statistical theory of estimation in the presence of measurement error. A parametric methodology for deconvolution when the underlying distribution is of the Pareto form is developed. Maximum likelihood estimation (MLE) of the parameters of the convolved distributions is considered. Standard errors of the estimated parameters are calculated from the inverse Fisher&rsquo / s information matrix and a jackknife method. Probability-probability (P-P) plots and Kolmogorov-Smirnov (K-S) goodnessof- fit tests are used to evaluate the fit of the posited distribution. A bootstrapping method is used to calculate the critical values of the K-S test statistic, which are not available.</p>

Magister Scientiae - MSc / The intention is to draw more specific connections between certain deconvolution methods and also to demonstrate the application of the statistical theory of estimation in the presence of measurement error. A parametric methodology for deconvolution when the underlying distribution is of the Pareto form is developed. Maximum likelihood estimation (MLE) of the parameters of the convolved distributions is considered. Standard errors of the estimated parameters are calculated from the inverse Fisher&rsquo;s information matrix and a jackknife method. Probability-probability (P-P) plots and Kolmogorov-Smirnov (K-S) goodnessof- fit tests are used to evaluate the fit of the posited distribution. A bootstrapping method is used to calculate the critical values of the K-S test statistic, which are not available. / South Africa

>Magister Scientiae - MSc / Estimation of population distributions, from samples that are contaminated by measurement errors, is a common problem. This study considers the problem of estimating the population distribution of independent random variables Xi, from error-contaminated samples ~i (.j = 1, ... , n) such that Yi = Xi + f·.i, where E is the measurement error, which is assumed independent of X. The measurement error ( is also assumed to be normally distributed. Since the observed distribution function is a convolution of the error distribution with the true underlying distribution, estimation of the latter is often referred to as a deconvolution problem. A thorough study of the relevant deconvolution literature in statistics is reported. We also deal with the specific case when X is assumed to follow a truncated Pareto form. If observations are subject to Gaussian errors, then the observed Y is distributed as the convolution of the finite-support Pareto and Gaussian error distributions. The convolved probability density function (PDF) and cumulative distribution function (CDF) of the finite-support Pareto and Gaussian distributions are derived. The intention is to draw more specific connections bet.ween certain deconvolution methods and also to demonstrate the application of the statistical theory of estimation in the presence of measurement error. A parametric methodology for deconvolution when the underlying distribution is of the Pareto form is developed. Maximum likelihood estimation (MLE) of the parameters of the convolved distributions is considered. Standard errors of the estimated parameters are calculated from the inverse Fisher's information matrix and a jackknife method. Probability-probability (P-P) plots and Kolmogorov-Smirnov (K-S) goodnessof- fit tests are used to evaluate the fit of the posited distribution. A bootstrapping method is used to calculate the critical values of the K-S test statistic, which are not available. Simulated data are used to validate the methodology. A real-life application of the methodology is illustrated by fitting convolved distributions to astronomical data

In this dissertation, we approach three different contributions in measurement error model (MEM). Initially, we carry out maximum penalized likelihood inference in MEMs under the normality assumption. The methodology is based on the method proposed by Firth (1993), which can be used to improve some asymptotic properties of the maximum likelihood estimators. In the second contribution, we develop two new estimation methods based on generalized fiducial inference for the precision parameters and the variability product under the Grubbs model considering the two-instrument case. One method is based on a fiducial generalized pivotal quantity and the other one is built on the method of the generalized fiducial distribution. Comparisons with two existing approaches are reported. Finally, we propose to study inference in a heteroscedastic MEM with known error variances. Instead of the normal distribution for the random components, we develop a model that assumes a skew-t distribution for the true covariate and a centered Students t distribution for the error terms. The proposed model enables to accommodate skewness and heavy-tailedness in the data, while the degrees of freedom of the distributions can be different. We use the maximum likelihood method to estimate the model parameters and compute them via an EM-type algorithm. All proposed methodologies are assessed numerically through simulation studies and illustrated with real datasets extracted from the literature. / Neste trabalho abordamos três contribuições diferentes em modelos com erros de medição (MEM). Inicialmente estudamos inferência pelo método de máxima verossimilhança penalizada em MEM sob a suposição de normalidade. A metodologia baseia-se no método proposto por Firth (1993), o qual pode ser usado para melhorar algumas propriedades assintóticas de os estimadores de máxima verossimilhança. Em seguida, propomos construir dois novos métodos de estimação baseados na inferência fiducial generalizada para os parâmetros de precisão e a variabilidade produto no modelo de Grubbs para o caso de dois instrumentos. O primeiro método é baseado em uma quantidade pivotal generalizada fiducial e o outro é baseado no método da distribuição fiducial generalizada. Comparações com duas abordagens existentes são reportadas. Finalmente, propomos estudar inferência em um MEM heterocedástico em que as variâncias dos erros são consideradas conhecidas. Nós desenvolvemos um modelo que assume uma distribuição t-assimétrica para a covariável verdadeira e uma distribuição t de Student centrada para os termos dos erros. O modelo proposto permite acomodar assimetria e cauda pesada nos dados, enquanto os graus de liberdade das distribuições podem ser diferentes. Usamos o método de máxima verossimilhança para estimar os parâmetros do modelo e calculá-los através de um algoritmo tipo EM. Todas as metodologias propostas são avaliadas numericamente em estudos de simulação e são ilustradas com conjuntos de dados reais extraídos da literatura

Modelos com erros de medição têm recebido a atenção de vários pesquisadores das mais diversas áreas de conhecimento. O principal objetivo desta dissertação consiste no estudo de um modelo funcional com erros de medição heteroscedásticos na presença de réplicas das observações. O modelo proposto estende resultados encontrados na literatura na medida em que as réplicas são parte do modelo, ao contrário de serem utilizadas para estimação das variâncias, doravante tratadas como conhecidas. Alguns procedimentos de estimação tais como o método de máxima verossimilhança, o método dos momentos e o método de extrapolação da simulação (SIMEX) na versão empírica são apresentados. Além disso, propõe-se o teste da razão de verossimilhanças e o teste de Wald com o objetivo de testar algumas hipóteses de interesse relacionadas aos parâmetros do modelo adotado. O comportamento dos estimadores de alguns parâmetros e das estatísticas propostas (resultados assintóticos) são analisados por meio de um estudo de simulação de Monte Carlo, utilizando-se diferentes números de réplicas. Por fim, a proposta é exemplificada com um conjunto de dados reais. Toda parte computacional foi desenvolvida em linguagem R (R Development Core Team, 2011) / Measurement error models have received the attention of many researchers of several areas of knowledge. The aim of this dissertation is to study a functional heteroscedastic measurement errors model with replicated observations. The proposed model extends results from the literature in that replicas are part of the model, as opposed to being used for estimation of the variances, now treated as known. Some estimation procedures such as maximum likelihood method, the method of moments and the empirical simulation-extrapolation method (SIMEX) are presented. Moreover, it is proposed the likelihood ratio test and Wald test in order to test hypotheses of interest related to the model parameters used. The behavior of the estimators of some parameters and statistics proposed (asymptotic results) are analyzed through Monte Carlo simulation study using different numbers of replicas. Finally, the proposal is illustrated with a real data set. The computational part was developed in R language (R Development Core Team, 2011)

Raman spectroscopy provides a powerful means of chemical identification in a variety of fields, partly because of its non-contact nature and the speed at which measurements can be taken. The development of powerful, inexpensive lasers and sensitive charge-coupled device (CCD) detectors has led to widespread use of commercial and scientific Raman systems. However, relatively little work has been done developing physics-based probabilistic models for Raman measurement systems and crafting inference algorithms within the framework of statistical estimation and detection theory. The objective of this thesis is to develop algorithms and performance bounds for the identification of chemicals from their Raman spectra. First, a Poisson measurement model based on the physics of a dispersive Raman device is presented. The problem is then expressed as one of deterministic parameter estimation, and several methods are analyzed for computing the maximum-likelihood (ML) estimates of the mixing coefficients under our data model. The performance of these algorithms is compared against the Cramer-Rao lower bound (CRLB). Next, the Raman detection problem is formulated as one of multiple hypothesis detection (MHD), and an approximation to the optimal decision rule is presented. The resulting approximations are related to the minimum description length (MDL) approach to inference. In our simulations, this method is seen to outperform two common general detection approaches, the spectral unmixing approach and the generalized likelihood ratio test (GLRT). The MHD framework is applied naturally to both the detection of individual target chemicals and to the detection of chemicals from a given class. The common, yet vexing, scenario is then considered in which chemicals are present that are not in the known reference library. A novel variation of nonnegative matrix factorization (NMF) is developed to address this problem. Our simulations indicate that this algorithm gives better estimation performance than the standard two-stage NMF approach and the fully supervised approach when there are chemicals present that are not in the library. Finally, estimation algorithms are developed that take into account errors that may be present in the reference library. In particular, an algorithm is presented for ML estimation under a Poisson errors-in-variables (EIV) model. It is shown that this same basic approach can also be applied to the nonnegative total least squares (NNTLS) problem. Most of the techniques developed in this thesis are applicable to other problems in which an object is to be identified by comparing some measurement of it to a library of known constituent signatures.

Les principales contributions de cette thèse concernent l'identification à temps continu des systèmes par modèles non entiers dans un contexte à erreurs en les variables. Deux classes de méthodes sont développées : la première classe est fondée sur les statistiques d'ordre trois et la deuxième est fondée sur les statistiques d'ordre quatre. Dans chaque classe, deux cas différents sont distingués : le premier cas suppose que tous les ordres de dérivation non entiers sont connus a priori et seuls les coefficients de l'équation différentielle non entière sont estimés en utilisant les estimateurs fondés sur les statistiques d'ordre supérieur. Le deuxième cas suppose que les ordres de dérivation sont commensurables à un ordre nu estimé au même titre que les coefficients de l'équation différentielle non entière par des techniques d'optimisation non linéaire combinées aux estimateurs fondés sur les cumulants d'ordre trois et quatre. Des exemples de simulation numérique illustrent les développements théoriques. Des applications pratiques sur la modélisation du phénomène de diffusion de chaleur dans un barreau d'Aluminium et sur la modélisation d'un système électronique ont montré la pertinence des méthodes développées. / This thesis deals with continuous-time system identification by fractional models in the EIV context. Two classes of methods are developed : the first class is based on third-order statistics and the second one is based on fourth-order statistics. Firstly, all differentiation orders are known a priori and only the coefficients of the differential equation are estimated using the developed algorithms based on higher-order statistics. Then, they are extended to estimate both the fractional differential equation coefficients and the commensurate order. Simulation examples display the theoretical developments on system identification in the EIV context. A practical application for modeling heat transfer phenomena in an aluminium rod and for modeling an electronic real system have shown the efficiency of the developed methods.