Ce mémoire est dédié à l’étude de la synthèse de l’estimation d’état en temps fini par une approche algébrique (les techniques développées au sein de l’équipe ALIEN) pour les systèmes linéaires à paramètres invariant dans le temps (LTI) sujets à des perturbations extérieures inconnues, les systèmes linéaires à paramètres variant dans le temps (LTV) et les systèmes linéaires à commutation en temps continu (SLC). Pour les systèmes LTI et LTV, une expression formelle de l’état en fonction des intégrales itérées des sorties et de l’entrée a été donnée. Pour les systèmes linéaires à commutation, en combinant les résultats de l’estimation d’état pour les systèmes LTI et de la détection de l’instant de commutation en temps réel présentée dans le chapitre 4, nous donnons la démarche principale de l’estimation en temps réel du mode courant et l’état continu du système. Pour ce faire, on applique certains outils mathématiques : la transformation de Laplace, les outils issus du calcul opérationnel et la théorie des distributions / This PhD thesis is dedicated to the synthesis of the state estimation in a finite time by an algebraic approach (the techniques developed within the ALIEN group) for the linear time-invariant systems (LTI) subject to the external unknown disturbances, the linear time-varying systems (LTV) and the switched linear systems (SLC) in continuous time. For the LTI and LTV systems, a formal expression of state as a function of iterated integrals of the output and the input is obtained. For switched linear systems, combining the results of state estimation for LTI systems and switch instant detection presented in Chapter 4, we give the main approach of current mode estimation and the continuous state estimation in real time. To do this, one applies some mathematical tools: Laplace transforms, the operational calculus and the theory of distribution

Orientador: Pedro Luis Dias Peres / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-05T03:23:54Z (GMT). No. of bitstreams: 1 Leite_ValterJuniordeSouza_D.pdf: 4310851 bytes, checksum: bcd0414d19eb46e02496290857fdf9bc (MD5) Previous issue date: 2005 / Resumo: Este trabalho trata da aplica¸c¿ao de funcionais de Lyapunov e Lyapunov-Krasovskii dependentes de parâmetro a alguns problemas selecionados da área de controle robusto, a saber: D-estabilidade robusta de polítipo de matrizes, D-estabilidade robusta de politopos de polinômios matriciais, estabilidade robusta de sistemas neutrais com atrasos variantes no tempo e controle robusto H8 de sistemas discretos no tempo com atraso nos estados. É utilizada a representação politópica para as incertezas dos sistemas estudados. São obtidas formulações convexas, na forma de desigualdades matriciais lineares, suficientes para a solução dos problemas selecionados. Essas condições podem ser resolvidas numericamente de maneira eficiente por meio de algoritmos especializados baseados em pontos interiores. Os resultados obtidos são menos conservadores que os encontrados na literatura, baseados em geral na estabilidade quadrática, isto é, as matrizes dos funcionais são fixas e independentes da incerteza / Abstract: This work deals with the application of parameter dependent Lyapunov and Lyapunov-Krasovskii functionals to some selected problems of robust control: robust D-stability of polytopes of matrices, robust D-stability of polytopes of polynomial matrices, robust stability of uncertain neutral systems with timevarying delays and robust H8 control of uncertain discrete time delay systems. The polytopic representation is used to describe the uncertainties. Convex formulations are obtained, in terms of inear matrix inequalities, that are sufficient for the solution of the selected problems. Those conditions can be solved in a efficient way through specialized interior point algorithms. The obtained results are less conservative than those from the literature, in general based on quadratic stability, i.e., the matrices in the functionals are fixed and do not depend on the uncertainty / Doutorado / Automação / Doutor em Engenharia Elétrica

Orientador: Pedro Luis Dias Peres / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-22T18:08:10Z (GMT). No. of bitstreams: 1 Agulhari_CristianoMarcos_D.pdf: 2096468 bytes, checksum: 0e762392c4ee0ab5e249ccd096ab4acf (MD5) Previous issue date: 2013 / Resumo: As principais contribuições desta tese consistem no desenvolvimento de métodos para a síntese de controladores e para a análise de estabilidade de sistemas lineares, variantes ou invariantes no tempo. Com relação aos sistemas invariantes no tempo, o objetivo é a síntese de controladores robustos de ordem reduzida para sistemas a tempo contínuo com parâmetros incertos. O método apresentado para a síntese baseia-se em uma técnica de dois estágios, em que um ganho de realimentação de estados é construído no primeiro estágio e posteriormente utilizado no segundo estágio, que fornece o controlador robusto desejado. Cada etapa consiste na resolução de condições sob a forma de desigualdades matriciais lineares. No caso de sistemas variantes no tempo, em geral, dependendo das informações disponíveis, dois modelos matemáticos podem ser utilizados. Por um lado, para sistemas cujos elementos variantes no tempo são limitados em norma, mas não são completamente conhecidos, é possível utilizar modelos dependentes de parâmetros variantes no tempo, que levam a uma representação politópica. Nesse caso, a técnica de estabilização proposta é baseada no método de dois estágios, para gerar controladores dependentes dos parâmetros. Supõe-se que os parâmetros sejam mensuráveis em tempo real, e os controladores são sintetizados de forma a serem robustos a ruídos nas medições. Por outro lado, se a dinâmica variante no tempo é conhecida, o sistema pode ser tratado diretamente sem que seja utilizado nenhum tipo de parametrização. Duas técnicas de síntese são propostas para esse caso: a construção de ganhos estabilizantes utilizando diretamente a matriz de transição de estados, e uma técnica de síntese projetada a partir de um novo critério para a verificação da estabilidade do sistema. A validade dos métodos propostos é ilustrada por meio de exemplos numéricos, que mostram a qualidade dos resultados que podem ser obtidos / Abstract: The main contributions of this thesis concern the development of methods for the stability analysis and the synthesis of controllers for linear systems, either time varying or time-invariant. Concerning time-invariant systems, the objective is the synthesis of reduced-order robust controllers for continuous-time systems with uncertain parameters. The method presented for the synthesis is based on a two-stage technique, in which a stabilizing state-feedback gain is constructed in the first stage and then applied on the second stage to search for the desired controller. Each stage consists in the resolution of conditions based on linear matrix inequalities. In the case of time-varying systems, depending on the amount of available information, two mathematical models may be used. On one hand, if the time-varying elements of the system are not entirely known, one can model the system as function of time-varying parameters, resulting on a polytopic representation. In this case, the stabilization method proposed is based on the two-stage technique, which yields parameter-dependent controllers. The parameters are supposed to be real-time measurable, and the controllers are robust with respect to noises and uncertainties on the measures. On the other hand, if the time-varying dynamics are known, the system may be directly handled without using any parameterization. Two synthesis techniques are proposed in this case: the construction of stabilizing gains by using the state transition matrix, and a synthesis technique derived from a new stability criterion for time-varying systems. The validity of the proposed methods is illustrated through numerical examples that show the efficiency of the results that can be obtained / Doutorado / Automação / Doutor em Engenharia Elétrica

Dynamical structure functions were developed as a partial structure representation of linear time-invariant systems to be used in the reconstruction of biological networks. Dynamical structure functions contain more information about structure than a system's transfer function, while requiring less a priori information for reconstruction than the complete computational structure associated with the state space realization. Early sufficient conditions for network reconstruction with dynamical structure functions severely restricted the possible applications of the reconstruction process to networks where each input independently controls a measured state. The first contribution of this thesis is to extend the previously established sufficient conditions to incorporate both necessary and sufficient conditions for reconstruction. These new conditions allow for the reconstruction of a larger number of networks, even networks where independent control of measured states is not possible. The second contribution of this thesis is to extend the robust reconstruction algorithm to all reconstructible networks. This extension is important because it allows for the reconstruction of networks from real data, where noise is present in the measurements of the system. The third contribution of this thesis is a Matlab toolbox that implements the robust reconstruction algorithm discussed above. The Matlab toolbox takes in input-output data from simulations or real-life perturbation experiments and returns the proposed Boolean structure of the network. The final contribution of this thesis is to increase the applicability of dynamical structure functions to more than just biological networks by applying our reconstruction method to wireless communication networks. The reconstruction of wireless networks produces a dynamic interference map that can be used to improve network performance or interpret changes of link rates in terms of changes in network structure, enabling novel anomaly detection and security schemes.

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Nesta dissertação é apresentado um estudo sobre a recuperação de sinais modelados por somas ponderadas de exponenciais complexas. Para tal, são introduzidos conceitos elementares em teoria de sinais e sistemas, em particular, os sistemas lineares invariantes no tempo, SLITs, que podem ser representados matematicamente por equações diferenciais, ou equações de diferenças, para sinais analógicos ou digitais, respectivamente. Equações deste tipo apresentam como solução somas ponderadas de exponenciais complexas, e assim fica estabelecida a relação entre os sistemas de tipo SLIT e o modelo em estudo. Além disso, são apresentadas duas combinações de métodos utilizadas na recuperação dos parâmetros dos sinais: métodos de Prony e mínimos quadrados, e métodos de Kung e mínimos quadrados, onde os métodos de Prony e Kung recuperam os expoentes das exponenciais e o método dos mínimos quadrados recupera os coeficientes lineares do modelo. Finalmente, são realizadas cinco simulações de recuperação de sinais, sendo a última, uma aplicação na área de modelos de qualidade de água. / A study on the recovery of signals modeled by weighted sums of complex exponentials complex is presented. For this, basic concepts of signals and systems theory are introduced. In particular, the linear time invariant systems (LTI Systems) are considered, which can be mathematically represented by differential equations or difference equations, respectively, for analog or digital signals. The solution of these types of equations is given by a weighted sum of complex exponentials, so the relationship between the LTI Systems and the model of study is established. Furthermore, two combinations of methods are used to recover the parameters of the signals: Prony and least squares methods, and Kung and least squares methods, where Prony and Kung methods are used to recover the exponents of the exponentials and the least square method is used to recover the linear coefficients of the model. Finally, five simulations are performed for the recovery of signals, the last one being an application in the area of water quality models.

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Nesta dissertação é apresentado um estudo sobre a recuperação de sinais modelados por somas ponderadas de exponenciais complexas. Para tal, são introduzidos conceitos elementares em teoria de sinais e sistemas, em particular, os sistemas lineares invariantes no tempo, SLITs, que podem ser representados matematicamente por equações diferenciais, ou equações de diferenças, para sinais analógicos ou digitais, respectivamente. Equações deste tipo apresentam como solução somas ponderadas de exponenciais complexas, e assim fica estabelecida a relação entre os sistemas de tipo SLIT e o modelo em estudo. Além disso, são apresentadas duas combinações de métodos utilizadas na recuperação dos parâmetros dos sinais: métodos de Prony e mínimos quadrados, e métodos de Kung e mínimos quadrados, onde os métodos de Prony e Kung recuperam os expoentes das exponenciais e o método dos mínimos quadrados recupera os coeficientes lineares do modelo. Finalmente, são realizadas cinco simulações de recuperação de sinais, sendo a última, uma aplicação na área de modelos de qualidade de água. / A study on the recovery of signals modeled by weighted sums of complex exponentials complex is presented. For this, basic concepts of signals and systems theory are introduced. In particular, the linear time invariant systems (LTI Systems) are considered, which can be mathematically represented by differential equations or difference equations, respectively, for analog or digital signals. The solution of these types of equations is given by a weighted sum of complex exponentials, so the relationship between the LTI Systems and the model of study is established. Furthermore, two combinations of methods are used to recover the parameters of the signals: Prony and least squares methods, and Kung and least squares methods, where Prony and Kung methods are used to recover the exponents of the exponentials and the least square method is used to recover the linear coefficients of the model. Finally, five simulations are performed for the recovery of signals, the last one being an application in the area of water quality models.

We consider the problem of Adaptive Control of finite-dimensional, stable, Linear Time Invariant (LTI) plants. Amongst such plants, the subclass regarding which an upper bound on the order is not known or which are known to be nonminimum phase (zeros in the unstable region) pose formidable problems in their own right. On one hand, if an upper bound on the order of the plant is not known, adaptive control usually involves some form of order estimation. On the other hand, when the plant is allowed to be either minimum phase or nonminimum phase, the adaptive control problem, as is well-known, becomes considerably-less tractable. In this study, the class of unknown plants considered is such that no information is available on the upper bound of the plant order and, further, the plant may be either minimum phase or nonminimum phase. Albeit known to be stable, such plants throw myriads of challenges in the context of adaptive control. Adaptive control involving such plants has been addressed [79] in a Model Reference Adaptive Control (MRAC) framework. There, the inputs and outputs of the unknown plant are the only quantities available by measurement in terms of which any form of modeling of the unknown plant may be made. Inputs to the reference model have been taken from certain restricted classes of bounded signals. In particular, the three classes of inputs considered are piecewise continuous bounded functions which asymptotically approach • a nonzero constant, • a sinusoid, and • a sinusoid with a nonzero shift. Moreover, the control law is such that adaptation is carried out at specific instants separated by progressively larger intervals of time. The schemes there have been proved to be e-optimal in the sense of a suitably formulated optimality criterion. If, however, the reference model inputs be extended to the class of piecewise continuous bounded functions, that would compound the complexity of the adaptive control problem. Only one attempt [78] in adaptive control in such a setting has come to our notice. The problem there has been tackled by an application of the theory of Pade Approximations to time moments of an LTI system. Based on a time moments estimation procedure, a simple adaptive scheme for Single-Input Single-Output (SISO) systems with only a cascade compensator has been reported. The first chapter is essentially meant to ensure that the problem we seek to address in the field of adaptive control indeed has scope for research. Having defined Adaptive Control, we selectively scan through the literature on LTI systems, with focus on MRAC. We look out in particular for studies involving plants of which not much is known regarding their order and systems which are possibly nonminimum phase. We found no evidence to assert that the problem of adaptive control of stable LTI systems, not necessarily minimum phase and of unknown upper bound on the order, was explored enough, save two attempts involving SISO systems. Taking absence of evidence (of in-depth study) for evidence of absence, we make a case for the problem and formally state it. We preview the thesis. We set two targets before us in Chapter 2. The first is to review one of the existing procedures attacking the problem we intend to address. Since the approach is based on the notion of time moments of an LTI system, and as we are to employ Pade Approximations as a tool, we uncover these concepts to the limited extent of our requirement. The adaptive procedure, Plant Command Modifier Scheme (PCMS) [78], for SISO plants is reported in some detail. It stands supported on an algorithm specially designed to estimate the time moments of an LTI system given no more than its input and output. Model following there has been sought to be achieved by matching the first few time moments of the reference model by the corresponding ones of the overall compensated plant. The plant time moment estimates have been taken to represent the unknown plant. The second of the goals is to analyze PCMS critically so that it may serve as a forerunner to our work. We conclude the chapter after accomplishing these goals. In Chapter 3, we devise a time moment estimator for SISO systems from a perspective which is conceptually equivalent to, yet functionally different from, that appropriated in [78]. It is a recipe to obtain estimates of time moments of a system by computing time moment estimates of system input and output signals measured up to current time. Pade approximations come by handy for this purpose. The lacunae exposed by a critical examination of PCMS in Chapter 2 guide us to progressively refine the estimator. Infirmities in the control part of PCMS too have come to light on our probing into it. A few of these will be fixed by way of fabricating two exclusively cascade compensators. We encounter some more issues, traceable to the estimator, which need redressal. Instead of directly fine-tuning the estimator itself, as is the norm, we propose the idea of 'estimating' the lopsidedness of the estimator by using it on the fully known reference model. This will enable us to effect corrections and obtain admissible estimates. Next, we explore the possibility of incorporating feedback compensation in addition to the existing cascade compensation. With output error minimization in mind, we come up with three schemes in this category. In the process, we anticipate the risk of instability due to feedback and handle it by means of an instability preventer with an inbuilt instability detector. Extensive simulations with minimum and rionminimum phase unknown plants employing the various schemes proposed are presented. A systematic study of simulation results reveals a dyad of hierarchies of progressively enhanced overall performance. One is in the sequence of the proposed schemes and the other in going for matching more and more moments. Based on our experiments we pick one of the feedback schemes as the best. Chapter 4 is conceived of as a bridge between SISO and multivariable systems. A transition from SISO to Multi-Input Multi-Output (MIMO) adaptive control is not a proposition confined to the mathematics of dimension-enhancement. A descent from the MIMO to the SISO case is expected to be relatively simple, though. So to transit as smoothly and gracefully as possible, some issues have to be placed in perspective before exploring multivariable systems. We succinctly debate on the efforts in pursuit of the exact vis-a-vis the accurate, and their implications. We then set some notations and formulate certain results which serve to unify and simplify the development in the subsequent three chapters. We list a few standard results from matrix theory which are to be of frequent use in handling multivariable systems. We derive control laws for Single-Input Multi-Output (SIMO) systems in Chapter 5. Expectedly, SIMO systems display traits of observability and uncontrollability. Results of illustrative simulations are furnished. In Chapter 6, we formulate control laws for Multi-Input Single-Output (MISO) systems. Characteristics of unobservability and controllability stand out there. We present case studies. Before actually setting foot onto MIMO systems, we venture to conjecture on what to expect there. We work out all the cascade and feedback adaptive schemes for square and nonsquare MIMO systems in Chapter 7. We show that MIMO laws when projected to MISO, SIMO and SISO cases agree with the corresponding laws in the respective cases. Thus the generality of our treatment of MIMO systems over other multivariable and scalar systems is established. We report simulations of instances depicting satisfactory performance and highlight the limitations of the schemes in tackling the family of plants of unknown upper bound on the order and possibly nonminimum phase. This forms the culmination of our exercise which took off from the reported work involving SISO systems [78]. Up to the end of the 7th chapter, we are in pursuit of solutions for the problem as general as in §1.4. For SISO systems, with input restrictions, the problem has been addressed in [79]. The laws proposed there carry out adaptation only at certain discrete instants; with respect to a suitably chosen cost, the final laws are proved to be e>optimal. In Chapter 8, aided by initial suboptimal control laws, we finally devise two algorithms with continuous-time adaptation and prove their optimality. Simulations with minimum and nonminimum phase plants reveal the effectiveness of the various laws, besides throwing light on the bootstrapping and auto-rectifying features of the algorithms. In the tail-piece, we summarize the work and wind up matters reserved for later deliberation. As we critically review the present work, we decant the take-home message. A short note on applications followed by some loud thinking as a spin-off of this report will take us to finis.