Although nonlinear model predictive control (NMPC) might be the best choice for a nonlinear plant, it is still not widely used. This is mainly due to the computational burden associated with solving online a set of nonlinear differential equations and a nonlinear dynamic optimization problem in real time. This thesis is concerned with strategies aimed at reducing the computational burden involved in different stages of the NMPC such as optimization problem, state estimation, and nonlinear model identification. A major part of the computational burden comes from function and derivative evaluations required in different parts of the NMPC algorithm. In this work, the problem is tackled using a recently introduced efficient tool, the automatic differentiation (AD). Using the AD tool, a function is evaluated together with all its partial derivative from the code defining the function with machine accuracy. A new NMPC algorithm based on nonlinear least square optimization is proposed. In a first–order method, the sensitivity equations are integrated using a linear formula while the AD tool is applied to get their values accurately. For higher order approximations, more terms of the Taylor expansion are used in the integration for which the AD is effectively used. As a result, the gradient of the cost function against control moves is accurately obtained so that the online nonlinear optimization can be efficiently solved. In many real control cases, the states are not measured and have to be estimated for each instance when a solution of the model equations is needed. A nonlinear extended version of the Kalman filter (EKF) is added to the NMPC algorithm for this purpose. The AD tool is used to calculate the required derivatives in the local linearization step of the filter automatically and accurately. Offset is another problem faced in NMPC. A new nonlinear integration is devised for this case to eliminate the offset from the output response. In this method, an integrated disturbance model is added to the process model input or output to correct the plant/model mismatch. The time response of the controller is also improved as a by–product. The proposed NMPC algorithm has been applied to an evaporation process and a two continuous stirred tank reactor (two–CSTR) process with satisfactory results to cope with large setpoint changes, unmeasured severe disturbances, and process/model mismatches. When the process equations are not known (black–box) or when these are too complicated to be used in the controller, modelling is needed to create an internal model for the controller. In this thesis, a continuous time recurrent neural network (CTRNN) in a state–space form is developed to be used in NMPC context. An efficient training algorithm for the proposed network is developed using AD tool. By automatically generating Taylor coefficients, the algorithm not only solves the differentiation equations of the network but also produces the sensitivity for the training problem. The same approach is also used to solve online the optimization problem of the NMPC. The proposed CTRNN and the predictive controller were tested on an evaporator and two–CSTR case studies. A comparison with other approaches shows that the new algorithm can considerably reduce network training time and improve solution accuracy. For a third case study, the ALSTOM gasifier, a NMPC via linearization algorithm is implemented to control the system. In this work a nonlinear state–space class Wiener model is used to identify the black–box model of the gasifier. A linear model of the plant at zero–load is adopted as a base model for prediction. Then, a feedforward neural network is created as the static gain for a particular output channel, fuel gas pressure, to compensate its strong nonlinear behavior observed in open–loop simulations. By linearizing the neural network at each sampling time, the static nonlinear gain provides certain adaptation to the linear base model. The AD tool is used here to linearize the neural network efficiently. Noticeable performance improvement is observed when compared with pure linear MPC. The controller was able to pass all tests specified in the benchmark problem at all load conditions.

Power Amplifiers (PAs) are the key building blocks of the emerging wireless radios systems. They dominate the power consumption and sources of distortion, especially when driven with modulated signals. Several approaches have been devised to characterize the nonlinearity of a PA. Among these approaches, dynamic amplitude (AM/AM) and phase (AM/PM) distortion characteristics are widely used to characterize the PA nonlinearity and its effects on the output signal in power, frequency or time domains, when driven with realistic modulated signals. The inherent nonlinear behaviour of PAs generally yield output signals with an unacceptable quality, an undesirable level of out-of-band emission, high Error Vector Magnitudes (EVMs) and low Adjacent Channel Power Ratios (ACPRs), which usually fail to meet the established performance standards. Traditionally, PAs are forced to operate deeply in their back-off region, far from their power capacity, in order to pass the mandatory spectrum mask (ACPR requirement) and to achieve acceptable EVM. Despite its simplicity, this solution is increasingly discarded, as it leads to cost and power inefficient radios. Alternatively, several linearization techniques, such as feedback, feed-forward and predistortion, have been devised to tackle PA nonlinearity and, consequently, improve the achievable the linearity versus power efficiency trade-off. Among these linearization techniques, the Digital Pre-Distortion (DPD) technique consists of incorporating an extra nonlinear function before the PA, in order to preprocess the input signal to the PA, so that the overall cascaded systems behave linearly. The overall linearity of the cascaded system (DPD plus PA) relies primarily on the ability of the DPD function to produce nonlinearities that are equal in magnitude and out-of-phase to those generated by the PA. Hence, a good understanding and accurate modeling of PA distortions is a crucial step in the construction of an adequate DPD function. This thesis explores DPD through techniques based on Artificial Neural Networks (ANNs). The choice of ANN as a modeling tool was motivated by its proven strength in modeling dynamic nonlinear systems. This thesis starts by providing a summary of the PA nonlinearity problem background, as well as an overview of the most well-known linearization techniques, with a special focus on DPD techniques. The thesis then discusses ANN structures and the learning parameters. Finally, a novel Two Hidden Layers ANN (2HLANN) model is suggested to predict the dynamic nonlinear behaviour of wideband PAs. An extensive validation of the 2HLANN model demonstrates its excellent modeling accuracy and linearization capability.

Power amplifiers (PAs) are important components of communication systems and are inherently nonlinear. When a non-constant modulus signal goes through a nonlinear PA, spectral regrowth (broadening) appears in the PA output, which in turn causes adjacent channel interference (ACI). Stringent limits on the ACI are imposed by regulatory bodies, and thus the extent of the PA nonlinearity must be controlled. PA linearization is often necessary to suppress spectral regrowth, contain adjacent channel interference, and reduce bit error rate (BER). This dissertation addresses the following aspects of power amplifier research: modeling, linearization, and spectral regrowth analysis. We explore the passband and baseband PA input/output relationships and show that they manifest differently when the PA exhibits long-term, short-term, or no memory effects. The so-called quasi-memoryless case is especially clarified. Four particular nonlinear models with memory are further investigated. We provide experimental results to support our analysis. The benefits of using the orthogonal polynomials as opposed to the conventional polynomials are explored, in the context of digital baseband PA modeling and predistorter design. A closed-form expression for the orthogonal polynomial basis is derived. We demonstrate the improvement in numerical stability associated with the use of orthogonal polynomials for predistortion. Spectral analysis can help to evaluate the suitability of a given PA for amplifying certain signals or to assist in predistortion linearization algorithm design. With the orthogonal polynomials that we derived, spectral analysis of the nonlinear PA becomes a straightforward task. We carry out nonlinear spectral analysis with digitally modulated signal as input. We demonstrate an analytical approach for evaluating the power spectra of filtered QPSK and OQPSK signals after nonlinear amplification. Many communications devices are nonlinear and have a peak power or peak amplitude constraint. In addition to possibly amplifying the useful signal, the nonlinearity also generates distortions. We focus on signal-to-noise-and-distortion ratio (SNDR) optimization within the family of amplitude limited memoryless nonlinearities. We obtain a link between the capacity of amplitude-limited nonlinear channels with Gaussian noise to the SNDR.

This dissertation introduces novel methods for solving highly challenging model- ing and control problems, motivated by advanced aerospace systems. Adaptable, ro- bust and computationally effcient, multi-resolution approximation algorithms based on Radial Basis Function Network and Global-Local Orthogonal Mapping approaches are developed to address various problems associated with the design of large scale dynamical systems. The main feature of the Radial Basis Function Network approach is the unique direction dependent scaling and rotation of the radial basis function via a novel Directed Connectivity Graph approach. The learning of shaping and rota- tion parameters for the Radial Basis Functions led to a broadly useful approximation approach that leads to global approximations capable of good local approximation for many moderate dimensioned applications. However, even with these refinements, many applications with many high frequency local input/output variations and a high dimensional input space remain a challenge and motivate us to investigate an entirely new approach. The Global-Local Orthogonal Mapping method is based upon a novel averaging process that allows construction of a piecewise continuous global family of local least-squares approximations, while retaining the freedom to vary in a general way the resolution (e.g., degrees of freedom) of the local approximations. These approximation methodologies are compatible with a wide variety of disciplines such as continuous function approximation, dynamic system modeling, nonlinear sig-nal processing and time series prediction. Further, related methods are developed for the modeling of dynamical systems nominally described by nonlinear differential equations and to solve for static and dynamic response of Distributed Parameter Sys- tems in an effcient manner. Finally, a hierarchical control allocation algorithm is presented to solve the control allocation problem for highly over-actuated systems that might arise with the development of embedded systems. The control allocation algorithm makes use of the concept of distribution functions to keep in check the "curse of dimensionality". The studies in the dissertation focus on demonstrating, through analysis, simulation, and design, the applicability and feasibility of these ap- proximation algorithms to a variety of examples. The results from these studies are of direct utility in addressing the "curse of dimensionality" and frequent redundancy of neural network approximation.

Power Amplifiers (PAs) are the key building blocks of the emerging wireless radios systems. They dominate the power consumption and sources of distortion, especially when driven with modulated signals. Several approaches have been devised to characterize the nonlinearity of a PA. Among these approaches, dynamic amplitude (AM/AM) and phase (AM/PM) distortion characteristics are widely used to characterize the PA nonlinearity and its effects on the output signal in power, frequency or time domains, when driven with realistic modulated signals. The inherent nonlinear behaviour of PAs generally yield output signals with an unacceptable quality, an undesirable level of out-of-band emission, high Error Vector Magnitudes (EVMs) and low Adjacent Channel Power Ratios (ACPRs), which usually fail to meet the established performance standards. Traditionally, PAs are forced to operate deeply in their back-off region, far from their power capacity, in order to pass the mandatory spectrum mask (ACPR requirement) and to achieve acceptable EVM. Despite its simplicity, this solution is increasingly discarded, as it leads to cost and power inefficient radios. Alternatively, several linearization techniques, such as feedback, feed-forward and predistortion, have been devised to tackle PA nonlinearity and, consequently, improve the achievable the linearity versus power efficiency trade-off. Among these linearization techniques, the Digital Pre-Distortion (DPD) technique consists of incorporating an extra nonlinear function before the PA, in order to preprocess the input signal to the PA, so that the overall cascaded systems behave linearly. The overall linearity of the cascaded system (DPD plus PA) relies primarily on the ability of the DPD function to produce nonlinearities that are equal in magnitude and out-of-phase to those generated by the PA. Hence, a good understanding and accurate modeling of PA distortions is a crucial step in the construction of an adequate DPD function. This thesis explores DPD through techniques based on Artificial Neural Networks (ANNs). The choice of ANN as a modeling tool was motivated by its proven strength in modeling dynamic nonlinear systems. This thesis starts by providing a summary of the PA nonlinearity problem background, as well as an overview of the most well-known linearization techniques, with a special focus on DPD techniques. The thesis then discusses ANN structures and the learning parameters. Finally, a novel Two Hidden Layers ANN (2HLANN) model is suggested to predict the dynamic nonlinear behaviour of wideband PAs. An extensive validation of the 2HLANN model demonstrates its excellent modeling accuracy and linearization capability.

O presente trabalho aborda o problema de estabilização local de sistemas não lineares quadráticos contínuos no tempo (possivelmente instáveis em malha aberta) e sujeitos a saturação de atuadores. Além disso o trabalho apresenta um estudo de técnicas de síntese de compensadores de anti-windup para sistemas quadráticos sujeitos à saturação de atuadores. A abordagem do estudo é comparativa em relação a duas formas de representação dos sistemas quadráticos. A primeira forma de abordagem é a Representação Algébrico-Diferencial — DAR (do inglês, Differential Algebraic Representation), aplicável a toda a classe de sistemas racionais. A segunda forma, por sua vez, consiste em uma decomposição quadrática, particular para sistemas quadráticos. Em ambos os casos, utiliza-se a não linearidade de zona morta e uma condição generalizada de setor para tratar da saturação. Para ambas representações, condições baseadas em Desigualdades Matriciais Lineares — LMIs (do inglês, Linear Matrix Inequalities) dependentes dos estados são obtidas para fornecer uma lei de controle linear, com o objetivo de estabilizar o sistema em malha fechada enquanto fornece uma região maximizada de estabilidade garantida associada a uma função de Lyapunov. A partir da mesma metodologia, são propostas técnicas de síntese de compensadores de anti-windup estáticos e dinâmicos. Exemplos numéricos são apresentados para verificar a eficácia dos métodos propostos. / This work addresses the problem of local stabilization of continuous-time quadratic systems (possibly open-loop unstable) and subject to actuator saturation. Furthermore, the work addresses a study of techniques for synthesis of anti-windup compensators for quadratic systems subject to actuator saturation. The study approach is comparative in the sense of considering two representations of quadratic systems. The first one is the Differential Algebraic Representation — DAR, suitable for the entire class of rational systems. The second representation consists in a quadratic decomposition, particular for quadratic systems. In both cases, it is used the deadzone nonlinearity and the generalized sector condition in order to deal with the saturation. For both representations, state-dependent Linear Matrix Inequalities — LMIs conditions are obtained to provide a control law with the aim of stabilize the closed-loop system while providing a region of guaranteed stability, associated to a Lyapunov function. Based on the same methodology, techniques are proposed for the synthesis of static and dynamic anti-windup compensators. Numerical examples are presented to verify the effectiveness of proposed methods.

Although nonlinear model predictive control (NMPC) might be the best choice for a nonlinear plant, it is still not widely used. This is mainly due to the computational burden associated with solving online a set of nonlinear differential equations and a nonlinear dynamic optimization problem in real time. This thesis is concerned with strategies aimed at reducing the computational burden involved in different stages of the NMPC such as optimization problem, state estimation, and nonlinear model identification. A major part of the computational burden comes from function and derivative evaluations required in different parts of the NMPC algorithm. In this work, the problem is tackled using a recently introduced efficient tool, the automatic differentiation (AD). Using the AD tool, a function is evaluated together with all its partial derivative from the code defining the function with machine accuracy. A new NMPC algorithm based on nonlinear least square optimization is proposed. In a first–order method, the sensitivity equations are integrated using a linear formula while the AD tool is applied to get their values accurately. For higher order approximations, more terms of the Taylor expansion are used in the integration for which the AD is effectively used. As a result, the gradient of the cost function against control moves is accurately obtained so that the online nonlinear optimization can be efficiently solved. In many real control cases, the states are not measured and have to be estimated for each instance when a solution of the model equations is needed. A nonlinear extended version of the Kalman filter (EKF) is added to the NMPC algorithm for this purpose. The AD tool is used to calculate the required derivatives in the local linearization step of the filter automatically and accurately. Offset is another problem faced in NMPC. A new nonlinear integration is devised for this case to eliminate the offset from the output response. In this method, an integrated disturbance model is added to the process model input or output to correct the plant/model mismatch. The time response of the controller is also improved as a by–product. The proposed NMPC algorithm has been applied to an evaporation process and a two continuous stirred tank reactor (two–CSTR) process with satisfactory results to cope with large setpoint changes, unmeasured severe disturbances, and process/model mismatches. When the process equations are not known (black–box) or when these are too complicated to be used in the controller, modelling is needed to create an internal model for the controller. In this thesis, a continuous time recurrent neural network (CTRNN) in a state–space form is developed to be used in NMPC context. An efficient training algorithm for the proposed network is developed using AD tool. By automatically generating Taylor coefficients, the algorithm not only solves the differentiation equations of the network but also produces the sensitivity for the training problem. The same approach is also used to solve online the optimization problem of the NMPC. The proposed CTRNN and the predictive controller were tested on an evaporator and two–CSTR case studies. A comparison with other approaches shows that the new algorithm can considerably reduce network training time and improve solution accuracy. For a third case study, the ALSTOM gasifier, a NMPC via linearization algorithm is implemented to control the system. In this work a nonlinear state–space class Wiener model is used to identify the black–box model of the gasifier. A linear model of the plant at zero–load is adopted as a base model for prediction. Then, a feedforward neural network is created as the static gain for a particular output channel, fuel gas pressure, to compensate its strong nonlinear behavior observed in open–loop simulations. By linearizing the neural network at each sampling time, the static nonlinear gain provides certain adaptation to the linear base model. The AD tool is used here to linearize the neural network efficiently. Noticeable performance improvement is observed when compared with pure linear MPC. The controller was able to pass all tests specified in the benchmark problem at all load conditions.

O presente trabalho aborda o problema de estabilização local de sistemas não lineares quadráticos contínuos no tempo (possivelmente instáveis em malha aberta) e sujeitos a saturação de atuadores. Além disso o trabalho apresenta um estudo de técnicas de síntese de compensadores de anti-windup para sistemas quadráticos sujeitos à saturação de atuadores. A abordagem do estudo é comparativa em relação a duas formas de representação dos sistemas quadráticos. A primeira forma de abordagem é a Representação Algébrico-Diferencial — DAR (do inglês, Differential Algebraic Representation), aplicável a toda a classe de sistemas racionais. A segunda forma, por sua vez, consiste em uma decomposição quadrática, particular para sistemas quadráticos. Em ambos os casos, utiliza-se a não linearidade de zona morta e uma condição generalizada de setor para tratar da saturação. Para ambas representações, condições baseadas em Desigualdades Matriciais Lineares — LMIs (do inglês, Linear Matrix Inequalities) dependentes dos estados são obtidas para fornecer uma lei de controle linear, com o objetivo de estabilizar o sistema em malha fechada enquanto fornece uma região maximizada de estabilidade garantida associada a uma função de Lyapunov. A partir da mesma metodologia, são propostas técnicas de síntese de compensadores de anti-windup estáticos e dinâmicos. Exemplos numéricos são apresentados para verificar a eficácia dos métodos propostos. / This work addresses the problem of local stabilization of continuous-time quadratic systems (possibly open-loop unstable) and subject to actuator saturation. Furthermore, the work addresses a study of techniques for synthesis of anti-windup compensators for quadratic systems subject to actuator saturation. The study approach is comparative in the sense of considering two representations of quadratic systems. The first one is the Differential Algebraic Representation — DAR, suitable for the entire class of rational systems. The second representation consists in a quadratic decomposition, particular for quadratic systems. In both cases, it is used the deadzone nonlinearity and the generalized sector condition in order to deal with the saturation. For both representations, state-dependent Linear Matrix Inequalities — LMIs conditions are obtained to provide a control law with the aim of stabilize the closed-loop system while providing a region of guaranteed stability, associated to a Lyapunov function. Based on the same methodology, techniques are proposed for the synthesis of static and dynamic anti-windup compensators. Numerical examples are presented to verify the effectiveness of proposed methods.

Le générateur de vapeur a un rôle d’échangeur thermique et de sûreté nucléaire. L’énergie du fluide primaire est transférée au circuit secondaire via un faisceau de tubes en U soutenus par des plaques entretoise. Un dépôt modifie les conditions de liaison et l’écoulement du fluide secondaire. Le tube peut alors entrer en instabilité fluide-élastique, qui aboutit à une ruine rapide. Cette thèse vise à mieux comprendre l’effet de la non-linéarité de contact sur la dynamique d’un tube en air rentrant en contact intermittent avec les entretoises et ses conséquences en présence d’une instabilité. La discrétisation des conditions de contact entre le tube et les plaques, par des obstacles circulaires répartis sur l’épaisseur, ainsi que l’utilisation de bases de réductions enrichies permettent des résolutions numériques non-linéaires fiables et rapides, numériquement valides pour de fortes non-linéarités et des amortissements modaux négatifs, et bien corrélées avec les mesures correspondantes. On analyse les évolutions du contenu spectral (DSP) en fonction de l’amplitude d’excitation : remplissage des anti-résonances, décalage et étalement des pics ; puis on met en évidence la pertinence d’une notion de raideur apparente d’un contact bilatéral permanent qui permet de décrire ces transitions. En présence d’un système libre instable, on montre enfin que la non-linéarité conduit à des réponses bornées ou stabilisées ouvrant ainsi la voie vers une extension des travaux réalisés vers des applications avec fluide réel ou simulé. / The steam generator is a heat exchanger and participates to the nuclear safety. Energy is transferred from the primary to the secondary fluid through many U-tubes maintained vertically by support plates. A sludge deposit tends to modify the boundary conditions and the secondary fluid flow. A fluid-elastic instability can then occur and lead to quick tube ruin. This thesis seeks a better understanding of the effect of contact nonlinearity on the dynamics of a tube in-air intermittently impacting the support plates and its consequences in regards with instability. The use of discretized contact conditions with circular obstacles distributed over the thickness of the plates and the use of enriched reduction bases allow quick and relevant nonlinear numerical simulations. These simulations are well correlated with experimental measurements and valid even with strong nonlinearity or negative modal damping. The evolution of power spectral densities (PSD) with growing excitation amplitude is analyzed: padding of the anti-resonances, peak shift and spread. It is then shown that an apparent stiffness associated with a permanent bilateral contact is pertinent to describe these transitions. In the case of an unstable linear system, one demonstrates that the nonlinearity keeps the responses bounded or stabilised, thus paving the way for future work with real or simulated fluid flows.

O presente trabalho aborda o problema de estabilização local de sistemas não lineares quadráticos contínuos no tempo (possivelmente instáveis em malha aberta) e sujeitos a saturação de atuadores. Além disso o trabalho apresenta um estudo de técnicas de síntese de compensadores de anti-windup para sistemas quadráticos sujeitos à saturação de atuadores. A abordagem do estudo é comparativa em relação a duas formas de representação dos sistemas quadráticos. A primeira forma de abordagem é a Representação Algébrico-Diferencial — DAR (do inglês, Differential Algebraic Representation), aplicável a toda a classe de sistemas racionais. A segunda forma, por sua vez, consiste em uma decomposição quadrática, particular para sistemas quadráticos. Em ambos os casos, utiliza-se a não linearidade de zona morta e uma condição generalizada de setor para tratar da saturação. Para ambas representações, condições baseadas em Desigualdades Matriciais Lineares — LMIs (do inglês, Linear Matrix Inequalities) dependentes dos estados são obtidas para fornecer uma lei de controle linear, com o objetivo de estabilizar o sistema em malha fechada enquanto fornece uma região maximizada de estabilidade garantida associada a uma função de Lyapunov. A partir da mesma metodologia, são propostas técnicas de síntese de compensadores de anti-windup estáticos e dinâmicos. Exemplos numéricos são apresentados para verificar a eficácia dos métodos propostos. / This work addresses the problem of local stabilization of continuous-time quadratic systems (possibly open-loop unstable) and subject to actuator saturation. Furthermore, the work addresses a study of techniques for synthesis of anti-windup compensators for quadratic systems subject to actuator saturation. The study approach is comparative in the sense of considering two representations of quadratic systems. The first one is the Differential Algebraic Representation — DAR, suitable for the entire class of rational systems. The second representation consists in a quadratic decomposition, particular for quadratic systems. In both cases, it is used the deadzone nonlinearity and the generalized sector condition in order to deal with the saturation. For both representations, state-dependent Linear Matrix Inequalities — LMIs conditions are obtained to provide a control law with the aim of stabilize the closed-loop system while providing a region of guaranteed stability, associated to a Lyapunov function. Based on the same methodology, techniques are proposed for the synthesis of static and dynamic anti-windup compensators. Numerical examples are presented to verify the effectiveness of proposed methods.