This thesis essentially deals with the development and numerical explorations of a few improved Monte Carlo filters for nonlinear dynamical systems with a view to estimating the associated states and parameters (i.e. the hidden states appearing in the system or process model) based on the available noisy partial observations. The hidden states are characterized, subject to modelling errors, by the weak solutions of the process model, which is typically in the form of a system of stochastic ordinary differential equations (SDEs). The unknown system parameters, when included as pseudo-states within the process model, are made to evolve as Wiener processes. The observations may also be modelled by a set of measurement SDEs or, when collected at discrete time instants, their temporally discretized maps. The proposed Monte Carlo filters aim at achieving robustness (i.e. insensitivity to variations in the noise parameters) and higher accuracy in the estimates whilst retaining the important feature of applicability to large dimensional nonlinear filtering problems. The thesis begins with a brief review of the literature in Chapter 1. The first development, reported in Chapter 2, is that of a nearly exact, semi-analytical, weak and explicit linearization scheme called Girsanov Corrected Linearization Method (GCLM) for nonlinear mechanical oscillators under additive stochastic excitations. At the heart of the linearization is a temporally localized rejection sampling strategy that, combined with a resampling scheme, enables selecting from and appropriately modifying an ensemble of locally linearized trajectories whilst weakly applying the Girsanov correction (the Radon- Nikodym derivative) for the linearization errors. Through their numeric implementations for a few workhorse nonlinear oscillators, the proposed variants of the scheme are shown to exhibit significantly higher numerical accuracy over a much larger range of the time step size than is possible with the local drift-linearization schemes on their own. The above scheme for linearization correction is exploited and extended in Chapter 3, wherein novel variations within a particle filtering algorithm are proposed to weakly correct for the linearization or integration errors that occur while numerically propagating the process dynamics. Specifically, the correction for linearization, provided by the likelihood or the Radon-Nikodym derivative, is incorporated in two steps. Once the likelihood, an exponential martingale, is split into a product of two factors, correction owing to the first factor is implemented via rejection sampling in the first step. The second factor, being directly computable, is accounted for via two schemes, one employing resampling and the other, a gain-weighted innovation term added to the drift field of the process SDE thereby overcoming excessive sample dispersion by resampling. The proposed strategies, employed as add-ons to existing particle filters, the bootstrap and auxiliary SIR filters in this work, are found to non-trivially improve the convergence and accuracy of the estimates and also yield reduced mean square errors of such estimates visà-vis those obtained through the parent filtering schemes. In Chapter 4, we explore the possibility of unscented transformation on Gaussian random variables, as employed within a scaled Gaussian sum stochastic filter, as a means of applying the nonlinear stochastic filtering theory to higher dimensional system identification problems. As an additional strategy to reconcile the evolving process dynamics with the observation history, the proposed filtering scheme also modifies the process model via the incorporation of gain-weighted innovation terms. The reported numerical work on the identification of dynamic models of dimension up to 100 is indicative of the potential of the proposed filter in realizing the stated aim of successfully treating relatively larger dimensional filtering problems. We propose in Chapter 5 an iterated gain-based particle filter that is consistent with the form of the nonlinear filtering (Kushner-Stratonovich) equation in our attempt to treat larger dimensional filtering problems with enhanced estimation accuracy. A crucial aspect of the proposed filtering set-up is that it retains the simplicity of implementation of the ensemble Kalman filter (EnKF). The numerical results obtained via EnKF-like simulations with or without a reduced-rank unscented transformation also indicate substantively improved filter convergence. The final contribution, reported in Chapter 6, is an iterative, gain-based filter bank incorporating an artificial diffusion parameter and may be viewed as an extension of the iterative filter in Chapter 5. While the filter bank helps in exploring the phase space of the state variables better, the iterative strategy based on the artificial diffusion parameter, which is lowered to zero over successive iterations, helps improve the mixing property of the associated iterative update kernels and these are aspects that gather importance for highly nonlinear filtering problems, including those involving significant initial mismatch of the process states and the measured ones. Numerical evidence of remarkably enhanced filter performance is exemplified by target tracking and structural health assessment applications. The thesis is finally wound up in Chapter 7 by summarizing these developments and briefly outlining the future research directions

Made available in DSpace on 2016-08-17T14:52:39Z (GMT). No. of bitstreams: 1 DISSERTACAO_DENIS FABRICIO SOUSA DE SA.pdf: 2409581 bytes, checksum: 4de5274676a1f75ffe2a1f6b46b1388c (MD5) Previous issue date: 2015-04-10 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The representation of dynamic systems or plants via mathematical models occupies an important position in control system design that allow the performance evaluation of the controller during his development stage. These models are also used as an alternative to solve the problem of the hardness or impracticability to install sensors that measure the controlled variables, the dynamic systems representations enable non-invasive measurement of these variables. As consequence the designer has an alternative way to perform adaptive and optimal sensorless control for a given process. In this dissertation is presented a proposal for control systems schemas and algorithms, based on recurrent neural networks (ANN) and Box-Jenkins models, that are dedicated to sensorless or indirect control of dynamic systems. The proposed models and algorithms are associated with the systems identification and recurrent ANN approaches. The algorithms developed for the AAN training are Backpropagation Accelerated and RLS types that are compared with classical methods and strategies to obtain it online parameters of indirect control of system for a thermal plant, where the actuator is Peltier cell. The performance the parametric models of the plant and adaptive PID digital controllers and linear quadratic regulator (DLQR) that are the main elements of the sensorless temperature control system, are evaluated by means of hybrid simulations, where the algorithms implemented in micro controllers and the plant represented by mathematical models. The performance results of the proposed sensorless control algorithms are promissory, not only, in terms of the control system performance, but also due to the reexibility to deploy it in other dynamic systems. / A representação de sistemas dinâmicos ou plantas por meio modelos matemáticos ocupa uma posição relevante no projeto de sistemas de controle, permitindo que o projetista avalie o desempenho dos controladores durante a fase de desenvolvimento do projeto. Estes modelos também são utilizados para resolver o problema da dificuldade ou impossibilidade da inserção de sensores em plantas para medição de variáveis controladas, onde os modelos viabilizam a mediação não invasiva destas variáveis, fornecendo uma alternativa para realização do controle indireto adaptativo e ótimo de um dado processo. Nesta dissertação apresenta-se o desenvolvimento de modelos propostos baseados em redes neurais artificiais recorrentes para o controle sensorless ou indireto da planta. Os modelos propostos estão associados com as abordagens de Identificação de Sistemas e de RNA's recorrentes. OS algoritmos desenvolvidos para o treinamento das RNAs são do tipo Backpropagation acelerado e RLS, que são comparados com estratégias e métodos clássicos, para obtenção online dos parâmetros do sistema de controle indireto de uma planta térmica, tendo como atuador uma célula Peltier. Para uns de avaliação de desempenho do sistema de controle indireto da planta, os modelos paramétricos e controladores digitais adaptativos do tipo PID e regulador linear quadrático (DLQR) são avaliados por meio de simulações híbridas, sendo os algoritmos dos controladores implementados em microcontroladores e a planta representada por modelos matemáticos. Os resultados apresentados são promissores, não são sentido do desempenho do sistema de controle, mas também nos custos reduzidos para seu desenvolvimento, operação e flexibilidade de aplicação em outros sistemas dinâmicos.