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This work presents three techniques for parameter identification for nonlinear systems. The methods presented are expanded from those presented in Adetola and Guay [3, 4, 5] and are intended to improve the performance of existing adaptive control systems. The first two methods exactly recover open-loop system parameters once a defined convergence condition is met. In either case, the true parameters are identified when the regressor matrix is of full rank and can be inverted. The third case uses a novel method developed in Adetola and Guay [5] to define a parameter uncertainty set. The uncertainty set is periodically updated to shrink around the true value of the parameters. Each method is shown to be applicable to a large class of linearly parameterized nonlinear discrete-time system. In each case, parameter convergence is guaranteed subject to an appropriate convergence condition, which has been related to a classical persistence of excitation condition. The effectiveness of the methods is demonstrated using a simulation example. The application of the uncertainty set technique to nonlinearly parameterized systems constitutes the main contribution of the thesis. The parameter uncertainty set method is generalized to the problem of adaptive estimation in nonlinearly parameterized systems, for both continuous-time and discrete-time cases. The method is demonstrated to perform well in simulation for a simplified model of a bioreactor operating under Monod kinetics. / Thesis (Master, Chemical Engineering) -- Queen's University, 2010-10-19 10:58:24.888

Thesis (M. Phil.)--University of Hong Kong, 1995. / Includes bibliographical references (leaves 83-86).

Longitudinal optical binding refers to the light induced self organisation of micro particles in one dimension. In this thesis I will present experimental and theoretical studies of the separation between two dielectric spheres in a counter-propagating (CP) geometry. I will explore the bistable nature of the bound sphere separation and its dependency on the refractive index mismatch between the spheres and the host medium, with an emphasis on the fibre separation. The physical under pining principle of longitudinal optical binding in the Mie regime is the refocusing effect of the light field from one sphere to its nearest neighbour. In a second set of experiments I developed means to visualise the field intensity distribution responsible for optical binding using two-photon fluorescence imaging from fluorescein added to the host medium. The experimental intensity distributions are compared to theoretical predictions and provide an in situ method to observe the binding process in real time. This coupling via the refocused light fields between the spheres is in detailed investigated experimentally and theoretically, in particular I present data and analysis on the correlated behaviour of the micro spheres in the presence of noise. The measurement of the decay times of the correlation functions of the modes of the optically bound array provides a methodology for determining the optical restoring forces acting in optical binding. Interestingly micro devices can be initiated by means of the light-matter interaction. Light induced forces and torques are exerted on such micro-objects that are then driven by the optical gradient or scattering force. I have experimentally investigate how the driving light interacts with and diffracts from the motor, utilising two-photon imaging. The micromotor rotation rate dependence on the light field parameters is explored and theoretically modelled. The results presented will show that the model can be used to optimise the system geometry and the micromotor.

A new system identification algorithm, multiple autoregressive exogenous (ARX) inputs-based Takagi-Sugeno (TS) fuzzy model, is developed to identify nonlinear behavior of structure-magnetorheological (MR) damper systems. It integrates a set of ARX models, clustering algorithms, and weighted least squares algorithm with a TS fuzzy model. Based on a set of input-output data that is generated from building structures equipped with MR dampers, premise parameters of the ARX-TS fuzzy model are determined by clustering algorithms. Once the premise part is constructed, consequent parameters of the ARX-TS fuzzy model are optimized by the weighted least squares algorithm. To demonstrate the effectiveness of the proposed ARX-TS fuzzy model, it is applied to a three-, an eight-, a twenty-story building structures. It is demonstrated from the numerical simulation that the proposed ARX-TS fuzzy algorithm is effective to identify nonlinear behavior of seismically excited building structures equipped with MR dampers. A new semiactive nonlinear fuzzy control (SNFC) algorithm is developed through integration of multiple Lyapunov-based state feedback gains, a Kalman filter, and a converting algorithm with TS fuzzy interpolation method. First, the nonlinear ARX-TS fuzzy model is decomposed into a set of linear dynamic models that are operated in only a local linear operating region. Based on the decomposed models, multiple Lyapunov-based state feedback controllers are formulated in terms of linear matrix inequalities (LMIs) such that the structure-MR damper system is globally asymptotically stable and the performance on transient responses is guaranteed. Then, the state feedback controllers are integrated with a Kalman filter and a converting algorithm using a TS fuzzy interpolation method to construct semiactive output feedback controllers. To demonstrate the effectiveness of the proposed SNFC algorithm, it is applied to a three-, an eight-, and a twenty-story building structures. It is demonstrated from the numerical simulation that the proposed SNFC algorithm is effective to control responses of seismically excited building structures equipped with MR dampers. In addition, it is shown that the proposed SNFC system is better than a traditional optimal algorithm, H2/linear quadratic Gaussian-based semiactive control strategy.

This thesis proposes nonlinear system identification techniques for the mathematical modeling of the human smooth pursuit system (SPS) with application to motor symptom quantification in Parkinson's disease (PD). The SPS refers to the complex neuromuscular system in humans that governs the smooth pursuit eye movements (SPEM). Insight into the SPS and its operation is of importance in a wide and steadily expanding array of application areas and research fields. The ultimate purpose of the work in this thesis is to attain a deeper understanding and quantification of the SPS dynamics and thus facilitate the continued development of novel commercial products and medical devices. The main contribution of this thesis is in the derivation and evaluation of several techniques for SPS characterization. While attempts to mathematically model the SPS have been made in the literature before, several key aspects of the problem have been previously overlooked.This work is the first one to devise dynamical models intended for extended-time experiments and also to consider systematic visual stimuli design in the context of SPS modeling. The result is a handful of parametric mathematical models outperforming current State-of-the-Art models in terms of prediction accuracy for rich input signals. As a complement to the parametric dynamical models, a non-parametric technique involving the construction of individual statistical models pertaining to specific gaze trajectories is suggested. Both the parametric and non-parametric models are demonstrated to successfully distinguish between individuals or groups of individuals based on eye movements.Furthermore, a novel approach to Wiener system identification using Volterra series is proposed and analyzed. It is exploited to confirm that the SPS in healthy individuals is indeed nonlinear, but that the nonlinearity of the system is significantly stronger in PD subjects. The nonlinearity in healthy individuals appears to be well-modeled by a static output function, whereas the nonlinear behavior introduced to the SPS by PD is dynamical.

Les programmes TV possède une structure qui, en général, est perdue quand les programmes sont diffusés. Les programmes qui ont été enregistrés via un enregistreur vidéo personnel ou disponibles via des services comme la TV à la demande, ne peuvent être visionnés que d’une façon linéaire. La navigation y est réalisée en utilisant les fonctions basiques d’avance/retour rapide. Dans ce contexte, la structuration automatique de programmes TV apporte une solution originale. En retrouvant la structure d’origine du programme, elle permet d’offrir aux utilisateurs des outils de navigation originaux. Elle peut également servir pour d’autres applications comme la construction des résumés vidéo, l’indexation et la recherche…Cette thèse s’intéresse ainsi à la structuration automatique des programmes TV. L’objectif est de retrouver automatiquement la structure d’origine d’un programme en déterminant le début et la fin de chaque partie qui le compose. L’approche proposée est complètement non-supervisée et adresse une large catégorie de programmes TV comme les jeux, les magazines, les journaux TV… Cette approche exploite les « séparateurs » qui sont de séquences courtes insérées dans les programmes pour en délimiter les différentes parties. Pour cela, une détection des récurrences audio et visuelles est réalisée sur un ensemble d’épisodes du même programme. Ces récurrences sont ensuite classées à l’aide d’arbres de décision pour en extraire les séparateurs. Les attributs utilisés pour la construction des arbres de décision porte sur la détection des applaudissements, la segmentation en scènes, la détection et le clustering des visages et des locuteurs. / TV programs have an underlying structure that is lost when these are broadcasted. The linear mode is the only available reading mode when viewing programs recorded using a Personal Video Recorder or through a TV-on-Demand service. The fast-forward/backward functions are the only available tools for browsing. In this context, program structuring becomes important in order to provide users with novel and useful browsing features. In addition to advanced browsing features, TV program structuring can also be used for summarization, indexing and querying, archiving, etc. This thesis addresses the problem of unsupervised TV program structuring. The idea is to automatically recover the original structure of the program by finding the start time of each part composing it. The proposed approach is completely unsupervised and addresses a large category of programs like TV games, magazines, news…. It is based on the detection of “separators” which are short audio/visual sequences that delimit the different parts of a program. To do so, audio and visual recurrences are first detected from a set of episodes of a same program. In order to extract the separators, the recurrences are then classified using decision trees. These are built based on attributes issued from techniques like applause detection, scenes segmentation, face and speaker detection and clustering.

Single Particle Tracking (SPT) plays an important role in the study of physical and dynamic properties of biomolecules moving in their native environment. To date, many algorithms have been developed for localization and parameter estimation in SPT. Though the performance of these methods is good when the signal level is high and the motion model simple, they begin to fail as the signal level decreases or model complexity increases. In addition, the inputs to the SPT algorithms are sequences of images that are cropped from a large data set and that focus on a single particle. This motivates us to seek machine learning tools to deal with that initial step of extracting data from larger images containing multiple particles. This thesis makes contributions to both data extraction question and to the problem of state and parameter estimation. First, we build upon the Expectation Maximization (EM) algorithm to create a generic framework for joint localization refinement and parameter estimation in SPT. Under the EM-based scheme, two representative methods are considered for generating the filtered and smoothed distributions needed by EM: Sequential Monte Carlo - Expectation Maximization (SMC-EM), and Unscented - Expectation Maximization (U-EM). The selection of filtering and smoothing algorithms is very flexible so long as they provide the necessary distributions for EM. The versatility and reliability of EM based framework have been validated via data-intensive modeling and simulation where we considered a variety of influential factors, such as a wide range of {\color{red}Signal-to-background ratios (SBRs)}, diffusion speeds, motion blur, camera types, image length, etc. Meanwhile, under the EM-based scheme, we make an effort to improve the overall computational efficiency by simplifying the mathematical expression of models, replacing filtering/smoothing algorithms with more efficient ones {\color{purple} (trading some accuracy for reduced computation time)}, and using parallel computation and other computing techniques. In terms of localization refinement and parameter estimation in SPT, we also conduct an overall quantitative comparison among EM based methods and standard two-step methods. Regarding the U-EM, we conduct transformation methods to make it adapted to the nonlinearities and complexities of measurement model. We also extended the application of U-EM to more complicated SPT scenarios, including time-varying parameters and additional observation models that are relevant to the biophysical setting. The second area of contribution is in the particle detection and extraction problem to create data to feed into the EM-based approaches. Here we build Particle Identification Networks (PINs) covering three different network architectures. The first, \PINCNN{}, is based on a standard Convolutional Neural Network (CNN) structure that has previously been successfully applied in particle detection and localization. The second, \PINRES, uses a Residual Neural Network (ResNet) architecture that is significantly deeper than the CNN while the third, \PINFPN{}, is based on a more advanced Feature Pyramid Network (FPN) that can take advantage of multi-scale information in an image. All networks are trained using the same collection of simulated data created with a range of SBRs and fluorescence emitter densities, as well as with three different Point Spread Functions (PSFs): a standard Born-Wolf model, a model for astigmatic imaging to allow localization in three dimensions, and a model of the Double-Helix engineered PSF. All PINs are evaluated and compared through data-intensive simulation and experiments under a variety of settings. In the final contribution, we link all above together to create an algorithm that takes in raw camera data and produces trajectories and parameter estimates for multiple particles in an image sequence.

Mathematical modeling of dynamical systems plays a central roll in science and engineering. This thesis is concerned with the process of finding a mathematical model, and it is divided into two parts - one that concentrates on nonlinear system identification and another one where an impulsive model of testosterone regulation is constructed and analyzed. In the first part of the thesis, a new latent variable framework for identification of a large class of nonlinear models is developed. In this framework, we begin by modeling the errors of a nominal predictor using a flexible stochastic model. The error statistics and the nominal predictor are then identified using the maximum likelihood principle. The resulting optimization problem is tackled using a majorization-minimization approach, resulting in a tuning parameter-free recursive identification method. The proposed method learns parsimonious predictive models. Many popular model structures can be expressed within the framework, and in the thesis it is applied to piecewise ARX models. In the first part, we also derive a recursive prediction error method based on the Hammerstein model structure. The convergence properties of the method are analyzed by application of the associated differential equation method, and conditions ensuring convergence are given. In the second part of the thesis, a previously proposed pulse-modulated feedback model of testosterone regulation is extended with infinite-dimensional dynamics, in order to better explain testosterone profiles observed in clinical data. It is then shown how the analysis of oscillating solutions for the finite-dimensional case can be extended to the infinte-dimensional case. A method for blind state estimation in impulsive systems is introduced, with the purpose estimating hormone concentrations that cannot be measured in a non-invasive way. The unknown parameters in the model are identified from clinical data and, finally, a method of incorporating exogenous signals portraying e.g. medical interventions is studied.

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