Tesis de Postgrado Acceso Abierto
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Browsing Tesis de Postgrado Acceso Abierto by Author "Agüero Vásquez, Juan Carlos"
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Thesis IDENTIFICACIÓN DE MODELOS DE VIBRACIONES PARA CONTROL DE SISTEMAS DE ÓPTICA ADAPTATIVA(2018) Gonzalez Perez, Karen Fernanda; Departamento de Electrónica; Agüero Vásquez, Juan Carlos; Carvajal Guerra, Rodrigo JavierIn all major ground-based astronomical observatories, adaptive optics (AO) has becomean intrinsic technique to bring scienti c observations closer to the diraction limitof the astronomical instruments. This is because AO enables the compensation of theoptical aberrations caused by atmospheric turbulence, as well as the vibrations of thestructure of the telescope induced by elements within the system instrumentation (suchas fans and cooling pumps), wind and movements of the telescope. Since vibrationsstrongly affect the performance of the AO systems and hinder the achievement of goodquality images, it is necessary to obtain a model of these vibrations to later developsimple but effective control techniques that can be implemented in real time. It is forthis reason that in this thesis it is proposed to characterize these vibrations by modelingthem as a linear combination of oscillators each one driven fed by a noise and identifyingthe continuous-time oscillators using regular sampling. The model of the oscillator isrepresented as continuous-time autoregressive model, obtaining its discrete-time equivalentmodel, in terms of the parameters of the model in continuous-time oscillator. Then,the model is identi ed using the method of Maximum Likelihood using local and globaloptimization algorithms.When a local optimization algorithm is used, a good initial estimation is required forthe parameters of the system. Then one performs the corresponding optimization, whichin this case is implemented using the algorithm of quasi Newton. On the other hand,when a global optimization algorithm is used, the equivalent model of sampled data isanalyzed for two cases: i) instantaneous sampling and ii) integrated sampling.Both types of optimization are analyzed in detail, illustrating the behavior of thelog-likelihood function through numerical examples that show that it presents severallocal maxima.Thesis IDENTIFICATION AND CONTROL METHODS UTILIZING RANK AND CARDINALITY OPTIMIZATION APPROACH(2017) Urrutia Bustos, Gabriel Andrés; Agüero Vásquez, Juan CarlosThis Thesis addresses a class of optimization problems that can be found in severalareas, such as system identi cation and control. Particularly, these problems are formulatedby using rank and cardinality constraints in order to obtain low rank matrices orinduce sparsity of the solution.Rank-constrained optimization problems are found in control and system identi cation.Low-order controller design problems are well known examples where the formulationutilizes Linear Matrix Inequalities (LMIs) and rank constraints over matrices forbounding the controller's order and closed loop stability degree.Promotion of sparsity in identi cation and control problems can bring many practicaladvantages in the nal solution. In model selection, by formulating the identi cationproblem with a cardinality (`0-norm) constraint over the parameter vector, a simpli edor speci c structure of the model can be obtained. In control applications sparsity canbe induced on the solution of an optimal control problem, thus limiting the number ofactive actuators at each time step.Although low-rank and sparsity are desirable characteristics in the solution of manyproblems of interest, solving these type of problems poses computational diculties.Many approaches that rely on approximations and speci c tailored solutions are availablein the literature in order to overcome the inherent complexity of the problem. However, in this work a novel rank-constraint representation is used which, aims to solve (not anapproximation but) a problem that is equivalent to the original in the sense that theyboth have the same global optimum. The resulting problem can also be solved usingstandard nonlinear programming tools.The work hereby presented is divided in three main parts. First, an overview of stateof-the art techniques for solving cardinality and rank-constrained problems is shown.The second part of the thesis presents optimization problems with cardinality constraintsin the eld of model selection, parameter estimation and optimal control.The third part of the thesis addresses a rank-constrained optimization problem whendesigning a low-order controller with prescribed degree of stability. The formulation ofthis problem includes LMI and rank constraints.
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