Resumo: Este trabalho tem como propósito utilizar técnicas de controle robusto para atenuação ativa de vibração mecânica em estruturas acopladas a atuadores e sensores piezelétricos. Os controladores são projetados segundo o enfoque de otimização convexa, com os requisitos envolvendo desigualdades matriciais lineares (LMIs). A proposta é ilustrar duas sínteses diferentes de realimentação via LMIs. A primeira é o projeto de controladores por realimentação de estados, estimados por um observador, considerando incertezas paramétricas do tipo politópicas. A segunda metodologia é baseada no controle H8 via realimentação do sinal de saída, considerando incertezas dinâmicas limitadas por norma. Os sensores/atuadores são posicionados em pontos ótimos utilizando-se a norma H8 como índice de desempenho. Os modelos matemáticos utilizados na síntese dos controladores foram obtidos a partir do método dos elementos finitos considerando o acoplamento eletromecânico entre os atuadores/sensores e a estrutura base ou a partir de métodos de identificação. Neste contexto, este trabalho também discute e exemplifica o algoritmo de realização de autosistemas (ERA). Três exemplos são solucionados para exemplificar a metodologia implementada: uma estrutura tipo placa, uma viga engastada-livre e a supressão ativa de flutter em um aerofólio 2-D, problema de grande interesse na indústria aeronáutica. Os resultados mostraram uma significante atenuação da vibração estrutural na faixa de freqüência de interesse e o atendimento dos requisitos impostos na fase de projeto. / Abstract: The proposal of this work is to use robust control techniques in order to suppress mechanical vibration in structures with pieozoelectric sensors and actuators coupled. The controllers are designed by convex optimization and the constraints are dealt through linear matrix inequalities (LMIs) frameworks. Two different methodologies to feedback the system by using LMIs are explained. The first one is the observer-based state-feedback considering polytopic uncertainties. The second one is the H output feedback control considering norm-bound uncertainties. The sensors/actuators are located in optimal placements by using H norm as performance index. The mathematical models used in the controller design were obtained by finite element methods considering eletromechanical effects between the host structure and piezoelectric sensors/actuators patches or by using identification methods. In this sense, it is also discussed the eigensystem realization algorithm (ERA). Three different applications are proposed and solved in order to illustrate the applicability of the methodology: a cantilever plate; a cantilever beam; and an active flutter suppression in a 2-D airfoil, a problem of considered interest in the aeronautic industry. The results showed the vibration suppression in the bandwidth of interest when submited to the requirements imposed by practical situations. / Orientador: Vicente Lopes Junior / Coorientador: Edvaldo Assunção / Banca: Vicente Lopes Junior / Banca: Marcelo Carvalho Minhoto Teixeira / Banca: Edilson Hiroshi Tamai / Mestre

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In this thesis a class of robust non-linear controllers for a gantry crane system are discussed. The gantry crane has three degrees of freedom, all of which are interrelated. These are the horizontal traverse of the cart, the vertical motion of the goods (i.e. rope length) and the swing angle made by the goods during the movement of the cart. The objective is to control all three degrees of freedom. This means achieving setpoint control for the cart and the rope length and cancellation of the swing oscillations. A mathematical model of the gantry crane system is developed using Lagrangian dynamics. In this thesis it is shown that a model of the gantry crane system can be represented as two sub models which are coupled by a term which includes the rope length as a parameter. The first system will consist of the cart and swing dynamics and the other system is the hoist dynamics. The mathematical model of these two systems will be derived independent of the other system. The model that is comprised of the two sub models is verified as an accurate model of a gantry crane system and it will be used to simulate the performance of the controllers using Matlab. For completeness a fully coupled mathematical model of the gantry crane system is also developed. A detailed design of a gain scheduled sliding mode controller is presented. This will guarantee the controller's robustness in the presence of uncertainties and bounded matched disturbances. This controller is developed to achieve cart setpoint and swing control while achieving rope length setpoint control. A non gain scheduled sliding mode controller is also developed to determine if the more complex gain scheduled sliding mode controller gives any significant improvement in performance. In the implementation of both sliding mode controllers, all system states must be available. In the real-time gantry crane system used in this thesis, the cart velocity and the swing angle velocity are not directly available from the system. They will be estimated using an alpha-beta state estimator. To overcome this limitation and provide a more practical solution an optimal output feedback model following controller is designed. It is demonstrated that by expressing the system and the model for which the system is to follow in a non-minimal state space representation, LQR techniques can be used to design the controller. This produces a dynamic controller that has a proper transfer function, and negates the need for the availability of all system states. This thesis presents an alternative method of solving the LQR problem by using a generic eigenvalue solution to solve the Riccati equation and thus determine the optimal feedback gains. In this thesis it is shown that by using a combination of sliding mode and H??? control techniques, a non-linear controller is achieved which is robust in the presence of a wide variety of uncertainties and disturbances. A supervisory controller is also described in this thesis. The supervisory control is made up of a feedforward and a feedback component. It is shown that the feedforward component is the crane operator's action, and the feedback component is a sliding mode controller which compensates as the system's output deviates from the desired trajectory because of the operator's inappropriate actions or external disturbances such as wind gusts and noise. All controllers are simulated using Matlab and implemented in real-time on a scale model of the gantry crane system using the program RTShell. The real-time results are compared against simulated results to determine the controller's performance in a real-time environment.

<p>Software is finding its way into an increasing range of devices (phones, medical equipment, cars...). A challenge is to design <i>verification</i> methods to ensure correctness of software. </p><p>We focus on <i>model checking</i>, an approach in which an abstract model of the implementation and a specification of requirements are provided. The task is to answer automatically whether the system conforms with its specification.We concentrate on (i) timed systems, and (ii) parameterized systems.</p><p><i>Timed systems </i>can be modeled and verified using the classical model of timed automata. Correctness is translated to language inclusion between two timed automata representing the implementation and the specification. We consider variants of timed automata, and show that the problem is at best highly complex, at worst undecidable.</p><p>A <i>parameterized system</i> contains a variable number of components. The problem is to verify correctness regardless of the number of components. <i>Regular model checking</i> is a prominent method which uses finite-state automata. We present a semi-symbolic minimization algorithm combining the partition refinement algorithm by Paige and Tarjan with decision diagrams.</p><p>Finally, we consider systems which are both timed and parameterized: <i>Timed Petri Nets</i> (<i>TPNs</i>), and <i>Timed Networks</i> (<i>TNs</i>). We present a method for checking safety properties of TPNs based on forward reachability analysis with acceleration. We show that verifying safety properties of TNs is undecidable when each process has at least two clocks, and explore decidable variations of this problem.</p>

We present a practical algorithm for computing the minimum volume n-dimensional ellipsoid that must contain m given points a₁,..., am ∈ Rn. This convex constrained problem arises in a variety of applied computational settings, particularly in data mining and robust statistics. Its structure makes it particularly amenable to solution by interior-point methods, and it has been the subject of much theoretical complexity analysis. Here we focus on computation. We present a combined interior-point and active-set method for solving this problem. Our computational results demonstrate that our method solves very large problem instances (m = 30,000 and n = 30) to a high degree of accuracy in under 30 seconds on a personal computer. / Singapore-MIT Alliance (SMA)

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 72-76).

This doctoral thesis is comprised of four papers that all relate to the subject of Time Series Analysis. The first paper of the thesis considers point estimation in a nonnegative, hence non-Gaussian, AR(1) model. The parameter estimation is carried out using a type of extreme value estimators (EVEs). A novel estimation method based on the EVEs is presented. The theoretical analysis is complemented with Monte Carlo simulation results and the paper is concluded by an empirical example. The second paper extends the model of the first paper of the thesis and considers semiparametric, robust point estimation in a nonlinear nonnegative autoregression. The nonnegative AR(1) model of the first paper is extended in three important ways: First, we allow the errors to be serially correlated. Second, we allow for heteroskedasticity of unknown form. Third, we allow for a multi-variable mapping of previous observations. Once more, the EVEs used for parameter estimation are shown to be strongly consistent under very general conditions. The theoretical analysis is complemented with extensive Monte Carlo simulation studies that illustrate the asymptotic theory and indicate reasonable small sample properties of the proposed estimators. In the third paper we construct a simple nonnegative time series model for realized volatility, use the results of the second paper to estimate the proposed model on S&amp;P 500 monthly realized volatilities, and then use the estimated model to make one-month-ahead forecasts. The out-of-sample performance of the proposed model is evaluated against a number of standard models. Various tests and accuracy measures are utilized to evaluate the forecast performances. It is found that forecasts from the nonnegative model perform exceptionally well under the mean absolute error and the mean absolute percentage error forecast accuracy measures. In the fourth and last paper of the thesis we construct a multivariate extension of the popular Diebold-Mariano test. Under the null hypothesis of equal predictive accuracy of three or more forecasting models, the proposed test statistic has an asymptotic Chi-squared distribution. To explore whether the behavior of the test in moderate-sized samples can be improved, we also provide a finite-sample correction. A small-scale Monte Carlo study indicates that the proposed test has reasonable size properties in large samples and that it benefits noticeably from the finite-sample correction, even in quite large samples. The paper is concluded by an empirical example that illustrates the practical use of the two tests.

A review of recent literature and the research effort underlying this dissertation indicates that fractional order differential equations have significant potential to advance dynamical system methods broadly. Particular promise exists in the area of control and estimation, even for systems where fractional order models do not arise “naturally”. This dissertation is aimed at further building of the base methodology with a focus on robust feedback control and state estimation. By setting the mathematical foundation with the fractional derivative Caputo definition, we can expand the concept of the fractional order calculus in a way that enables us to build corresponding controllers and estimators in the state-space form. For the robust eigenstructure assignment, we first examine the conditioning problem of the closed-loop eigenvalues and stability robustnesss criteria for the fractional order system, and we find a unique application of an n-dimensional rotation algorithm developed by Mortari, to solve the robust eigenstructure assignment problem in a novel way. In contradistinction to the existing Fractional Kalman filter developed by using Gru ̈ndwald-Letnikov definition, the new Fractional Kalman filter that we establish by utilizing Caputo definition and our algorithms provide us with powerful means for solving practical state estimation problems for fractional order systems.

Geometric errors may compromise the quality of radiation therapy treatments. Optimization methods that account for errors can reduce their effects. The first paper of this thesis introduces minimax optimization to account for systematic range and setup errors in intensity-modulated proton therapy. The minimax method optimizes the worst case outcome of the errors within a given set. It is applied to three patient cases and shown to yield improved target coverage robustness and healthy structure sparing compared to conventional methods using margins, uniform beam doses, and density override. Information about the uncertainties enables the optimization to counterbalance the effects of errors. In the second paper, random setup errors of uncertain distribution---in addition to the systematic range and setup errors---are considered in a framework that enables scaling between expected value and minimax optimization. Experiments on a phantom show that the best and mean case tradeoffs between target coverage and critical structure sparing are similar between the methods of the framework, but that the worst case tradeoff improves with conservativeness. Minimax optimization only considers the worst case errors. When the planning criteria cannot be fulfilled for all errors, this may have an adverse effect on the plan quality. The third paper introduces a method for such cases that modifies the set of considered errors to maximize the probability of satisfying the planning criteria. For two cases treated with intensity-modulated photon and proton therapy, the method increased the number of satisfied criteria substantially. Grasping for a little less sometimes yields better plans. In the fourth paper, the theory for multicriteria optimization is extended to incorporate minimax optimization. Minimax optimization is shown to better exploit spatial information than objective-wise worst case optimization, which has previously been used for robust multicriteria optimization. The fifth and sixth papers introduce methods for improving treatment plans: one for deliverable Pareto surface navigation, which improves upon the Pareto set representations of previous methods; and one that minimizes healthy structure doses while constraining the doses of all structures not to deteriorate compared to a reference plan, thereby improving upon plans that have been reached with too weak planning goals. / <p>QC 20130516</p>

Motivated by an electric power portfolio selection problem, a sampling method is developed for simulation-based robust design that builds on existing multi-objective statistical improvement methods. It uses a Bayesian surrogate model regressed on both design and noise variables, and makes use of methods for estimating epistemic model uncertainty in environmental uncertainty metrics. Regions of the design space are sequentially sampled in a manner that balances exploration of unknown designs and exploitation of designs thought to be Pareto optimal, while regions of the noise space are sampled to improve knowledge of the environmental uncertainty. A scalable test problem is used to compare the method with design of experiments (DoE) and crossed array methods, and the method is found to be more efficient for restrictive sample budgets. Experiments with the same test problem are used to study the sensitivity of the methods to numbers of design and noise variables. Lastly, the method is demonstrated on an electric power portfolio simulation code.