When two or more chaotic systems are coupled, they may exhibit synchronized chaotic oscillations. The synchronization of chaos is usually understood as the regime of chaotic oscillations in which the corresponding variables or coupled systems are equal to each other. This kind of synchronized chaos is most frequently observed in systems specifically designed to be able to produce this behaviour. In this thesis, one particular type of synchronization, called impulsive synchronization, is investigated and applied to low dimensional chaotic, hyperchaotic and spatiotemporal chaotic systems. This synchronization technique requires driving one chaotic system, called response system, by samples of the state variables of the other chaotic system, called drive system, at discrete moments. Equi-Lagrange stability and equi-attractivity in the large property of the synchronization error become our major concerns when discussing the dynamics of synchronization to guarantee the convergence of the error dynamics to zero. Sufficient conditions for equi-Lagrange stability and equi-attractivity in the large are obtained for the different types of chaos-generating systems used. The issue of robustness of synchronized chaotic oscillations with respect to parameter variations and time delay, is also addressed and investigated when dealing with impulsive synchronization of low dimensional chaotic and hyperchaotic systems. Due to the fact that it is impossible to design two identical chaotic systems and that transmission and sampling delays in impulsive synchronization are inevitable, robustness becomes a fundamental issue in the models considered. Therefore it is established, in this thesis, that under relatively large parameter perturbations and bounded delay, impulsive synchronization still shows very desired behaviour. In fact, criteria for robustness of this particular type of synchronization are derived for both cases, especially in the case of time delay, where sufficient conditions for the synchronization error to be equi-attractivity in the large, are derived and an upper bound on the delay terms is also obtained in terms of the other parameters of the systems involved. The theoretical results, described above, regarding impulsive synchronization, are reconfirmed numerically. This is done by analyzing the Lyapunov exponents of the error dynamics and by showing the simulations of the different models discussed in each case. The application of the theory of synchronization, in general, and impulsive synchronization, in particular, to communication security, is also presented in this thesis. A new impulsive cryptosystem, called induced-message cryptosystem, is proposed and its properties are investigated. It was established that this cryptosystem does not require the transmission of the encrypted signal but instead the impulses will carry the information needed for synchronization and for retrieving the message signal. Thus the security of transmission is increased and the time-frame congestion problem, discussed in the literature, is also solved. Several other impulsive cryptosystems are also proposed to accommodate more solutions to several security issues and to illustrate the different properties of impulsive synchronization. Finally, extending the applications of impulsive synchronization to employ spatiotemporal chaotic systems, generated by partial differential equations, is addressed. Several possible models implementing this approach are suggested in this thesis and few questions are raised towards possible future research work in this area.

ABSTRACT ROBUST CONTROL CHARTS &Ccedil / etiny&uuml / rek, Aysun M. Sc., Department of Statistics Supervisor: Dr. BariS S&uuml / r&uuml / c&uuml / Co-Supervisor: Assoc. Prof. Dr. Birdal Senoglu December 2006, 82 pages Control charts are one of the most commonly used tools in statistical process control. A prominent feature of the statistical process control is the Shewhart control chart that depends on the assumption of normality. However, violations of underlying normality assumption are common in practice. For this reason, control charts for symmetric distributions for both long- and short-tailed distributions are constructed by using least squares estimators and the robust estimators -modified maximum likelihood, trim, MAD and wave. In order to evaluate the performance of the charts under the assumed distribution and investigate robustness properties, the probability of plotting outside the control limits is calculated via Monte Carlo simulation technique.

This paper explores the problem of electrical sports equipment includes 2D-animation, storage media and the safety-protection over out of control of speed and the supporting supervisory control apparatus. This paper succeeded in developing a highly efficient DSP-based motor driver system in the form of a jogging machine which employs IVSC and RISC control law. The simulation and experimental results show that the proposed system meets the requirements of servo tracking with excellent transient, steady state responses and robustness. This paper design a multi-functional FPGA uses in control system of sports equipment to provide the designing flexibility for different scales, solutions to the difficulties of production and maintenance, and the extension for future development of sports equipment.

Vulnerability of buildings to disproportionate (or progressive) collapse has become an increasingly important performance issue following the collapses of the Alfred P. Murrah Federal Building in Oklahoma City in 1995 and the World Trade Center in 2001. Although considerable research has been conducted on this topic, there are still numerous unresolved research issues. This dissertation is aimed at developing structural models and analysis procedures for robustness assessment of steel building structures typical of construction practices in the United States, and assessing the performance of these typical structures. Beam-column connections are usually the most vulnerable elements in steel buildings structures suffering local damage. Models of three typical frame connections for use in robustness assessment have been developed with different techniques, depending on the experimental data available to support such models. A probabilistic model of a pre-Northridge moment-resisting connection was developed through finite element simulations, in which the uncertainties in the initial flaw size, beam yield strength and fracture toughness of the weld were considered. A macro-model for a bolted T-stub connections was developed by considering the behavior of each connection element individually (i.e. T-stub, shear tab and panel zone) and assembling the elements to form a complete connection model, which was subsequently calibrated to experimental data. For modeling riveted connections in older steel buildings that might be candidates for rehabilitation, a new method was proposed to take advantage of available experimental data from tests of earthquake-resistant connections and to take into account the effects of the unequal compressive and tensile stiffnesses of top and bottom parts in a connection and catenary action. These connection models were integrated into nonlinear finite element models of structural systems to allow the effect of catenary and other large-deformation action on the behavior of the frames and their connections following initial local structural damage to be assessed. The performance of pre-Northridge moment-resisting frames was assessed with both mean-centered deterministic and probabilistic assessment procedures; the significance of uncertainties in collapse assessment was examined by comparing the results from both procedures. A deterministic assessment of frames with full and partial-strength bolted T-stub connections was conducted considering three typical beam spans in both directions. The vulnerability of an older steel building with riveted connections was also analyzed deterministically. The contributions from unreinforced masonry infill panels and reinforced concrete slabs on the behavior of the building were investigated. To meet the need for a relatively simple procedure for preliminary vulnerability assessment, an energy-based nonlinear static pushdown analysis procedure was developed. This procedure provides an alternative method of static analysis of disproportionate collapse vulnerability that can be used as an assessment tool for regular building frames subjected to local damage. Through modal analysis, dominant vibration modes of a damaged frame were first identified. The structure was divided into two parts, each of which had different vibration characteristics and was modeled by a single degree-of-freedom (SDOF) system separately. The predictions were found to be sufficiently close to the results of a nonlinear dynamic time history analysis (NTHA) that the method would be useful for collapse-resistant design of buildings with regular steel framing systems.

This thesis describes the application of multivariate methods in a novel approach to the formulation of tablets for direct compression. It begins with a brief historical review, followed by a basic introduction to key aspects of tablet formulation and multivariate data analysis. The bulk of the thesis is concerned with the novel approach, in which excipients were characterised in terms of multiple physical or (in most cases) spectral variables. By applying Principal Component Analysis (PCA) the descriptive variables are summarized into a few latent variables, usually termed scores or principal properties (PP’s). In this way the number of descriptive variables is dramatically reduced and the excipients are described by orthogonal continuous variables. This means that the PP’s can be used as ordinary variables in a statistical experimental design. The combination of latent variables and experimental design is termed multivariate design or experimental design in PP’s. Using multivariate design many excipients can be included in screening experiments with relatively few experiments. The outcome of experiments designed to evaluate the effects of differences in excipient composition of formulations for direct compression is, of course, tablets with various properties. Once these properties, e.g. disintegration time and tensile strength, have been determined with standardised tests, quantitative relationships between descriptive variables and tablet properties can be established using Partial Least Squares Projections to Latent Structures (PLS) analysis. The obtained models can then be used for different purposes, depending on the objective of the research, such as evaluating the influence of the constituents of the formulation or optimisation of a certain tablet property. Several examples of applications of the described methods are presented. Except in the first study, in which the feasibility of this approach was first tested, the disintegration time of the tablets has been studied more carefully than other responses. Additional experiments have been performed in order to obtain a specific disintegration time. Studies of mixtures of excipients with the same primary function have also been performed to obtain certain PP’s. Such mixture experiments also provide a straightforward approach to additional experiments where an interesting area of the PP space can be studied in more detail. The robustness of a formulation with respect to normal batch-to-batch variability has also been studied. The presented approach to tablet formulation offers several interesting alternatives, for both planning and evaluating experiments.

Hydraulic systems are widely applied in industry for position or force control. However, due to hydraulic system nonlinearities, it is difficult to achieve a precise model valid over a large range of frequencies and movements. The work in this dissertation focuses on a high performance hydraulic test bench which involves three main hydraulic components, i.e. two high performance servovalves, a double rod actuator, and a specific intermediate block connecting the servovalves and actuator. This rig has been designed for testing aerospace or automotive components in real conditions (e.g. wear and ageing effects). The main objectives of this dissertation are first the development of a virtual prototype based on a precise model which is derived from the physical principles and experimental works, and then second the synthesis of several nonlinear control laws of this actuation system in a large operating range with a good robustness to the perturbations. The proposed model based on Bond Graph shows a very good agreement with experimental results not only at low frequencies, but also at high frequencies. Moreover, its performances are improved at high frequencies by introducing the dynamic effects due to the intermediate block. Besides, multivariable and monovariable control strategies, based on respectively the backstepping and the model-free method, are developed and implemented on the test bench. All the control strategies proposed have been validated by simulations and experiments. Results show they lead to better tracking precision and robustness performance compared to the conventional control techniques.

Maximum likelihood is an ubiquitous method used in the estimation of generalized linear mixed model (GLMM). However, the method entails computational difficulties and relies on the normality assumption for random effects. We propose a second-order least squares (SLS) estimator based on the first two marginal moments of the response variables. The proposed estimator is computationally feasible and requires less distributional assumptions than the maximum likelihood estimator. To overcome the numerical difficulties of minimizing an objective function that involves multiple integrals, a simulation-based SLS estimator is proposed. We show that the SLS estimators are consistent and asymptotically normally distributed under fairly general conditions in the framework of GLMM. Missing data is almost inevitable in longitudinal studies. Problems arise if the missing data mechanism is related to the response process. This thesis develops the proposed estimators to deal with response data missing at random by either adapting the inverse probability weight method or applying the multiple imputation approach. In practice, some of the covariates are not directly observed but are measured with error. It is well-known that simply substituting a proxy variable for the unobserved covariate in the model will generally lead to biased and inconsistent estimates. We propose the instrumental variable method for the consistent estimation of GLMM with covariate measurement error. The proposed approach does not need any parametric assumption on the distribution of the unknown covariates. This makes the method less restrictive than other methods that rely on either a parametric distribution of the covariates, or to estimate the distribution using some extra information. In the presence of data outliers, it is a concern that the SLS estimators may be vulnerable due to the second-order moments. We investigated the robustness property of the SLS estimators using their influence functions. We showed that the proposed estimators have a bounded influence function and a redescending property so they are robust to outliers. The finite sample performance and property of the SLS estimators are studied and compared with other popular estimators in the literature through simulation studies and real world data examples.

In the thesis robust routing design problems in resilient networks are considered. In the first part computational complexity of such problems are discussed. The following cases are considered: - path protection and path restoration - failure-dependent and failure-independent restoration - cases with and without stub-release - single-link failures and multiple-link failures (shared risk link group) - non-bifurcated (unsplittable) flows and bifurcated flows For each of the related optimization cases a mixed-integer (in the non-bifurcated cases) or linear programming formulation (in all bifurcated cases) is presented, and their computational complexity is investigated. For the NP-hard cases original NP-hardness proofs are provided, while for the polynomial cases compact linear programming formulations (which prove the polynomiality in the question) are discussed. Moreover, pricing problems related to each of the considered NP-hard problems are discussed. The second part of the thesis deals with various routing strategies in networks where the uncertainty issues are modeled using the polyhedral model. In such networks two extrema are possible. The simplest in terms of implementation, and simultaneously the least effective strategy, is the robust stable routing. On the other hand, the most effective strategy, i.e., the dynamic routing, is virtually impossible to implement in real world networks. Therefore, the major aim of this part of the thesis is to present novel routing strategies that merge the simplicity of the robust stable routing with the efficiency of the dynamic routing

Flexible structures are increasingly used in various applications such as aerospace, automotive and so on. Since they are lightly damped and susceptible to vibrations, active vibration control is desirable. In practice, in addition to achieving effective vibration reduction, we have also to consider the required control energy to avoid the energy insufficiency, the control input to avoid control saturation and reduce the effects of measurement noises. On the other hand, as flexible structures have infinite number of resonant modes and only the first few can be employed in the system modeling and the controller design, there always exist neglected high-frequency dynamics, which can induce the spillover instability. Furthermore, the parametric uncertainties on modal parameters can degrade the control performances and even destabilize the closed-loop system. In this context, a quantitative robust control methodology for active vibration control of flexible structure is proposed in this thesis. Phase and gain control polices are first proposed to enforce frequency-dependent phase and gain requirements on the controller, which can be realized by the output feedback H1 control design. The phase and gain control polices based H1 control can make a trade-off among the complete set of control objectives and offer a qualitative robust controller. Especially, the LPV H1 control is used to reduce the required control energy for LPV systems. The generalized polynomial chaos (gPC) framework with finite element analysis is employed for uncertainty quantification. It allows us to investigate the effects of structural property uncertainties on natural frequencies and achieve their probabilistic information. Then, in the presence of parametric and dynamic uncertainties, µ / v analysis and the random algorithm using Monte Carlo Method are used to quantitatively ensure the closed-loop stability and performance robustness properties both in deterministic and probabilistic senses. The proposed quantitative robust control methodology is thus developed by employing various techniques from automatic control and mechanical engineering, thus reducing the gap between them for robust vibration control of flexible structures. Its effectiveness are verified by numerical simulations and experimental validation on LTI and LPV non-collocated piezoelectric cantilever beams.

Maximum likelihood is an ubiquitous method used in the estimation of generalized linear mixed model (GLMM). However, the method entails computational difficulties and relies on the normality assumption for random effects. We propose a second-order least squares (SLS) estimator based on the first two marginal moments of the response variables. The proposed estimator is computationally feasible and requires less distributional assumptions than the maximum likelihood estimator. To overcome the numerical difficulties of minimizing an objective function that involves multiple integrals, a simulation-based SLS estimator is proposed. We show that the SLS estimators are consistent and asymptotically normally distributed under fairly general conditions in the framework of GLMM. Missing data is almost inevitable in longitudinal studies. Problems arise if the missing data mechanism is related to the response process. This thesis develops the proposed estimators to deal with response data missing at random by either adapting the inverse probability weight method or applying the multiple imputation approach. In practice, some of the covariates are not directly observed but are measured with error. It is well-known that simply substituting a proxy variable for the unobserved covariate in the model will generally lead to biased and inconsistent estimates. We propose the instrumental variable method for the consistent estimation of GLMM with covariate measurement error. The proposed approach does not need any parametric assumption on the distribution of the unknown covariates. This makes the method less restrictive than other methods that rely on either a parametric distribution of the covariates, or to estimate the distribution using some extra information. In the presence of data outliers, it is a concern that the SLS estimators may be vulnerable due to the second-order moments. We investigated the robustness property of the SLS estimators using their influence functions. We showed that the proposed estimators have a bounded influence function and a redescending property so they are robust to outliers. The finite sample performance and property of the SLS estimators are studied and compared with other popular estimators in the literature through simulation studies and real world data examples.