A computationally efficient estimation technique is presented for a class of nonlinear systems consisting of memoryless nonlinearities combined with linear dynamic processes. The modeling approach is based on a useful sampled-data method for simulating such systems by adding a system state for each nonlinear element. The nonlinear estimator is next developed along the lines of the Kalman filter, but in contrast to the Extended Kalman Filter (EKF) the present approach does not require the linearization step after each recursive cycle. In addition, it also appears free from the well known divergence problems associated with the EKF. It is demonstrated that this new method is directly applicable to those feedback systems with both major nonlinearities, for example saturating gain blocks, and stochastic disturbances-- an example extremely difficult to handle with EKF techniques. / Master of Science

An estimator for Nonlinear system estimation using Jump Matrix Technique is developed. The idea of the Jump Matrix Technique is to break up the nonlinear system into linear and nonlinear subsystems. The linear subsystem projection, during the sampling interval, is on the basis of the transition matrix of the linear subsystem. At each sampling instant, the system variables are updated using an instantaneous "jump" in the values. The estimator for the nonlinear case is developed on the lines of Kalman filter for the linear case. The Jump Matrix technique is used for system simulation for three different nonlinear systems and then estimation of the system state is carried out using the above mentioned estimator. The system response and the estimated states are considered and the effect of change in system noise parameters is observed. Feedback control of nonlinear system response using the estimated state variables is investigated. Two different systems are considered and their responses are changed using feedback of linear combination of the system state variables. / Master of Science

We use a perturbation analysis to predict some of the instabilities in a single-machine quasi-infinite busbar system. The system’s behavior is described by the so-called swing equation, which is a nonlinear second-order ordinary-differential equation with additive and multiplicative harmonic terms having the frequency Ω. When Ω≈ω₀, and Ω≈2ω₀, where ω₀ is the linear natural frequency of the machine, we use digital-computer simulations to exhibit some of the complicated responses of the machine, including period-doubling bifurcations, chaotic motions, and unbounded motions (loss of synchronism). To predict the onset of these complicated behaviors, we use the method of multiple scales to develop approximate closed-form expressions for the periodic responses of the machine. Then, we use various techniques to determine the stability of the analytical solutions. The analytically predicted periodic solutions and conditions for their instability are in good agreement with the digital-computer results. / Master of Science

Peter McCullagh (1983) outlined the theory of quasi-likelihood estimation in generalized linear models. Chiu (1988) showed that an iterated, reweighted least squares procedure applied to the periodogram produces estimates of spectral density model parameters for Gaussian univariate time series which have the same asymptotic variance as those produced by maximizing the true likelihood. In this dissertation, McCullagh's theory is combined with a functional analysis approach and extended to parametric estimation of the spectral density matrix components of a non-Gaussian bivariate time series. An asymptotic optimality theorem is given, which shows optimality of an iterated, reweighted least squares procedure within a class of procedures. However, the principal application of the theory is for parametric spectral estimation in the case of an observed "contaminated" Gaussian series X(t)+N(t), where the noise series is uncorrelated with the X series, and it is desired to estimate the spectrum of the X series. Previous literature suggests removing contaminated bands of the periodogram prior to analysis, but the results of the dissertation may be used to unbiasedly estimate the spectrum of f without a precise knowledge of which bands are contaminated. / Ph. D.

Three methods are developed to study the response of nonlinear systems to combined deterministic and stochastic excitations. They are a second-order closure method, a generalized method of equivalent linearization, and a reduced non-Gaussian closure scheme. Primary resonances of single- and two-degree-of-freedom systems in the presence of different internal (autoparametric) resonances are investigated. We propose these methods to overcome some of the limitations of the existing methods of solution and explain some observed experimental results in the context of the response of randomly excited nonlinear systems. These include non-Gaussian responses, broadening effects, and shift in the resonant frequency. When available, the results of these methods are compared with those obtained by using the exact stationary solutions of the Fokker-Planck-Kolmogorov equation. It is found that the presence of the nonlinearities bend the frequency-response curves and this causes multi-valued regions for the mean-square responses. The multi-valuedness is responsible for a jump phenomenon. The results show that for some range of parameters, noise can expand the stability region of the mean response. As applications, we study the response of a shallow arch, a string, and a hinged-clamped beam to random excitations. / Ph. D.

A geometric model of a reinjected cuspidal horseshoe is constructed, that resembles the standard horseshoe, but where the set of points that escape are now reinjected and contribute to richer dynamics. We show it is observed in the unfolding of a three-dimensional vector field possessing an inclination-flip homoclinic orbit with a resonant hyperbolic equilibrium. We use techniques from classical dynamical systems theory and rigorous computational symbolic dynamics with algebraic topology to show that for suitable parameters the flow contains a strange attractor. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection

by Hon-chor Lee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaf 56). / by Hon-chor Lee. / Introduction --- p.1 / Series expansion for the conductivity of a linear random resistor network / Chapter 1. --- Introduction --- p.4 / Chapter 2. --- Comparison of the EMA with symbolic simulations in 2D --- p.5 / Chapter 3. --- Comparison of the EMA with Bergman and Kantor's findings --- p.6 / Chapter 4. --- Conclusion --- p.7 / Current moments of linear random resistor network / Chapter 1. --- Introduction --- p.10 / Chapter 2. --- Review of the definition of current moment --- p.10 / Chapter 3. --- Tremblay et. al.'s findings and symbolic simulation of current moments --- p.11 / Chapter 4. --- Conclusion --- p.13 / Effective medium theory for strongly nonlinear composites: comparison with numerical simulations / Chapter 1. --- Introduction --- p.15 / Chapter 2. --- Variational principles --- p.16 / Chapter 3. --- Formalism of EMA --- p.17 / Chapter 4. --- Comparison with numerical simulations --- p.19 / Chapter 5. --- Discussion --- p.21 / Percolative conduction in two-component strongly nonlinear composites / Chapter 1. --- Introduction --- p.25 / Chapter 2. --- Spherical inclusions --- p.25 / Chapter 3. --- Effective medium approximation in the vicinity of the percolation threshold --- p.27 / Chapter 4. --- Acknowledgment --- p.29 / Percolation Effects in Two Component Strongly Nonlinear Composites: Universal Scaling Behaviours / Chapter 1. --- Introduction --- p.31 / Chapter 2. --- General Scaling Relations for Two-Component Composites --- p.33 / Chapter 3. --- Estimate of Critical Exponents --- p.35 / Chapter 4. --- Numerical Simulations --- p.38 / Chapter 5. --- Discussions and Conclusions --- p.40 / Chapter 6. --- Acknowledgment --- p.40 / Improved effective medium theory for strongly nonlinear composites / Chapter 1. --- Introduction --- p.46 / Chapter 2. --- Formalism of Improved EMA --- p.47 / Chapter 3. --- Comparisons with numerical simulations and HS bound --- p.50 / Chapter 4. --- Discussions --- p.51 / Conclusion --- p.54

by Leung, Kwok Kong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 67). / Text in English; abstracts in English and Chinese. / by Leung, Kwok Kong. / Abstract --- p.ii / Acknowledgement --- p.iii / Contents --- p.iv / List of Figures --- p.vi / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Transmittance in Metal-Dielectric Multilayers --- p.4 / Chapter 2.1 --- Introduction --- p.4 / Chapter 2.2 --- Transfer matrix approach --- p.5 / Chapter 2.3 --- Transfer matrix simulation --- p.7 / Chapter 2.4 --- Physical explanation --- p.14 / Chapter Chapter 3. --- Optical Nonlinear Response of Composite Layer --- p.17 / Chapter 3.1 --- Transfer matrix formalism for oblique incidence --- p.18 / Chapter 3.1.1 --- Transfer matrix method in nonlinear region --- p.18 / Chapter 3.1.2 --- S-polarization --- p.19 / Chapter 3.1.3 --- P-polarization --- p.19 / Chapter 3.1.4 --- Backward propagation technique --- p.22 / Chapter 3.2 --- Nonlinear phase shift --- p.22 / Chapter 3.3 --- Transfer matrix method approach --- p.24 / Chapter 3.4 --- Analytic solution formalism --- p.26 / Chapter Chapter 4. --- Study of Photonic Band Gap of Nonlinear Dielectrics --- p.33 / Chapter 4.1 --- Introduction --- p.33 / Chapter 4.2 --- Nonlinear response of single thin nonlinear layer --- p.34 / Chapter 4.3 --- Nonlinear response of δ-function between two linear dielectric --- p.37 / Chapter 4.4 --- Photonic band structure --- p.41 / Chapter 4.4.1 --- Photonic band structure of linear thin films --- p.41 / Chapter 4.4.2 --- Photonic band structure of linear layers --- p.42 / Chapter 4.5 --- Photonic band gap of nonlinear dielectric multilayers --- p.46 / Chapter Chapter 5. --- Optical Limiting of Composite Material --- p.49 / Chapter 5.1 --- Transmittance of periodic multilayer structures --- p.50 / Chapter 5.1.1 --- Transmittance properties at low intensity --- p.50 / Chapter 5.1.2 --- Transmittance at high intensity: optical limiting effect --- p.52 / Chapter 5.2 --- The effect of layer thickness on optical limiting --- p.53 / Chapter 5.3 --- Optical limiting property of PBG materials --- p.55 / Chapter Chapter 6. --- Conclusion --- p.63 / Chapter Appendix A. --- Effective dielectric function --- p.64 / Bibliography --- p.67

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Civil Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 207-211. / by Hugo Scaletti Farina. / Ph.D.

Thesis. 1976. Ph.D.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERONAUTICS. / Vita. / Bibliography : leaves 226-229. / Ph.D.