Showing papers on "Nonlinear system published in 2001"

A New Approach to Linear Filtering and Prediction Problems

Abstract: The clssical filleting and prediclion problem is re-examined using the Bode-Shannon representation of random processes and the ?stat-tran-sition? method of analysis of dynamic systems. New result are: (1) The formulation and Methods of solution of the problm apply, without modification to stationary and nonstationary stalistics end to growing-memory and infinile -memory filters. (2) A nonlinear difference (or differential) equalion is dericed for the covariance matrix of the optimal estimalion error. From the solution of this equation the coefficients of the difference, (or differential) equation of the optimal linear filter are obtained without further caleulations. (3) Tke fillering problem is shoum to be the dual of the nois-free regulator problem. The new method developed here, is applied to do well-known problems, confirming and extending, earlier results. The discussion is largely, self-contatained, and proceeds from first principles; basic concepts of the theory of random processes are reviewed in the Appendix.

Dynamic Equations on Time Scales: An Introduction with Applications

Abstract: Preface * The Time Scales Calculus * First Order Linear Equations * Second Order Linear Equations * Self-Adjoint Equations * Linear Systems and Higher Order Equations * Dynamic Inequalities * Linear Symplectic Dynamic Systems * Extensions * Solutions to Selected Problems * Bibliography * Index

Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: dependence on recording region and brain state.

Abstract: We compare dynamical properties of brain electrical activity from different recording regions and from different physiological and pathological brain states Using the nonlinear prediction error and an estimate of an effective correlation dimension in combination with the method of iterative amplitude adjusted surrogate data, we analyze sets of electroencephalographic (EEG) time series: surface EEG recordings from healthy volunteers with eyes closed and eyes open, and intracranial EEG recordings from epilepsy patients during the seizure free interval from within and from outside the seizure generating area as well as intracranial EEG recordings of epileptic seizures As a preanalysis step an inclusion criterion of weak stationarity was applied Surface EEG recordings with eyes open were compatible with the surrogates' null hypothesis of a Gaussian linear stochastic process Strongest indications of nonlinear deterministic dynamics were found for seizure activity Results of the other sets were found to be inbetween these two extremes

Nonequilibrium statistical mechanics

Abstract: 1. Brownian Motion and Langevin equations 2. Fokker-Planck equations 3. Master equations 4. Reaction rates 5. Kinetic models 6. Quantum dynamics 7. Linear response theory 8. Projection operators 9. Nonlinear problems 10. The paradoxes of irreversibility Appendices

Kalman Filtering and Neural Networks

Abstract: From the Publisher: Kalman filtering is a well-established topic in the field of control and signal processing and represents by far the most refined method for the design of neural networks. This book takes a nontraditional nonlinear approach and reflects the fact that most practical applications are nonlinear. The book deals with important applications in such fields as control, financial forecasting, and idle speed control.

Nonlinear Dynamics and Chaos

Abstract: Nonlinear dynamics deals with more-or-less regular fluctuations in system variables caused by feedback intrinsic to the system (as opposed to external forces). Chaos is the most exotic form of nonlinear dynamics, in which deterministic interactions produce apparently irregular fluctuations, and small changes in the initial state of the system are magnified through time.7 Keywords: chaos; population cycles; population dynamics; nonlinear time-series analysis

A simple white noise analysis of neuronal light responses.

Abstract: A white noise technique is presented for estimating the response properties of spiking visual system neurons. The technique is simple, robust, efficient and well suited to simultaneous recordings from multiple neurons. It provides a complete and easily interpretable model of light responses even for neurons that display a common form of response nonlinearity that precludes classical linear systems analysis. A theoretical justification of the technique is presented that relies only on elementary linear algebra and statistics. Implementation is described with examples. The technique and the underlying model of neural responses are validated using recordings from retinal ganglion cells, and in principle are applicable to other neurons. Advantages and disadvantages of the technique relative to classical approaches are discussed.

Mathematical methods in image reconstruction

Abstract: 1. Introduction 2. Integral geometry 3. Tomography 4. Stability and resolution 5. Reconstruction algorithms 6. Problems that have peculiarities 7. Nonlinear tomography.

Holographic Renormalization

Abstract: We systematically develop the procedure of holographic renormalization for RG flows dual to asymptotically AdS domain walls All divergences of the on-shell bulk action can be cancelled by adding covariant local boundary counterterms determined by the near-boundary behavior of bulk fields This procedure defines a renormalized action from which correlation functions are obtained by functional differentiation The correlators are finite and well behaved at coincident points Ward identities, corrected for anomalies, are satisfied The correlators depend on parts of the solution of the bulk field equations which are not determined by near-boundary analysis In principle a full nonlinear solution is required, but one can solve linearized fluctuation equations to define a bulk-to-boundary propagator from which 2-point correlation functions are easily obtained We carry out the procedure explicitly for two known RG flows obtained from the maximal gauged D=5 supergravity theory, obtaining new results on correlators of vector currents and related scalar operators and giving further details on a recent analysis of the stress tensor sector

Extending the Applicability of the Nonlinear Poisson−Boltzmann Equation: Multiple Dielectric Constants and Multivalent Ions†

Abstract: A new version of the DelPhi program, which provides numerical solutions to the nonlinear Poisson−Boltzmann (PB) equation, is reported. The program can divide space into multiple regions containing ...

A geometric approach to nonlinear fault detection and isolation

Abstract: We present a differential geometric approach to the problem of fault detection and isolation for nonlinear systems. A necessary condition for the problem to be solvable is derived in terms of an unobservability distribution, which is computable by means of suitable algorithms. The existence and regularity of such a distribution implies the existence of changes of coordinates in the state and in the output space which induce an "observable" quotient subsystem unaffected by all fault signals but one. For this subsystem, a fault detection filter is designed.

Creep, Hysteresis, and Vibration Compensation for Piezoactuators: Atomic Force Microscopy Application

Abstract: Structural vibrations and hysteresis nonlinearities in piezoactuators have been fundamental limitations when using these actuators for high-speed precision-positioning applications. Positioning speed (bandwidth) is limited by structural vibrations, typically, to about one-tenth the fundamental vibrational frequency of the piezoprobe. Further, precision in positioning is limited by hysteresis nonlinearities, which can result in signie cant errors for large-range positioning applications. This paper shows that signie cant improvements in precision and bandwidth can be achieved by using an inversion-based approach to compensate for hysteresis and vibrations in the piezodynamics. Theapproach decouplestheinversion into 1 )inversion of thehysteresisnonlinearity and 2 )inversion ofthe structuraldynamics,toe ndaninputvoltageproe lethatachievesprecisiontracking ofa desiredpositiontrajectory. Theapproachisappliedtoapiezoactuator,andexperimentalresultsshowthatanorderofmagnitudeimprovement in positioning speed is achieved, while maintaining precision tracking of the desired position trajectory. I. Introduction P IEZOACTUATORS can achieve nanometer resolution positioning and are hence increasingly being used for ultraprecision positioning in aerospace applications, 1;2 vibration control, scanning probe microscopy for surface characterization, and nanofabrication. 3i5 Two major limitations of present positioning techniquesusing piezoactuatorsare 1 )lowoperating bandwidthdue to positioning errors caused by structural vibrations at high speeds and 2) low precision for relatively large-range displacements (due to errors caused by hysteresis nonlinearities ), resulting in restricted positioning range. This paper presents a method to improve both the accuracy and the speed of piezoactuators by using an inversionbased approach to e nd the voltage input to the piezoactuators that compensates for the hysteresis nonlinearities and the structural vibrations. This approach e rst decouples the system dynamics into two separate subsystems that model 1 ) the hysteresis nonlinearity

Stable Adaptive Neural Network Control

Abstract: While neural network control has been successfully applied in various practical applications, many important issues, such as stability, robustness, and performance, have not been extensively researched for neural adaptive systems. Motivated by the need for systematic neural control strategies for nonlinear systems, Stable Adaptive Neural Network Control offers an in-depth study of stable adaptive control designs using approximation-based techniques, and presents rigorous analysis for system stability and control performance. Both linearly parameterized and multi-layer neural networks (NN) are discussed and employed in the design of adaptive NN control systems for completeness. Stable adaptive NN control has been thoroughly investigated for several classes of nonlinear systems, including nonlinear systems in Brunovsky form, nonlinear systems in strict-feedback and pure-feedback forms, nonaffine nonlinear systems, and a class of MIMO nonlinear systems. In addition, the developed design methodologies are not only applied to typical example systems, but also to real application-oriented systems, such as the variable length pendulum system, the underactuated inverted pendulum system and nonaffine nonlinear chemical processes (CSTR).

On an output feedback finite-time stabilization problem

Abstract: Studies the problem of finite-time output feedback stabilization for the double integrator system. A class of output feedback controllers that can achieve global finite-time stability for the double integrator system are constructed based on a "finite-time separation principle." Furthermore, it is shown that the closed-loop system resulting from our control law can maintain its local finite-time stability regardless of some nonlinear perturbations. Thus, our control law actually applies to a large class of nonlinear second order systems.

Nonlinear limits to the information capacity of optical fibre communications.

Abstract: The exponential growth in the rate at which information can be communicated through an optical fibre is a key element in the 'information revolution' However, as for all exponential growth laws, physical limits must be considered The nonlinear nature of the propagation of light in optical fibre has made these limits difficult to elucidate Here we use a key simplification to investigate the theoretical limits to the information capacity of an optical fibre arising from these nonlinearities The success of our approach lies in relating the nonlinear channel to a linear channel with multiplicative noise, for which we are able to obtain analytical results In fundamental distinction to linear channels with additive noise, the capacity of a nonlinear channel does not grow indefinitely with increasing signal power, but has a maximal value The ideas presented here may have broader implications for other nonlinear information channels, such as those involved in sensory transduction in neurobiology These have been often examined using additive noise linear channel models but, as we show here, nonlinearities can change the picture qualitatively

Two-dimensional phase unwrapping with use of statistical models for cost functions in nonlinear optimization

Abstract: Interferometric radar techniques often necessitate two-dimensional (2-D) phase unwrapping, defined here as the estimation of unambiguous phase data from a 2-D array known only modulo 2pi rad. We develop a maximum a posteriori probability (MAP) estimation approach for this problem, and we derive an algorithm that approximately maximizes the conditional probability of its phase-unwrapped solution given observable quantities such as wrapped phase, image intensity, and interferogram coherence. Examining topographic and differential interferometry separately, we derive simple, working models for the joint statistics of the estimated and the observed signals. We use generalized, nonlinear cost functions to reflect these probability relationships, and we employ nonlinear network-flow techniques to approximate MAP solutions. We apply our algorithm both to a topographic interferogram exhibiting rough terrain and layover and to a differential interferogram measuring the deformation from a large earthquake. The MAP solutions are complete and are more accurate than those of other tested algorithms.

Self-consistent fluid model for a quantum electron gas

Abstract: It is shown that, for a large class of statistical mixtures, the Wigner-Poisson (or Hartree) system can be reduced to an effective Schroedinger-Poisson system, in which the Schroedinger equation contains a new nonlinearity. For the case of a zero-temperature one-dimensional electron gas, this additional nonlinearity is of the form vertical bar {Psi} vertical bar{sup 4}. In the long-wavelength limit, the results obtained from the effective Schroedinger-Poisson system are in agreement with those of the Wigner-Poisson system. The reduced model is further used to describe the stationary states of a quantum electron gas and the two-stream instability.

Noisy Clockwork: Time Series Analysis of Population Fluctuations in Animals

Abstract: Both biotic interactions and abiotic random forcing are crucial influences on population dynamics. This frequently leads to roughly equal importance of deterministic and stochastic forces. The resulting tension between noise and determinism makes ecological dynamics unique, with conceptual and methodological challenges distinctive from those in other dynamical systems. The theory for stochastic, nonlinear ecological dynamics has been developed alongside methods to test models. A range of dynamical components has been considered-density dependence, environmental and demographic stochasticity, and climatic forcing-as well as their often complex interactions. We discuss recent advances in understanding ecological dynamics and testing theory using long-term data and review how dynamical forces interact to generate some central field and laboratory time series.

Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles

Abstract: This thesis is devoted to nonlinear control, reduction, and classification of underactuated mechanical systems. Reduction and nonlinear control of high-order underactuated systems with kinetic symmetry is the main focus of this thesis. Our main contribution is to find explicit change of coordinates and control that transform several classes of underactuated systems, which appear in robotics and aerospace applications, into cascade nonlinear systems with structural properties that are convenient for control design purposes. The obtained cascade normal forms are three classes of nonlinear systems, namely, systems in strict feedback form, feedforward form, and nontriangular linear-quadratic form. The triangular normal forms of underactuated systems can be controlled using existing backstepping and feedforwarding procedures. However, control of the nontriangular normal forms is a major open problem. We address this problem for important classes of nontriangular systems of interest by introducing a new stabilization method based on the solutions of fixed-point equations as stabilizing nonlinear state feedback laws. As a result of the reduction process, one obtains a reduced nonlinear subsystem in cascade with a linear subsystem. For many classes of underactuated systems, this reduced nonlinear subsystem is physically meaningful. In fact, the reduced nonlinear subsystem is itself a Lagrangian system with a well-defined lower-order configuration vector. The key analytical tools that allow reduction of high-order underactuated systems using transformations in explicit forms are “normalized generalized momentums and their integrals” (whenever integrable). Both of them can be obtained from the Lagrangian of the system. Based on some basic properties of underactuated systems as actuation/passivity of shape variables, integrability/non-integrability of appropriate normalized momentums, and presence/lack of input coupling; I managed to classify underactuated systems to 8 classes. Examples of these 8 classes cover almost all major applications in robotics, aerospace systems, and benchmark systems. For underactuated systems with nonholonomic velocity constrains and symmetry, we obtained normal forms as the cascade of the constraint equation and a reduced-order Lagrangian control system which is underactuated or fully-actuated. (Abstract shortened by UMI.) (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

Energy Pumping in Nonlinear Mechanical Oscillators: Part II—Resonance Capture

Abstract: We study energy pumping in an impulsively excited, two-degrees-of-freedom damped system with essential (nonlinearizable) nonlinearities by means of two analytical techniques. First, we transform the equations of motion using the action-angle variables of the underlying Hamiltonian system and bring them into the form where two-frequency averaging can be applied. We then show that energy pumping is due to resonance capture in the 1:1 resonance manifold of the system, and perform a perturbation analysis in an O (√e) neighborhood of this manifold in order to study the attracting region responsible for the resonance capture. The second method is based on the assumption of 1:1 internal resonance in the fast dynamics of the system, and utilizes complexification and averaging to develop analytical approximations to the nonlinear transient responses of the system in the energy pumping regime. The results compare favorably to numerical simulations. The practical implications of the energy pumping phenomenon are discussed.

Spectral compensation for flow cytometry: Visualization artifacts, limitations, and caveats

Abstract: Background: In multicolor flow cytometric analysis, compensation for spectral overlap is nearly always necessary. For the most part, such compensation has been relatively simple, producing the desired rectilinear distributions. However, in the realm of multicolor analysis, visualization of compensated often results in unexpected distributions, principally the appearance of a large number of events on the axis, and even more disconcerting, an inability to bring the extent of compensated data down to “autofluorescence” levels. Materials and Methods: A mathematical model of detector measurements with variable photon intensities, spillover parameters, measurement errors, and data storage characteristics was used to illustrate sources of apparent error in compensated data. Immunofluorescently stained cells were collected under conditions of limiting light collection and high spillover between detectors to confirm aspects of the model. Results: Photon-counting statistics contribute a nonlinear error to compensated parameters. Measurement errors and log-scale binning error contribute linear errors to compensated parameters. These errors are most apparent with the use of red or far-red fluorochromes (where the emitted light is at low intensity) and with large spillover between detectors. Such errors can lead to data visualization artifacts that can easily lead to incorrect conclusions about data, and account for the apparent “undercompensation” previously described for multicolor staining. Conclusions: There are inescapable errors arising from imperfect measurements, photon-counting statistics, and even data storage methods that contribute both linearly and nonlinearly to a “spreading” of a properly compensated autofluorescence distribution. This phenomenon precludes the use of “quadrant” statistics or gates to analyze affected data; it also precludes visual adjustment of compensation. Most importantly, it is impossible to properly compensate data using standard visual graphical interfaces (histograms or dot plots). Computer-assisted compensation is required, as well as careful gating and experimental design to determine the distinction between positive and negative events. Finally, the use of special staining controls that employ all reagents except for the one of interest (termed fluorescence minus one, or “FMO” controls) becomes necessary to accurately identify expressing cells in the fully stained sample. Cytometry 45: 194 ‐205, 2001. © 2001 Wiley-Liss, Inc.

Nonlinear and Robust Control of PDE Systems

Abstract: We present here because it will be so easy for you to access the internet service. As in this new era, much technology is sophistically offered by connecting to the internet. No any problems to face, just for this day, you can really keep in mind that the book is the best book for you. We offer the best here to read. After deciding how your feeling will be, you can enjoy to visit the link and get the book.

Theoretical Numerical Analysis: A Functional Analysis Framework

Abstract: Preface 1 Linear Spaces 2 Linear Operators on Normed Spaces 3 Approximation Theory 4 Nonlinear Equations and Their Solution by Iteration 5 Finite Difference Method 6 Sobolev Spaces 7 Variational Formulations of Elliptic Boundary Value Problems 8 The Galerkin Method and Its Variants 9 Finite Element Analysis 10 Elliptic Variational Inequalities and Their Numerical Approximations 11 Numerical Solution of Fredholm Integral Equations of the Second Kind 12 Boundary Integral Equations References Index.

Solitons in Field Theory and Nonlinear Analysis

Abstract: Preface * Primer of Field Theory * Sigma Models * Multiple Instantons and Characteristic Classes * Generalized Abelian Higgs Equations * Chern-Simons Systems: Abelian Case * Chern-Simons Systems: Non-Abelian Case * Electroweak Vortices * Dyons * Ordinary Differential Equations * Strings in Cosmology * Vortices and Antivortices * Born-Infeld Solutions * References * Bibliography * Index