Identification of Dynamical Systems with Small Noise PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Identification of Dynamical Systems with Small Noise PDF full book. Access full book title Identification of Dynamical Systems with Small Noise by Yury A. Kutoyants. Download full books in PDF and EPUB format.
Author: Yury A. Kutoyants
Publisher:
ISBN: 9789401110211
Category :
Languages : en
Pages : 314
Get Book
Book Description
Author: Yury A. Kutoyants
Publisher:
ISBN: 9789401110211
Category :
Languages : en
Pages : 314
Get Book
Book Description
Author: Yury A. Kutoyants
Publisher: Springer Science & Business Media
ISBN: 9401110204
Category : Mathematics
Languages : en
Pages : 308
Get Book
Book Description
Small noise is a good noise. In this work, we are interested in the problems of estimation theory concerned with observations of the diffusion-type process Xo = Xo, 0 ~ t ~ T, (0. 1) where W is a standard Wiener process and St(') is some nonanticipative smooth t function. By the observations X = {X , 0 ~ t ~ T} of this process, we will solve some t of the problems of identification, both parametric and nonparametric. If the trend S(-) is known up to the value of some finite-dimensional parameter St(X) = St((}, X), where (} E e c Rd , then we have a parametric case. The nonparametric problems arise if we know only the degree of smoothness of the function St(X), 0 ~ t ~ T with respect to time t. It is supposed that the diffusion coefficient c is always known. In the parametric case, we describe the asymptotical properties of maximum likelihood (MLE), Bayes (BE) and minimum distance (MDE) estimators as c --+ 0 and in the nonparametric situation, we investigate some kernel-type estimators of unknown functions (say, StO,O ~ t ~ T). The asymptotic in such problems of estimation for this scheme of observations was usually considered as T --+ 00 , because this limit is a direct analog to the traditional limit (n --+ 00) in the classical mathematical statistics of i. i. d. observations. The limit c --+ 0 in (0. 1) is interesting for the following reasons.
Author: Frank Moss
Publisher: Cambridge University Press
ISBN: 0521352290
Category : Mathematics
Languages : en
Pages : 410
Get Book
Book Description
A specially written review of all areas of noise and nonlinear in natural environments.
Author: Arunabha Bagchi
Publisher:
ISBN:
Category : Electronic noise
Languages : en
Pages : 82
Get Book
Book Description
The present dissertation is a study of identifying parameters of a continuous-time dynamical system with noisy observation and with or without noise in the state of the system. In identifying parameters of a continuous-time dynamical system, the difficulty arises when the observation noise covariance is unknown. The present paper solves this problem in the case of a linear time invariant system with white noise affecting additively both the state and the observation. Likelihood functional cannot be obtained when the observation noise covariance is unknown. A similar procedure, however, works and the estimates are obtained by finding roots of an appropriate functional. It is shown that the estimates obtained are weakly consistent. In the special case of no noise in the state, it is further shown that similar procedure yields estimates that are strongly consistent. Consistency is proved under certain sufficient condition called the 'Identifiability Condition'. This condition is studied in detail and computational algorithm for determining the estimates is discussed.
Author: Rolf Isermann
Publisher: Springer
ISBN: 9783642422676
Category : Technology & Engineering
Languages : en
Pages : 0
Get Book
Book Description
Precise dynamic models of processes are required for many applications, ranging from control engineering to the natural sciences and economics. Frequently, such precise models cannot be derived using theoretical considerations alone. Therefore, they must be determined experimentally. This book treats the determination of dynamic models based on measurements taken at the process, which is known as system identification or process identification. Both offline and online methods are presented, i.e. methods that post-process the measured data as well as methods that provide models during the measurement. The book is theory-oriented and application-oriented and most methods covered have been used successfully in practical applications for many different processes. Illustrative examples in this book with real measured data range from hydraulic and electric actuators up to combustion engines. Real experimental data is also provided on the Springer webpage, allowing readers to gather their first experience with the methods presented in this book. Among others, the book covers the following subjects: determination of the non-parametric frequency response, (fast) Fourier transform, correlation analysis, parameter estimation with a focus on the method of Least Squares and modifications, identification of time-variant processes, identification in closed-loop, identification of continuous time processes, and subspace methods. Some methods for nonlinear system identification are also considered, such as the Extended Kalman filter and neural networks. The different methods are compared by using a real three-mass oscillator process, a model of a drive train. For many identification methods, hints for the practical implementation and application are provided. The book is intended to meet the needs of students and practicing engineers working in research and development, design and manufacturing.
Author: Odell R. Reynolds
Publisher:
ISBN: 9781423573463
Category : Differentiable dynamical systems
Languages : en
Pages : 155
Get Book
Book Description
Sensor noise is an unavoidable fact of life when it comes to measurements on physical systems, as is the case in feedback control. Therefore, it must be properly addressed during dynamic system identification. In this work, a novel approach is developed toward the treatment of measurement noise in dynamical systems. This approach hinges on proper stochastic modeling, and it can be adapted easily to many different scenarios, where it yields consistently good parameter estimates. The Generalized Minimum Variance algorithm developed and used in this work is based on the theory behind the minimum variance identification process, and the estimate produced is a fixed point of a mapping based on the minimum variance solution. Additionally, the algorithm yields an accurate prediction of the estimation error. This algorithm is applied to many different noise models associated with three basic identification problems. First, continuous-time systems are identified using frequency domain measurements. Next, a discrete-time plant is identified using discrete-time measurements. Finally, the physical parameters of a continuous-time plant are identified using sampled measurements of the continuous-time input and output. Validation of the estimates is performed correctly, and the results are compared with other, more common, identification algorithms.
Author: Nils Berglund
Publisher: Springer
ISBN: 9781849965477
Category : Mathematics
Languages : en
Pages : 276
Get Book
Book Description
Stochastic Differential Equations have become increasingly important in modelling complex systems in physics, chemistry, biology, climatology and other fields. This book examines and provides systems for practitioners to use, and provides a number of case studies to show how they can work in practice.
Author: Shankar Sastry
Publisher:
ISBN:
Category : Electric circuits, Nonlinear
Languages : en
Pages : 12
Get Book
Book Description
The dynamics of a large class of non-linear systems are described implicitly, i.e., as a combination of algebraic and differential equations. These dynamics admit of jump behavior. We extend the deterministic theory to a stochastic theory since: (1) the deterministic theory is restrictive; (2) the macroscopic deterministic description of dynamics frequently arises from an aggregation of microscopically fluctuating dynamics; and (3) to robustify the deterministic one in the limit that the intensity of the additive white noise tends to zero. We study the modelling issues involved in applying this stochastic theory to the study of the noise behavior of a multivibrator circuit, discuss the limitations of our methodology for certain classes of systems and present a modified approach for the analysis of sample functions of noisy non-linear circuits.
Author: Walter Henry Kroy
Publisher:
ISBN:
Category : Random noise theory
Languages : en
Pages : 182
Get Book
Book Description
Author: C. Heij
Publisher:
ISBN:
Category : Differentiable dynamical systems
Languages : en
Pages : 308
Get Book
Book Description
