Download or read book Estimation for Bilinear Stochastic Systems written by Alan S. Willsky and published by . This book was released on 1974 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modeling and Estimation with Bilinear Stochastic Systems written by Roger W. Brockett and published by . This book was released on 1979 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Estimation and Analysis of Nonlinear Stochastic Systems written by Steven Irl Marcus and published by . This book was released on 1975 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: The algebraic and geometric structure of certain classes of nonlinear stochastic systems is exploited in order to obtain useful stability and estimation results. First, the class of bilinear stochastic systems (or linear systems with multiplicative noise) is discussed. The stochastic stability of bilinear systems driven by colored noise is considered; in the case that the system evolves on a solvable Lie group, necessary and sufficient conditions for stochastic stability are derived. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups are also discussed. The study of estimation problems involving bilinear systems is motivated by several practical applications involving rotational processes in three dimensions. Two classes of estimation problems are considered. First it is proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. Finally, the theory of harmonic analysis is used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces.
Download or read book On the State and Parameter Estimation of Stochastic Bilinear Systems written by Ali Shadman-Valavi and published by . This book was released on 1978 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis written by György Terdik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of the present work is a systematic statistical analysis of bilinear processes in the frequency domain. The first two chapters are devoted to the basic theory of nonlinear functions of stationary Gaussian processes, Hermite polynomials, cumulants and higher order spectra, multiple Wiener-Itô integrals and finally chaotic Wiener-Itô spectral representation of subordinated processes. There are two chapters for general nonlinear time series problems.
Download or read book Bilinear Stochastic Processes and Time Series written by Zhigiang Tang and published by . This book was released on 1987 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: In engineering, biology, ecology, medicine, economics and social science, some processes are essentially bilinear, and some could be approximated accurately by bilinear processes under certain conditions. In this thesis the bilinear stochastic process and bilinear time series are discussed. Bilinear models essentially are nonlinear; the superposition rule is not valid. A useful property, which characterizes the bilinear feature among the nonlinear ones, is emphasized. The solutions of deterministic bilinear systems and bilinear stochastic processes are given. The direct method uses the Lie algebraic structure. For bilinear stochastic processes, the decomposition to a cascade form is a generalization of the Volterra-series expansion. Because a correction term exists in bilinear stochastic differential equations, the decomposition has two different forms; both of them are convergent. The lth -order stationarity and asymptotic stationarity of bilinear stochastic processes and time series are well defined, and the conditions on parameters for lth -order stationarity are derived. Affine bilinear models in time-series form are shown to be more general than bilinear models, and more readily fit certain data. A special high-order scalar affine bilinear time-series model can be transferred to a first-order, vector, affine, bilinear model, but need higher dimension than the linear ARMA model. For first-order affine bilinear time series two possible methods of parameter estimation are presented. The moment method uses the relationships between the parameters, and the second and third-moments to estimate parameters. The inverse method uses the output data to estimate the input, which is compared with the standard white Gaussian random sequence, and the method chooses the parameters of the model to make certain criterion optimal. For the general non-Gaussian time series an identification procedure using the inverse method is proposed. Some examples of analysis and parameter estimation of bilinear models are provided.
Download or read book Analysis of Bilinear Stochastic Systems written by Alan S. Willsky and published by . This book was released on 1974 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Energy Estimates and Model Order Reduction for Stochastic Bilinear Systems written by Martin Redmann and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we investigate a large-scale stochastic system with bilinear drift and linear diffusion term. Such high dimensional systems appear for example when discretizing a stochastic partial differential equations in space. We study a particular model order reduction technique called balanced truncation (BT) to reduce the order of spatially-discretized systems and hence reduce computational complexity. We introduce suitable Gramians to the system and prove energy estimates that can be used to identify states which contribute only very little to the system dynamics. When BT is applied the reduced system is obtained by removing these states from the original system. The main contribution of this paper is an L2-error bound for BT for stochastic bilinear systems. This result is new even for deterministic bilinear equations. In order to achieve it, we develop a new technique which is not available in the literature so far.
Download or read book Estimation for Certain Nonlinear Stochastic Systems written by Steven I. Marcus and published by . This book was released on 1975 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently a great deal of attention has gone into the study of classes of deterministic nonlinear systems described either by bilinear differential state equations or Volterra series input-output relations. In addition, a number of results have been obtained for the stochastic analogs of these systems. In this note the authors describe a class of systems for which they can construct optimal finite-dimensional nonlinear filters. A complete study of this problem is given in another paper.
Download or read book Discrete time Stochastic Systems written by Torsten Söderström and published by Springer Science & Business Media. This book was released on 2002-07-26 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive introduction to the estimation and control of dynamic stochastic systems provides complete derivations of key results. The second edition includes improved and updated material, and a new presentation of polynomial control and new derivation of linear-quadratic-Gaussian control.
Download or read book Stochastic Systems and State Estimation written by Terrence P. McGarty and published by Wiley-Interscience. This book was released on 1974 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modelling and Application of Stochastic Processes written by Uday B. Desai and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of modelling and application of stochastic processes is too vast to be exhausted in a single volume. In this book, attention is focused on a small subset of this vast subject. The primary emphasis is on realization and approximation of stochastic systems. Recently there has been considerable interest in the stochastic realization problem, and hence, an attempt has been made here to collect in one place some of the more recent approaches and algorithms for solving the stochastic realiza tion problem. Various different approaches for realizing linear minimum-phase systems, linear nonminimum-phase systems, and bilinear systems are presented. These approaches range from time-domain methods to spectral-domain methods. An overview of the chapter contents briefly describes these approaches. Also, in most of these chapters special attention is given to the problem of developing numerically ef ficient algorithms for obtaining reduced-order (approximate) stochastic realizations. On the application side, chapters on use of Markov random fields for modelling and analyzing image signals, use of complementary models for the smoothing problem with missing data, and nonlinear estimation are included. Chapter 1 by Klein and Dickinson develops the nested orthogonal state space realization for ARMA processes. As suggested by the name, nested orthogonal realizations possess two key properties; (i) the state variables are orthogonal, and (ii) the system matrices for the (n + l)st order realization contain as their "upper" n-th order blocks the system matrices from the n-th order realization (nesting property).
Download or read book Optimization and Control of Bilinear Systems written by Panos M. Pardalos and published by Springer Science & Business Media. This book was released on 2010-03-14 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers developments in bilinear systems theory Focuses on the control of open physical processes functioning in a non-equilibrium mode Emphasis is on three primary disciplines: modern differential geometry, control of dynamical systems, and optimization theory Includes applications to the fields of quantum and molecular computing, control of physical processes, biophysics, superconducting magnetism, and physical information science
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1989 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recursive Estimation and Control for Stochastic Systems written by Hanfu Chen and published by John Wiley & Sons. This book was released on 1985 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained reference for statisticians and engineers in system and control theory, analyzes the effect of convergent recursive estimation algorithms and stochastic approximation on the dependent noise case and the classic independent case. It discusses control and adaptive control problems related to recursive estimation, and introduces the combined probabilistic and differential equation method of data analysis.
Download or read book Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis written by Gyorgy Terdik and published by . This book was released on 1999-07-30 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of the present work is a systematic statistical analysis of bilinear processes in the frequency domain. The first two chapters are devoted to the basic theory of nonlinear functions of stationary Gaussian processes, Hermite polynomials, cumulants and higher order spectra, multiple Wiener-ItA integrals and finally chaotic Wiener-ItA spectral representation of subordinated processes. There are two chapters for general nonlinear time series problems.
Download or read book Variable Structure Systems with Application to Economics and Biology written by R. R. Mohler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings of the Second US-Italy Seminar on Variable Structure Systems is published in this volume. Like the first seminar, its conception evolved from common research interests on bilinear systems at the Istituto di Automatica of Rome University and at the Electrical and Computer Engineering Department of Oregon State University. Again, the seminar was focused on variable structure systems in general. In this case, however, emphasis is given to applications in biology and economics along with theoretical investi gations which are so necessary to establish a unified theory and to motivate further developments in these applications of social significance. By bringing together the talents of social and biological scientists with those of engineers and mathematicians from throughout Italy and the United States, the seminar was intended to yield a cross-pollination of significant results and a base for more meaningful future research. The editors are encouraged by the progress, with which they hope the reader will agree, is made in this direction. No pretense is made, however, that completely satisfactory integration of theore tical results and applications has been accomplished at this time. Among the more important conclusions which have resulted from this seminar are that bilinear and more general variable structure models arise in a natural manner from basic principles for certain biological and economic processes.
