Download or read book Stability and Control Analysis of Stochastic Bilinear Systems written by Philip L. Wing and published by . This book was released on 1994 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Bilinear Systems written by G. Koch and published by . This book was released on 1972 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Identification of Discrete time Stochastic Bilinear Systems written by C. S. Kubrusly and published by . This book was released on 1980 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dual Control of Stochastic Bilinear Systems written by Verlin Gene Russon and published by . This book was released on 1996 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 1977 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bilinear systems due to their variable structure properties offer more versatility in modelling of nonlinear processes than linear systems. The state estimation problem for a continuous bilinear system with a continuous observation model is studied and the results are extended to the case where the observations are of a discrete nature. It is shown that the optimal filter is of infinite dimension and a suboptimal solution based on the use of the conditional best estimate of the state in the multiplicative term, rather than the actual state, is proposed. The filter dimension is reduced to two and the mean and the variance equations are provided. A recursive maximum likelihood procedure operating on the proposed filter is used for the parameter identification. Both the likelihood functional and the gradient equations are provided. Computation of the gradient is dependent on computing the partial derivatives of the proposed filter equations with respect to the parameters. Simulation of the sample functions of bilinear systems using closed form solutions is discussed and a complete solution for the scalar case is provided. Parametric conditions for obtaining closed form solutions to the vector cases are supplied. A number of numerical examples illustrating the feasibility and performance of the proposed filter and parameter identification schemes are included. Both scalar and multivariable computational examples are considered.
Download or read book On discrete stochastic bilinear systems stability written by C. S. Kubrusly and published by . This book was released on 1984 with total page 39 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 Identification of multiplicative parameters in stochastic bilinear systems written by C. S. Kubrusly and published by . This book was released on 1983 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stability of bilinear systems in a stochastic environment written by and published by . This book was released on 1906 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: É considerado o problema da estabilidade de sistemas dinâmicos bilineares em ambiente estocástico. Após a apresentação de uma coletânea de resultados já existentes, são propostas novas condições de estabilidade para sistemas discretos utilizando o método direto de Lyapunov. Tais resultados são comparados com os já existentes.
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 Stochastic Optimal Control of Single Input Discrete Bilinear Systems written by K. N. Swamy and published by . This book was released on 1974 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal control of a class of single-input, discrete, stochastic bilinear systems is discussed. The control is assumed to be unbounded and the cost functional quadratic in state. A closed-form solution has been obtained for the stochastic control problem with perfect state observation, and with additive and multiplicative noise in the state equation. It is demonstrated that the presence of noise considerably simplifies the analysis compared to the deterministic case by virtue of integration over certain sets of measure zero. When the state equation has additive noise and the observation equation is noisy, a perturbation controller is obtained to minimize the instantaneous mean-square departure from the nominal, which is chosen to be the solution to the deterministic optimal control problem.
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 On Stochastic Modelling for Discrete Bilinear Systems in Hilbert Space written by C. S. Kubrusly and published by . This book was released on 1987 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Control of a Stochastic Bilinear System written by O. L. R. Jacobs and published by . This book was released on 1976 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Bilinear Control Systems written by David Elliott and published by Springer Science & Business Media. This book was released on 2009-09-01 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical theory of control became a ?eld of study half a century ago in attempts to clarify and organize some challenging practical problems and the methods used to solve them. It is known for the breadth of the mathematics it uses and its cross-disciplinary vigor. Its literature, which can befoundinSection93ofMathematicalReviews,wasatonetimedominatedby the theory of linear control systems, which mathematically are described by linear di?erential equations forced by additive control inputs. That theory led to well-regarded numerical and symbolic computational packages for control analysis and design. Nonlinear control problems are also important; in these either the - derlying dynamical system is nonlinear or the controls are applied in a n- additiveway.Thelastfourdecadeshaveseenthedevelopmentoftheoretical work on nonlinear control problems based on di?erential manifold theory, nonlinear analysis, and several other mathematical disciplines. Many of the problems that had been solved in linear control theory, plus others that are new and distinctly nonlinear, have been addressed; some resulting general de?nitions and theorems are adapted in this book to the bilinear case.
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).
