Uncertain Information and Linear Systems

Uncertain Information and Linear Systems PDF

Author: Tofigh Allahviranloo

Publisher: Springer Nature

Published: 2019-09-23

Total Pages: 257

ISBN-13: 3030313247

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This book identifies the important uncertainties to use in real-world problem modeling. Having information about several types of ambiguities, vagueness, and uncertainties is vital in modeling problems that involve linguistic variables, parameters, and word computing. Today, since most of our real-world problems are related to decision-making at the right time, we need to apply intelligent decision science. Clearly, in order to have an appropriate and flexible mathematical model, every intelligent system requires real data on our environment. Presenting problems that can be represented using mathematical models to create a system of linear equations, this book discusses the latest insights into uncertain information.

Uncertain Information and Linear Systems

Uncertain Information and Linear Systems PDF

Author: Tofigh Allahviranloo

Publisher:

Published: 2020

Total Pages: 257

ISBN-13: 9783030313258

DOWNLOAD EBOOK →

This book identifies the important uncertainties to use in real-world problem modeling. Having information about several types of ambiguities, vagueness, and uncertainties is vital in modeling problems that involve linguistic variables, parameters, and word computing. Today, since most of our real-world problems are related to decision-making at the right time, we need to apply intelligent decision science. Clearly, in order to have an appropriate and flexible mathematical model, every intelligent system requires real data on our environment. Presenting problems that can be represented using mathematical models to create a system of linear equations, this book discusses the latest insights into uncertain information.

Robust Control of Uncertain Dynamic Systems

Robust Control of Uncertain Dynamic Systems PDF

Author: Rama K. Yedavalli

Publisher: Springer Science & Business Media

Published: 2013-12-05

Total Pages: 217

ISBN-13: 1461491320

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This textbook aims to provide a clear understanding of the various tools of analysis and design for robust stability and performance of uncertain dynamic systems. In model-based control design and analysis, mathematical models can never completely represent the “real world” system that is being modeled, and thus it is imperative to incorporate and accommodate a level of uncertainty into the models. This book directly addresses these issues from a deterministic uncertainty viewpoint and focuses on the interval parameter characterization of uncertain systems. Various tools of analysis and design are presented in a consolidated manner. This volume fills a current gap in published works by explicitly addressing the subject of control of dynamic systems from linear state space framework, namely using a time-domain, matrix-theory based approach. This book also: Presents and formulates the robustness problem in a linear state space model framework. Illustrates various systems level methodologies with examples and applications drawn from aerospace, electrical and mechanical engineering. Provides connections between lyapunov-based matrix approach and the transfer function based polynomial approaches. Robust Control of Uncertain Dynamic Systems: A Linear State Space Approach is an ideal book for first year graduate students taking a course in robust control in aerospace, mechanical, or electrical engineering.

Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data

Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data PDF

Author: Oleksandr Nakonechnyi

Publisher: CRC Press

Published: 2022-09-01

Total Pages: 233

ISBN-13: 1000795136

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This monograph is devoted to the construction of optimal estimates of values of linear functionals on solutions to Cauchy and two-point boundary value problems for systems of linear first-order ordinary differential equations, from indirect observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing the minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax or guaranteed estimates. It is established that these estimates are expressed explicitly via solutions to some uniquely solvable linear systems of ordinary differential equations of the special type. The authors apply these results for obtaining the optimal estimates of solutions from indirect noisy observations. Similar estimation problems for solutions of boundary value problems for linear differential equations of order n with general boundary conditions are considered. The authors also elaborate guaranteed estimation methods under incomplete data of unknown right-hand sides of equations and boundary data and obtain representations for the corresponding guaranteed estimates. In all the cases estimation errors are determined.

Uncertain Information and Linear Systems

Uncertain Information and Linear Systems PDF

Author: Tofigh Allahviranloo

Publisher: Springer

Published: 2020-10-07

Total Pages: 257

ISBN-13: 9783030313265

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This book identifies the important uncertainties to use in real-world problem modeling. Having information about several types of ambiguities, vagueness, and uncertainties is vital in modeling problems that involve linguistic variables, parameters, and word computing. Today, since most of our real-world problems are related to decision-making at the right time, we need to apply intelligent decision science. Clearly, in order to have an appropriate and flexible mathematical model, every intelligent system requires real data on our environment. Presenting problems that can be represented using mathematical models to create a system of linear equations, this book discusses the latest insights into uncertain information.

Control of Uncertain Systems with Bounded Inputs

Control of Uncertain Systems with Bounded Inputs PDF

Author: Sophie Tarbouriech

Publisher: Springer

Published: 2014-03-12

Total Pages: 186

ISBN-13: 9783662176528

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In practical control problems, many constraints have to be handled in order to design controllers which operate in a real environment. By combining results on robust control and saturating control, this book attempts to provide positive help for practical situations and, as one of the first books to merge the two control fields, it should generate considerable interest in scientific/acad emic circles. The ten chapters, which deal with stabilization and control of both linear and nonlinear systems, are each independent in their approach - some deal purely with theoretical results whilst others concentrate on ways in which the theory can be applied. The book's unity is secured by the desire to formulate control design requirements through constraints on input and model uncertainty description.

Estimators for Uncertain Dynamic Systems

Estimators for Uncertain Dynamic Systems PDF

Author: A.I. Matasov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 428

ISBN-13: 9401153221

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When solving the control and design problems in aerospace and naval engi neering, energetics, economics, biology, etc., we need to know the state of investigated dynamic processes. The presence of inherent uncertainties in the description of these processes and of noises in measurement devices leads to the necessity to construct the estimators for corresponding dynamic systems. The estimators recover the required information about system state from mea surement data. An attempt to solve the estimation problems in an optimal way results in the formulation of different variational problems. The type and complexity of these variational problems depend on the process model, the model of uncertainties, and the estimation performance criterion. A solution of variational problem determines an optimal estimator. Howerever, there exist at least two reasons why we use nonoptimal esti mators. The first reason is that the numerical algorithms for solving the corresponding variational problems can be very difficult for numerical imple mentation. For example, the dimension of these algorithms can be very high.

State Observers for Linear Systems with Uncertainty

State Observers for Linear Systems with Uncertainty PDF

Author: S. K. Korovin

Publisher: Walter de Gruyter

Published: 2009

Total Pages: 253

ISBN-13: 3110218127

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This book presents the basic concepts and recent developments of linear control problems with perturbations. The presentation concerns both continuous and discrete dynamical systems. It is self-contained and illustrated by numerous examples. From the contents: Notion of state observers Observability Observers of full-phase vectors for fully determined linear systems Functional observers for fully determined linear systems Asymptotic observers for linear systems with uncertainty Observers for bilinear and discrete systems

State Observers for Linear Systems with Uncertainty

State Observers for Linear Systems with Uncertainty PDF

Author: Sergey K. Korovin

Publisher: Walter de Gruyter

Published: 2009-09-04

Total Pages: 253

ISBN-13: 3110218135

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This book presents the basic concepts and recent developments of linear control problems with perturbations. The presentation concerns both continuous and discrete dynamical systems. It is self-contained and illustrated by numerous examples. From the contents: Notion of state observers Observability Observers of full-phase vectors for fully determined linear systems Functional observers for fully determined linear systems Asymptotic observers for linear systems with uncertainty Observers for bilinear and discrete systems

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