Modelling and Parameter Estimation of Dynamic Systems

Modelling and Parameter Estimation of Dynamic Systems
Author: J.R. Raol
Publisher: IET
Total Pages: 405
Release: 2004-08-13
Genre: Mathematics
ISBN: 0863413633

This book presents a detailed examination of the estimation techniques and modeling problems. The theory is furnished with several illustrations and computer programs to promote better understanding of system modeling and parameter estimation.

Numerical Data Fitting in Dynamical Systems

Numerical Data Fitting in Dynamical Systems
Author: Klaus Schittkowski
Publisher: Springer Science & Business Media
Total Pages: 416
Release: 2002-12-31
Genre: Computers
ISBN: 9781402010798

Real life phenomena in engineering, natural, or medical sciences are often described by a mathematical model with the goal to analyze numerically the behaviour of the system. Advantages of mathematical models are their cheap availability, the possibility of studying extreme situations that cannot be handled by experiments, or of simulating real systems during the design phase before constructing a first prototype. Moreover, they serve to verify decisions, to avoid expensive and time consuming experimental tests, to analyze, understand, and explain the behaviour of systems, or to optimize design and production. As soon as a mathematical model contains differential dependencies from an additional parameter, typically the time, we call it a dynamical model. There are two key questions always arising in a practical environment: 1 Is the mathematical model correct? 2 How can I quantify model parameters that cannot be measured directly? In principle, both questions are easily answered as soon as some experimental data are available. The idea is to compare measured data with predicted model function values and to minimize the differences over the whole parameter space. We have to reject a model if we are unable to find a reasonably accurate fit. To summarize, parameter estimation or data fitting, respectively, is extremely important in all practical situations, where a mathematical model and corresponding experimental data are available to describe the behaviour of a dynamical system.

Identification of Dynamic Systems

Identification of Dynamic Systems
Author: Rolf Isermann
Publisher: Springer
Total Pages: 705
Release: 2011-04-08
Genre: Technology & Engineering
ISBN: 9783540871552

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.

Bounding Approaches to System Identification

Bounding Approaches to System Identification
Author: M. Milanese
Publisher: Springer Science & Business Media
Total Pages: 569
Release: 2013-06-29
Genre: Science
ISBN: 1475795459

In response to the growing interest in bounding error approaches, the editors of this volume offer the first collection of papers to describe advances in techniques and applications of bounding of the parameters, or state variables, of uncertain dynamical systems. Contributors explore the application of the bounding approach as an alternative to the probabilistic analysis of such systems, relating its importance to robust control-system design.

Estimators for Uncertain Dynamic Systems

Estimators for Uncertain Dynamic Systems
Author: A.I. Matasov
Publisher: Springer Science & Business Media
Total Pages: 428
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 9401153221

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.

Optimization and Dynamical Systems

Optimization and Dynamical Systems
Author: Uwe Helmke
Publisher: Springer Science & Business Media
Total Pages: 409
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 1447134672

This work is aimed at mathematics and engineering graduate students and researchers in the areas of optimization, dynamical systems, control sys tems, signal processing, and linear algebra. The motivation for the results developed here arises from advanced engineering applications and the emer gence of highly parallel computing machines for tackling such applications. The problems solved are those of linear algebra and linear systems the ory, and include such topics as diagonalizing a symmetric matrix, singular value decomposition, balanced realizations, linear programming, sensitivity minimization, and eigenvalue assignment by feedback control. The tools are those, not only of linear algebra and systems theory, but also of differential geometry. The problems are solved via dynamical sys tems implementation, either in continuous time or discrete time , which is ideally suited to distributed parallel processing. The problems tackled are indirectly or directly concerned with dynamical systems themselves, so there is feedback in that dynamical systems are used to understand and optimize dynamical systems. One key to the new research results has been the recent discovery of rather deep existence and uniqueness results for the solution of certain matrix least squares optimization problems in geomet ric invariant theory. These problems, as well as many other optimization problems arising in linear algebra and systems theory, do not always admit solutions which can be found by algebraic methods.

Optimal Estimation of Dynamic Systems

Optimal Estimation of Dynamic Systems
Author: John L. Crassidis
Publisher: CRC Press
Total Pages: 606
Release: 2004-04-27
Genre: Mathematics
ISBN: 1135439273

Most newcomers to the field of linear stochastic estimation go through a difficult process in understanding and applying the theory.This book minimizes the process while introducing the fundamentals of optimal estimation. Optimal Estimation of Dynamic Systems explores topics that are important in the field of control where the signals received are used to determine highly sensitive processes such as the flight path of a plane, the orbit of a space vehicle, or the control of a machine. The authors use dynamic models from mechanical and aerospace engineering to provide immediate results of estimation concepts with a minimal reliance on mathematical skills. The book documents the development of the central concepts and methods of optimal estimation theory in a manner accessible to engineering students, applied mathematicians, and practicing engineers. It includes rigorous theoretial derivations and a significant amount of qualitiative discussion and judgements. It also presents prototype algorithms, giving detail and discussion to stimulate development of efficient computer programs and intelligent use of them. This book illustrates the application of optimal estimation methods to problems with varying degrees of analytical and numercial difficulty. It compares various approaches to help develop a feel for the absolute and relative utility of different methods, and provides many applications in the fields of aerospace, mechanical, and electrical engineering.

Dynamic Estimation and Control of Power Systems

Dynamic Estimation and Control of Power Systems
Author: Abhinav Kumar Singh
Publisher: Academic Press
Total Pages: 264
Release: 2018-10-04
Genre: Technology & Engineering
ISBN: 0128140062

Dynamic estimation and control is a fast growing and widely researched field of study that lays the foundation for a new generation of technologies that can dynamically, adaptively and automatically stabilize power systems. This book provides a comprehensive introduction to research techniques for real-time estimation and control of power systems. Dynamic Estimation and Control of Power Systems coherently and concisely explains key concepts in a step by step manner, beginning with the fundamentals and building up to the latest developments of the field. Each chapter features examples to illustrate the main ideas, and effective research tools are presented for signal processing-based estimation of the dynamic states and subsequent control, both centralized and decentralized, as well as linear and nonlinear. Detailed mathematical proofs are included for readers who desire a deeper technical understanding of the methods. This book is an ideal research reference for engineers and researchers working on monitoring and stability of modern grids, as well as postgraduate students studying these topics. It serves to deliver a clear understanding of the tools needed for estimation and control, while also acting as a basis for readers to further develop new and improved approaches in their own research. - Offers the first concise, single resource on dynamic estimation and control of power systems - Provides both an understanding of estimation and control concepts and a comparison of results - Includes detailed case-studies, including MATLAB codes, to explain and demonstrate the concepts presented

Handbook of Statistical Systems Biology

Handbook of Statistical Systems Biology
Author: Michael Stumpf
Publisher: John Wiley & Sons
Total Pages: 624
Release: 2011-09-09
Genre: Science
ISBN: 1119952042

Systems Biology is now entering a mature phase in which the key issues are characterising uncertainty and stochastic effects in mathematical models of biological systems. The area is moving towards a full statistical analysis and probabilistic reasoning over the inferences that can be made from mathematical models. This handbook presents a comprehensive guide to the discipline for practitioners and educators, in providing a full and detailed treatment of these important and emerging subjects. Leading experts in systems biology and statistics have come together to provide insight in to the major ideas in the field, and in particular methods of specifying and fitting models, and estimating the unknown parameters. This book: Provides a comprehensive account of inference techniques in systems biology. Introduces classical and Bayesian statistical methods for complex systems. Explores networks and graphical modeling as well as a wide range of statistical models for dynamical systems. Discusses various applications for statistical systems biology, such as gene regulation and signal transduction. Features statistical data analysis on numerous technologies, including metabolic and transcriptomic technologies. Presents an in-depth presentation of reverse engineering approaches. Provides colour illustrations to explain key concepts. This handbook will be a key resource for researchers practising systems biology, and those requiring a comprehensive overview of this important field.

Intelligent Algorithms for Analysis and Control of Dynamical Systems

Intelligent Algorithms for Analysis and Control of Dynamical Systems
Author: Rajesh Kumar
Publisher: Springer Nature
Total Pages: 202
Release: 2020-10-31
Genre: Technology & Engineering
ISBN: 9811580456

This book explores various intelligent algorithms including evolutionary algorithms, swarm intelligence-based algorithms for analysis and control of dynamical systems. Both single-input–single-output (SISO) and multi-input–multi-output (MIMO) systems are explored for analysis and control purposes. The applications of intelligent algorithm vary from approximation to optimal control design. The applications of intelligent algorithms not only improve understanding of a dynamical system but also enhance the control efficacy. The intelligent algorithms are now readily applied to all fields of control including linear control, nonlinear control, digital control, optimal control, etc. The book also discusses the main benefits attained due to the application of algorithms to analyze and control.