Optimal Input Signals For Parameter Estimation

The aim of this book is to provide methods and algorithms for the optimization of input signals so as to estimate parameters in systems described by PDE’s as accurate as possible under given constraints. The optimality conditions have their background in the optimal experiment design theory for regression functions and in simple but useful results on the dependence of eigenvalues of partial differential operators on their parameters. Examples are provided that reveal sometimes intriguing geometry of spatiotemporal input signals and responses to them. An introduction to optimal experimental design for parameter estimation of regression functions is provided. The emphasis is on functions having a tensor product (Kronecker) structure that is compatible with eigenfunctions of many partial differential operators. New optimality conditions in the time domain and computational algorithms are derived for D-optimal input signals when parameters of ordinary differential equations are estimated. They are used as building blocks for constructing D-optimal spatio-temporal inputs for systems described by linear partial differential equations of the parabolic and hyperbolic types with constant parameters. Optimality conditions for spatially distributed signals are also obtained for equations of elliptic type in those cases where their eigenfunctions do not depend on unknown constant parameters. These conditions and the resulting algorithms are interesting in their own right and, moreover, they are second building blocks for optimality of spatio-temporal signals. A discussion of the generalizability and possible applications of the results obtained is presented.

Identification and System Parameter Estimation 1982 covers the proceedings of the Sixth International Federation of Automatic Control (IFAC) Symposium. The book also serves as a tribute to Dr. Naum S. Rajbman. The text covers issues concerning identification and estimation, such as increasing interrelationships between identification/estimation and other aspects of system theory, including control theory, signal processing, experimental design, numerical mathematics, pattern recognition, and information theory. The book also provides coverage regarding the application and problems faced by several engineering and scientific fields that use identification and estimation, such as biological systems, traffic control, geophysics, aeronautics, robotics, economics, and power systems. Researchers from all scientific fields will find this book a great reference material, since it presents topics that concern various disciplines.

This book is a self-contained text devoted to the numerical determination of optimal inputs for system identification. It presents the current state of optimal inputs with extensive background material on optimization and system identification. The field of optimal inputs has been an area of considerable research recently with important advances by R. Mehra, G. c. Goodwin, M. Aoki, and N. E. Nahi, to name just a few eminent in vestigators. The authors' interest in optimal inputs first developed when F. E. Yates, an eminent physiologist, expressed the need for optimal or preferred inputs to estimate physiological parameters. The text assumes no previous knowledge of optimal control theory, numerical methods for solving two-point boundary-value problems, or system identification. As such it should be of interest to students as well as researchers in control engineering, computer science, biomedical en gineering, operations research, and economics. In addition the sections on beam theory should be of special interest to mechanical and civil en gineers and the sections on eigenvalues should be of interest to numerical analysts. The authors have tried to present a balanced viewpoint; however, primary emphasis is on those methods in which they have had first-hand experience. Their work has been influenced by many authors. Special acknowledgment should go to those listed above as well as R. Bellman, A. Miele, G. A. Bekey, and A. P. Sage. The book can be used for a two-semester course in control theory, system identification, and optimal inputs.

Trends and Progress in System Identification is a three-part book that focuses on model considerations, identification methods, and experimental conditions involved in system identification. Organized into 10 chapters, this book begins with a discussion of model method in system identification, citing four examples differing on the nature of the models involved, the nature of the fields, and their goals. Subsequent chapters describe the most important aspects of model theory; the ""classical"" methods and time series estimation; application of least squares and related techniques for the estimation of dynamic system parameters; the maximum likelihood and error prediction methods; and the modern development of statistical methods. Non-parametric approaches, identification of nonlinear systems by piecewise approximation, and the minimax identification are then explained. Other chapters explore the Bayesian approach to system identification; choice of input signals; and choice and effect of different feedback configurations in system identification. This book will be useful for control engineers, system scientists, biologists, and members of other disciplines dealing withdynamical relations.

Dynamic System Identification: Experiment Design and Data Analysis

This book focuses on the analysis and design of advanced techniques for on-line automatic computational monitoring of pipelines and pipe networks. It discusses how to improve the systems’ security considering mathematical models of the flow, historical flow rate and pressure data, with the main goal of reducing the number of sensors installed along a pipeline. The techniques presented in the book have been implemented in digital systems to enhance the abilities of the pipeline network’s operators in recognizing anomalies. A real leak scenario in a Mexican water pipeline is used to illustrate the benefits of these techniques in locating the position of a leak. Intended for an interdisciplinary audience, the book addresses researchers and professionals in the areas of mechanical, civil and control engineering. It covers topics on fluid mechanics, instrumentation, automatic control, signal processing, computing, construction and diagnostic technologies.

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

This book provides a comprehensive treatment of the development and present state of the theory of sensitivity of dynamic systems. It is intended as a textbook and reference for researchers and scientists in electrical engineering, control and information theory as well as for mathematicians. The extensive and structured bibliography provides an overview of the literature in the field and points out directions for further research.