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This book is all about finite wordlength errors in digital filters, con trollers and estimators, and how to minimize the deleterious effects of these errors on the performance of these devices. This does by no means imply that all about finite wordlength errors in filters, controllers and estimators is to be found in this book. We first ventured into the world of finite wordlength effects in 1987 when Gang Li began his PhD thesis in this area. Our more experienced readers might well say 'This shows', but we believe that the extent of our new contributions largely offsets our relative inexperience about the subject that might surface here and there in the book. Our naive view on the subject of finite wordlength errors in 1987 could probably be summarized as follows: • numerical errors due to finite wordlength encoding and roundoff are something that one has to live with, and there is probably not much that can be done about them except to increase the wordlength by improvements on the hardware; • these errors are as old as finite arithmetic and numerical analysis and they must therefore be well understood by now; • thus, if something can be done to minimize their effects, it must have been analysed and put into practice a long time ago. It is almost fair to say that we were wrong on all counts.
System and Control theory is one of the most exciting areas of contemporary engineering mathematics. From the analysis of Watt's steam engine governor - which enabled the Industrial Revolution - to the design of controllers for consumer items, chemical plants and modern aircraft, the area has always drawn from a broad range of tools. It has provided many challenges and possibilities for interaction between engineering and established areas of 'pure' and 'applied' mathematics. This impressive volume collects a discussion of more than fifty open problems which touch upon a variety of subfields, including: chaotic observers, nonlinear local controlability, discrete event and hybrid systems, neural network learning, matrix inequalities, Lyapunov exponents, and many other issues. Proposed and explained by leading researchers, they are offered with the intention of generating further work, as well as inspiration for many other similar problems which may naturally arise from them. With extensive references, this book will be a useful reference source - as well as an excellent addendum to the textbooks in the area.
This book deals with the issue of fundamental limitations in filtering and control system design. This issue lies at the very heart of feedback theory since it reveals what is achievable, and conversely what is not achievable, in feedback systems. The subject has a rich history beginning with the seminal work of Bode during the 1940's and as subsequently published in his well-known book Feedback Amplifier Design (Van Nostrand, 1945). An interesting fact is that, although Bode's book is now fifty years old, it is still extensively quoted. This is supported by a science citation count which remains comparable with the best contemporary texts on control theory. Interpretations of Bode's results in the context of control system design were provided by Horowitz in the 1960's. For example, it has been shown that, for single-input single-output stable open-loop systems having rela tive degree greater than one, the integral of the logarithmic sensitivity with respect to frequency is zero. This result implies, among other things, that a reduction in sensitivity in one frequency band is necessarily accompa nied by an increase of sensitivity in other frequency bands. Although the original results were restricted to open-loop stable systems, they have been subsequently extended to open-loop unstable systems and systems having nonminimum phase zeros.
Written by leading researchers, this book collects a number of articles considering the problems of finite-precision computing in digital controllers and filters. Topics range from analysis of fragility and finite-precision effects to the design of low-complexity digital controllers.
In this new edition of the Handbook of Signal Processing Systems, many of the chapters from the previous editions have been updated, and several new chapters have been added. The new contributions include chapters on signal processing methods for light field displays, throughput analysis of dataflow graphs, modeling for reconfigurable signal processing systems, fast Fourier transform architectures, deep neural networks, programmable architectures for histogram of oriented gradients processing, high dynamic range video coding, system-on-chip architectures for data analytics, analysis of finite word-length effects in fixed-point systems, and models of architecture. There are more than 700 tables and illustrations; in this edition over 300 are in color. This new edition of the handbook is organized in three parts. Part I motivates representative applications that drive and apply state-of-the art methods for design and implementation of signal processing systems; Part II discusses architectures for implementing these applications; and Part III focuses on compilers, as well as models of computation and their associated design tools and methodologies.
This volume features computational tools that can be applied directly and are explained with simple calculations, plus an emphasis on control system principles and ideas. Includes worked examples, MATLAB macros, and solutions manual.
Thank you for opening the second edition of this monograph, which is devoted to the study of a class of nonsmooth dynamical systems of the general form: ::i; = g(x,u) (0. 1) f(x, t) 2: 0 where x E JRn is the system's state vector, u E JRm is the vector of inputs, and the function f (-, . ) represents a unilateral constraint that is imposed on the state. More precisely, we shall restrict ourselves to a subclass of such systems, namely mechanical systems subject to unilateral constraints on the position, whose dynamical equations may be in a first instance written as: ii= g(q,q,u) (0. 2) f(q, t) 2: 0 where q E JRn is the vector of generalized coordinates of the system and u is an in put (or controller) that generally involves a state feedback loop, i. e. u= u(q, q, t, z), with z= Z(z, q, q, t) when the controller is a dynamic state feedback. Mechanical systems composed of rigid bodies interacting fall into this subclass. A general prop erty of systems as in (0. 1) and (0. 2) is that their solutions are nonsmooth (with respect to time): Nonsmoothness arises primarily from the occurence of impacts (or collisions, or percussions) in the dynamical behaviour, when the trajectories attain the surface f(x, t) = O. They are necessary to keep the trajectories within the subspace = {x : f(x, t) 2: O} of the system's state space.
Adaptive Control provides techniques for automatic, real-time adjustments in controller parameters with a view to achieving and/or maintaining a desirable level of system performance in the presence of unknown or variable process parameters. Many aspects of the field are dealt with in coherent and orderly fashion, starting with the problems posed by system uncertainties and moving on to the presentation of solutions and their practical significance. Within the general context of recent developments, the book looks at: • synthesis and analysis of parameter adaptation algorithms; • recursive plant-model identification in open and closed loop; • robust digital control for adaptive control; • direct and indirect adaptive control; and • practical aspects and applications. To reflect the importance of digital computers for the application of adaptive control techniques, discrete-time aspects are emphasized. To guide the reader, the book contains various applications of adaptive control techniques.
This eagerly awaited follow-up to Nonlinear Control Systems incorporates recent advances in the design of feedback laws, for the purpose of globally stabilizing nonlinear systems via state or output feedback. The author is one of the most prominent researchers in the field.