Operator Approach to Linear Control Systems

The idea of optimization runs through most parts of control theory.

Author: A. Cheremensky

Publisher: Springer Science & Business Media

ISBN: 9789400901278

Category: Science

Page: 398

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The idea of optimization runs through most parts of control theory. The simplest optimal controls are preplanned (programmed) ones. The problem of constructing optimal preplanned controls has been extensively worked out in literature (see, e. g. , the Pontrjagin maximum principle giving necessary conditions of preplanned control optimality). However, the concept of op timality itself has a restrictive character: it is limited by what one means under optimality in each separate case. The internal contradictoriness of the preplanned control optimality ("the better is the enemy of the good") yields that the practical significance of optimal preplanned controls proves to be not great: such controls are usually sensitive to unregistered disturbances (includ ing the round-off errors which are inevitable when computer devices are used for forming controls), as there is the effect of disturbance accumulation in the control process which makes controls to be of little use on large time inter vals. This gap is mainly provoked by oversimplified settings of optimization problems. The outstanding result of control theory established in the end of the first half of our century is that controls in feedback form ensure the weak sensitivity of closed loop systems with respect to "small" unregistered internal and external disturbances acting in them (here we do not need to discuss performance indexes, since the considered phenomenon is of general nature). But by far not all optimal preplanned controls can be represented in a feedback form.
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Nonlinear Feedback Control Systems

Nonlinear analytic mappings. Nonlinear Lipschitz operators. Nonlinear feedback systems. Optimal design of nonlinear feedback control systems. Coprime factorizations of nonlinear mappings for control systems. Nonlinear system identification.

Author: Rui J. P. DeFigueiredo

Publisher:

ISBN: UOM:39015029976142

Category: Feedback control systems.

Page: 220

View: 314

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Nonlinear analytic mappings. Nonlinear Lipschitz operators. Nonlinear feedback systems. Optimal design of nonlinear feedback control systems. Coprime factorizations of nonlinear mappings for control systems. Nonlinear system identification.
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Linear Operators and Linear Systems

Publisher Description

Author: Jonathan R. Partington

Publisher: Cambridge University Press

ISBN: 0521546192

Category: Mathematics

Page: 166

View: 479

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Linear systems can be regarded as a causal shift-invariant operator on a Hilbert space of signals, and by doing so this book presents an introduction to the common ground between operator theory and linear systems theory. The book therefore includes material on pure mathematical topics such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic functions, which would be entirely suitable for a course in functional analysis; at the same time, the book includes applications to partial differential equations, to the stability and stabilization of linear systems, to power signal spaces (including some recent material not previously available in books), and to delay systems, treated from an input/output point of view. Suitable for students of analysis, this book also acts as an introduction to a mathematical approach to systems and control for graduate students in departments of applied mathematics or engineering.
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SIAM Journal on Applied Mathematics

[ 3 ] S. BARNETT , Some topics in algebraic systems theory : A survey , Recent
Mathematical Developments in Control , D. J. ... [ 24 ] W. A. WOLOVICH ,
Differential operator approach to linear system analysis and design , J. Franklin
Inst . , 301 ...

Author:

Publisher:

ISBN: UCAL:B3627700

Category: Mathematics

Page:

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Analysis and Synthesis of Delta Operator Systems

A systematic approach to a class of approximations to the pulse transfer function
of a system consisting of a ZOH and a linear continuous-time plant has been
presented in [15]. In [33], the problem of digital controller structures realized has ...

Author: Hongjiu Yang

Publisher: Springer

ISBN: 9783642287749

Category: Technology & Engineering

Page: 276

View: 844

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This book is devoted to analysis and design on delta operator systems. When sampling is fast, a dynamical system will become difficult to control, which can be seen in wide real world applications. Delta operator approach is very effective to deal with fast sampling systems. Moreover, it is easy to observe and analyze the control effect with different sampling periods in delta operator systems. The framework of this book has been carefully constructed for delta operator systems to handle sliding mode control, time delays, filter design, finite frequency and networked control. These problems indeed are especially important and significant in automation and control systems design. Through the clear framework of the book, readers can easily go through the learning process on delta operator systems via a precise and comfortable learning sequence. Following this enjoyable trail, readers will come out knowing how to use delta operator approach to deal with control problems under fast sampling case. This book should be a good reference for academies, post-graduates scientists and engineers working in the field of control science and control engineering.
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SIAM Journal on Control and Optimization

( 38 ) O . J . STAFFANS AND G . Weiss , Transfer functions of regular linear
systems , Part III : Inversions and duality , Integral Equations Operator Theory , 49
( 2004 ) , pp . 517 - 558 . ( 39 ) V . L . SYRMOS , C . T . ABDALLAH , P . DORATO
 ...

Author: Society for Industrial and Applied Mathematics

Publisher:

ISBN: UCSD:31822036010981

Category: Control theory

Page:

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Automatic and Remote Control

It has been my experience that non - linear control systems have different forms
of response for different initial states . ... The dominant operator approach to the
synthesis of adaptive systems is based on the state - space technique , therefore
 ...

Author: International Federation of Automatic Control. Congress

Publisher:

ISBN: UCSD:31822015400740

Category: Automatic control

Page:

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Linear Operators and Linear Systems

This book presents an introduction to the common ground between operator theory and linear systems theory.

Author: Jonathan Richard Partington

Publisher:

ISBN: 0511186134

Category: Electronic books

Page: 166

View: 822

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This book presents an introduction to the common ground between operator theory and linear systems theory. Suitable for students of functional analysis, this book also acts as an introduction to a mathematical approach to systems and control for graduate students in departments of applied mathematics or engineering.
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Fundamentals of Linear State Space Systems

... we present the linear operator approach . This gives a much more geometrical
understanding of some of the basic arithmetic computations we have been
performing all along . Without this approach , certain linear system theory and
control ...

Author: John S. Bay

Publisher: McGraw-Hill Science, Engineering & Mathematics

ISBN: STANFORD:36105023086288

Category: Science

Page: 571

View: 630

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This book addresses two primary deficiencies in the linear systems textbook market: a lack of development of state space methods from the basic principles and a lack of pedagogical focus. The book uses the geometric intuition provided by vector space analysis to develop in a very sequential manner all the essential topics in linear state system theory that a senior or beginning graduate student should know. It does this in an ordered, readable manner, with examples drawn from several areas of engineering. Because it derives state space methods from linear algebra and vector spaces and ties all the topics together with diverse applications, this book is suitable for students from any engineering discipline, not just those with control systems backgrounds and interests. It begins with the mathematical preliminaries of vectors and spaces, then emphasizes the geometric properties of linear operators. It is from this foundation that the studies of stability, controllability and observability, realizations, state feedback, observers, and Kalman filters are derived. There is a direct and simple path from one topic to the next. The book includes both discrete- and continuous-time systems, introducing them in parallel and emphasizing each in appropriate context. Time-varying systems are discussed from generality and completeness, but the emphasis is on time-invariant systems, and only in time-domain; there is no treatment of matrix fraction descriptions or polynomial matrices. Tips for using MATLAB are included in the form of margin notes, which are placed wherever topics with applicable MATLAB commands are introduced. These notes direct the reader to an appendix, where a MATLAB command reference explains command usage. However, an instructor or student who is not interested in MATLAB usage can easily skip these references without interrupting the flow of text.
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Recent Trends in Systems Theory

The Differential Operator Approach to Linear System Analysis and Design * by
W. A. WOLOVICH Division of Engineering and the Lefschetz Center for Dynamic
Systems Brown University , Providence , Rhode Island ABSTRACT : The time ...

Author: Samuel D. Bedrosian

Publisher: Elsevier Science & Technology

ISBN: WISC:89042829101

Category: Functional analysis

Page: 239

View: 901

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Modelling Human Operators in Control System Design

In the design of man-machine systems it is essential that the human operator be represented by a suitable model for communication purposes.

Author: Robert Sutton

Publisher: Wiley-Blackwell

ISBN: STANFORD:36105030086594

Category: Technology & Engineering

Page: 212

View: 669

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In the design of man-machine systems it is essential that the human operator be represented by a suitable model for communication purposes. A model can treat the human operator as a simple linear control element, take a nonlinear approach, or estimate the human operator transfer function and associated remnant to see if these lie within acceptable bounds. Covers all these approaches as well as introduces fuzzy logic as a new and promising modeling mechanism. With interest in both restructurable and reconfigurable controls, particularly with aerospace and marine applications on the rise, and the need for system designers to employ these complex technologies more often, it provides a means for engineers to optimize the overall performance of man-machine control systems.
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Operator Based Nonlinear Control Systems

Specifically, this book addresses uncertain nonlinearity.

Author: Mingcong Deng

Publisher: John Wiley & Sons

ISBN: 9781118813898

Category: Science

Page: 280

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Enables readers to master and apply the operator-theoretic approach Control of nonlinear systems is a multidisciplinary field involving electrical engineering, computer science, and control engineering. Specifically, this book addresses uncertain nonlinearity. Beginning with how real plants are modeled as operator-based plants, the author develops a systematic methodology that enables readers to understand a quantitative stability result, a critical factor in any nonlinear control system's stability and performance. Operator-Based Nonlinear Control Systems: Design and Applications focuses on the operator-theoretic approach, offering detailed examples on how to apply it to network controlled systems. In addition to current research results, the author explores future research directions and applications of the operator-theoretic approach. The book begins with an introduction that defines nonlinear systems. Next, it covers: Robust right coprime factorization for nonlinear plants with uncertainties Robust stability of operator-based nonlinear control systems Tracking issues and fault detection issues in nonlinear control systems Operator-based nonlinear control systems with smart actuators Nonlinear feedback control for large-scale systems using a distributed control system device Throughout the book, discussions of actual applications help readers understand how the operator-theoretic approach works in practice. Operator-Based Nonlinear Control Systems is recommended for students and professionals in control theory engineering and applied mathematics. Working with this expertly written and organized book, they will learn how to obtain robust right coprime factorization for modeled plants. Moreover, they will discover state-of-the-technology research results on robust stability conditions as well as the latest system output tracking and fault detection issues that are challenging today's researchers.
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NASA Contractor Report

Simulation of system dynamics and environment and evaluation of operator
performance . ... The second approach , the quasilinear transfer function
approach , is more general and is applicable in vehicle control system analyses .

Author: United States. National Aeronautics and Space Administration

Publisher:

ISBN: UOM:39015006388576

Category: Astronautics

Page:

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Control Theory and Advanced Technology

A linear feedback control law is proposed for the discrete time sliding mode
control of servo systems . It is developed , using the delta operator , which is an
approximation of the differential operator . The linear control strategy provides the
 ...

Author:

Publisher:

ISBN: UOM:39015030235298

Category: Control theory

Page:

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Nonlinear Model based Process Control

( 1986 ) extended IMC to non - linear lumped parameter systems by an operator
approach . The key issue was inversion of the non - linear process model in the
control law , and a Newton - type method was adopted . Li and Biegler ( 1988 ) ...

Author: Rashid M. Ansari

Publisher: Springer

ISBN: UOM:39015042470024

Category: Science

Page: 232

View: 205

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The series Advances in Industrial Control aims to report and encourage technology transfer in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. New theory, new controllers, actuators, sensors, new industrial processes, computer methods, new applications, new philosophies ... , new challenges. Much of this development work resides in industrial reports, feasibility study papers and the reports of advanced collaborative projects. The series offers an opportunity for researchers to present an extended exposition of such new work in all aspects of industrial control for wider and rapid dissemination. The last decade has seen considerable interest in reviving the fortunes of non linear control. In contrast to the approaches of the 60S, 70S and 80S a very pragmatic agenda for non-linear control is being pursued using the model-based predictive control paradigm. This text by R. Ansari and M. Tade gives an excellent synthesis of this new direction. Two strengths emphasized by the text are: (i) four applications found in refinery processes are used to give the text a firm practical continuity; (ii) a non-linear model-based control architecture is used to give the method a coherent theoretical framework.
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Control and Estimation of Distributed Parameter Systems

When L is especially a self - adjoint operator , we will derive a stronger geometric
character of X by introducing a new approach . The result is then applied to
stabilization of a linear system with a self - adjoint L as a coefficient operator .

Author: International Conference on Control of Distributed Parameter Systems 1

Publisher: Birkhauser

ISBN: UOM:39015016982277

Category: Technology & Engineering

Page: 434

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IEEE International Convention Record

In terms of the inverse optimal control problem, this is equivalent to stating: Given
a manual control system, under what ... Roig ( 1962) used this approach in
comparing the performance of a human operator against a linear controller which
 ...

Author:

Publisher:

ISBN: UCSD:31822004294203

Category: Radio

Page:

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Dissertation Abstracts International

The polymers synthesized both ( linear and crosslinked ) were investigated in -
vitro for their bile acid sequestering activity which revealed the linear water
soluble polymers had values of ... A dynamical system approach to classification
and recognition of analog input information . ... Two new approaches to achieve
this goal are presented : homotopy operator approach and least - squares
approach .

Author:

Publisher:

ISBN: STANFORD:36105020028358

Category: Dissertations, Academic

Page:

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Linear Time Varying Systems

The aim of this book is to propose a new approach to analysis and control of linear time-varying systems.

Author: Henri Bourlès

Publisher: Springer Science & Business Media

ISBN: 9783642197260

Category: Technology & Engineering

Page: 638

View: 607

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The aim of this book is to propose a new approach to analysis and control of linear time-varying systems. These systems are defined in an intrinsic way, i.e., not by a particular representation (e.g., a transfer matrix or a state-space form) but as they are actually. The system equations, derived, e.g., from the laws of physics, are gathered to form an intrinsic mathematical object, namely a finitely presented module over a ring of operators. This is strongly connected with the engineering point of view, according to which a system is not a specific set of equations but an object of the material world which can be described by equivalent sets of equations. This viewpoint makes it possible to formulate and solve efficiently several key problems of the theory of control in the case of linear time-varying systems. The solutions are based on algebraic analysis. This book, written for engineers, is also useful for mathematicians since it shows how algebraic analysis can be applied to solve engineering problems. Henri Bourlès is a Professor and holds the industrial automation chair at the Conservatoire national des arts et métiers in France. He has been teaching automation for over 20 years in engineering and graduate schools. Bogdan Marinescu is currently research engineer at the French Transmission System Operator (RTE) and Associate Professor at SATIE-Ecole Normale Supérieure de Cachan.
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