Phase Portraits of Control Dynamical Systems

The present book is the outcome of efforts of giving vivid geometrical representation to control dynamical systems (CDSs) ... and, in particular, the phase plane of CDS) in giving as complete as possible a description of such systems.


Author: A.G. Butkovskiy

Publisher: Springer Science & Business Media

ISBN: 9789401132589

Category: Science

Page: 170

View: 195

Nonlinear Dynamical Systems and Control

The method of isoclines is a technique for generating solution curves in the two-dimensional state space (that is, the phase plane) for various initial conditions. In particular, given the second-order nonlinear dynamical system (2.230) ...


Author: Wassim M. Haddad

Publisher: Princeton University Press

ISBN: 9781400841042

Category: Mathematics

Page: 944

View: 466

Nonlinear Dynamical Systems and Control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. Dynamical system theory lies at the heart of mathematical sciences and engineering. The application of dynamical systems has crossed interdisciplinary boundaries from chemistry to biochemistry to chemical kinetics, from medicine to biology to population genetics, from economics to sociology to psychology, and from physics to mechanics to engineering. The increasingly complex nature of engineering systems requiring feedback control to obtain a desired system behavior also gives rise to dynamical systems. Wassim Haddad and VijaySekhar Chellaboina provide an exhaustive treatment of nonlinear systems theory and control using the highest standards of exposition and rigor. This graduate-level textbook goes well beyond standard treatments by developing Lyapunov stability theory, partial stability, boundedness, input-to-state stability, input-output stability, finite-time stability, semistability, stability of sets and periodic orbits, and stability theorems via vector Lyapunov functions. A complete and thorough treatment of dissipativity theory, absolute stability theory, stability of feedback systems, optimal control, disturbance rejection control, and robust control for nonlinear dynamical systems is also given. This book is an indispensable resource for applied mathematicians, dynamical systems theorists, control theorists, and engineers.

Encyclopaedia of Mathematics

in the dynamics of a system with holonomic, ideal constraints, not explicitly dependent on the time, the phase space ... [A2] BUTKovsky, A.G. [A.G. BUTkovskis): Phase portraits of control dynamical systems, Kluwer, 1990 (translated from ...


Author: M. Hazewinkel

Publisher: Springer

ISBN: 9781489937919

Category: Mathematics

Page: 929

View: 324

Encyclopaedia of Mathematics

in the dynamics of a system with holonomic, ideal constraints, not explicitly dependent on the time, the phase space is the tangent or ... Phase portraits of control dynamical systems, Kluwer, 1990 (translated from the Russian).


Author: Michiel Hazewinkel

Publisher: Springer Science & Business Media

ISBN: 9789401512374

Category: Mathematics

Page: 506

View: 459

This ENCYCLOPAEDIA OF MA THEMA TICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Estimators for Uncertain Dynamic Systems

A.G. Butkovskiy : Phase Portraits of Control Dynamical Systems . 1991 , 180 pp . ISBN 0-7923-1057-8 A.A. Zhigljavsky : Theory of the Global Random Search . 1991 , 360 pp . ISBN 0-7923-1122-1 G. Ruhe : Algorithmic Aspects of Flows in ...


Author: A.I. Matasov

Publisher: Springer Science & Business Media

ISBN: 0792352785

Category: Technology & Engineering

Page: 420

View: 763

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.

The Dynamic Systems of Basic Economic Growth Models

Other Mathematics and Its Applications titles of interest: A.G. Butkovskiy: Phase Portraits of Control Dynamical Systems. 1991, 180 pp. ISBN 0-7923-1057-8 A.A. Zhigljavsky: Theory of the Global Random Search. 1991, 360 pp.


Author: Bjarne S. Jensen

Publisher: Springer Science & Business Media

ISBN: 9789401110365

Category: Mathematics

Page: 356

View: 912

Two central problems in the pure theory of economic growth are analysed in this monograph: 1) the dynamic laws governing the economic growth processes, 2) the kinematic and geometric properties of the set of solutions to the dynamic systems. With allegiance to rigor and the emphasis on the theoretical fundamentals of prototype mathematical growth models, the treatise is written in the theorem-proof style. To keep the exposition orderly and as smooth as possible, the economic analysis has been separated from the purely mathematical issues, and hence the monograph is organized in two books. Regarding the scope and content of the two books, an "Introduction and Over view" has been prepared to offer both motivation and a brief account. The introduc tion is especially designed to give a recapitulation of the mathematical theory and results presented in Book II, which are used as the unifying mathematical framework in the analysis and exposition of the different economic growth models in Book I. Economists would probably prefer to go directly to Book I and proceed by consult ing the mathematical theorems of Book II in confirming the economic theorems in Book I. Thereby, both the independence and interdependence of the economic and mathematical argumentations are respected.

Systems and Control Theory for Power Systems

rized some of the bifurcation - theoretic problems associated with control of voltage collapse . ... [ 10 ] A.G.BUTKOVSKIY , Phase portraits of control dynamical systems , Kluwer , Dordrecht , The Netherlands 1991 .


Author: Joe H. Chow

Publisher: Springer Science & Business Media

ISBN: 0387944389

Category: Computers

Page: 413

View: 538

The articles in this volume cover power system model reduction, transient and voltage stability, nonlinear control, robust stability, computation and optimization and have been written by some of the leading researchers in these areas. This book should be of interest to power and control engineers, and applied mathematicians.

Optimization and Control of Bilinear Systems

Lecture Notes in Economics and Mathematical Systems. New York, Springer, pp. 54–63. ... In Novikov S.P., ed., Mathematical Methods in System Theory. Nauka, Moscow (in Russian). ... Phase Portraits of Control Dynamical Systems.


Author: Panos M. Pardalos

Publisher: Springer Science & Business Media

ISBN: 0387736697

Category: Science

Page: 370

View: 803

Covers developments in bilinear systems theory Focuses on the control of open physical processes functioning in a non-equilibrium mode Emphasis is on three primary disciplines: modern differential geometry, control of dynamical systems, and optimization theory Includes applications to the fields of quantum and molecular computing, control of physical processes, biophysics, superconducting magnetism, and physical information science

Deterministic Learning Theory for Identification Recognition and Control

This major problem can be easily solved when the dynamical models within the recognition system are disposed in a parallel ... Two dynamical systems are considered as topologically equivalent if their phase portraits are qualitatively ...


Author: Cong Wang

Publisher: CRC Press

ISBN: 9781351837644

Category: Technology & Engineering

Page: 207

View: 235

Deterministic Learning Theory for Identification, Recognition, and Control presents a unified conceptual framework for knowledge acquisition, representation, and knowledge utilization in uncertain dynamic environments. It provides systematic design approaches for identification, recognition, and control of linear uncertain systems. Unlike many books currently available that focus on statistical principles, this book stresses learning through closed-loop neural control, effective representation and recognition of temporal patterns in a deterministic way. A Deterministic View of Learning in Dynamic Environments The authors begin with an introduction to the concepts of deterministic learning theory, followed by a discussion of the persistent excitation property of RBF networks. They describe the elements of deterministic learning, and address dynamical pattern recognition and pattern-based control processes. The results are applicable to areas such as detection and isolation of oscillation faults, ECG/EEG pattern recognition, robot learning and control, and security analysis and control of power systems. A New Model of Information Processing This book elucidates a learning theory which is developed using concepts and tools from the discipline of systems and control. Fundamental knowledge about system dynamics is obtained from dynamical processes, and is then utilized to achieve rapid recognition of dynamical patterns and pattern-based closed-loop control via the so-called internal and dynamical matching of system dynamics. This actually represents a new model of information processing, i.e. a model of dynamical parallel distributed processing (DPDP).

Applied Digital Control

Butkovskiy, A.G., Phase Portraits of Control Dynamical Systems, Kluwer Academic Publishers, 1991. Carr, J. J., Data Acquisition and Control: Microcomputer Applications for Scientists and Engineers, TAB Books, USA, 1988.


Author: J. R. Leigh

Publisher: Courier Dover Publications

ISBN: 9780486450513

Category: Technology & Engineering

Page: 524

View: 395

An essential core text, this volume develops theoretical foundations and explains how control systems work in real industrial situations. Several case histories assist students in visualizing applications. 1992 edition.