Continuous Time Dynamical Systems

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Continuous Time Dynamical Systems

B.M. Mohan,S.K. Kar
Continuous Time Dynamical Systems Book PDF

Author : B.M. Mohan,S.K. Kar
Publisher : CRC Press
Page : 250 pages
File Size : 41,5 Mb
Release : 2012-10-24
Category : Technology & Engineering
ISBN : 9781466517295

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Continuous Time Dynamical Systems by B.M. Mohan,S.K. Kar Pdf

Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost functional. This book, Continuous Time Dynamical Systems: State Estimation and Optimal Control with Orthogonal Functions, considers different classes of systems with quadratic performance criteria. It then attempts to find the optimal control law for each class of systems using orthogonal functions that can optimize the given performance criteria. Illustrated throughout with detailed examples, the book covers topics including: Block-pulse functions and shifted Legendre polynomials State estimation of linear time-invariant systems Linear optimal control systems incorporating observers Optimal control of systems described by integro-differential equations Linear-quadratic-Gaussian control Optimal control of singular systems Optimal control of time-delay systems with and without reverse time terms Optimal control of second-order nonlinear systems Hierarchical control of linear time-invariant and time-varying systems

Nonlinear Dynamics and Chaos

Steven H. Strogatz
Nonlinear Dynamics and Chaos Book PDF

Author : Steven H. Strogatz
Publisher : CRC Press
Page : 532 pages
File Size : 42,6 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9780429961113

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Nonlinear Dynamics and Chaos by Steven H. Strogatz Pdf

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

An Introduction to Dynamical Systems

Rex Clark Robinson
An Introduction to Dynamical Systems Book PDF

Author : Rex Clark Robinson
Publisher : American Mathematical Soc.
Page : 763 pages
File Size : 47,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821891353

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An Introduction to Dynamical Systems by Rex Clark Robinson Pdf

This book gives a mathematical treatment of the introduction to qualitative differential equations and discrete dynamical systems. The treatment includes theoretical proofs, methods of calculation, and applications. The two parts of the book, continuous time of differential equations and discrete time of dynamical systems, can be covered independently in one semester each or combined together into a year long course. The material on differential equations introduces the qualitative or geometric approach through a treatment of linear systems in any dimension. There follows chapters where equilibria are the most important feature, where scalar (energy) functions is the principal tool, where periodic orbits appear, and finally, chaotic systems of differential equations. The many different approaches are systematically introduced through examples and theorems. The material on discrete dynamical systems starts with maps of one variable and proceeds to systems in higher dimensions. The treatment starts with examples where the periodic points can be found explicitly and then introduces symbolic dynamics to analyze where they can be shown to exist but not given in explicit form. Chaotic systems are presented both mathematically and more computationally using Lyapunov exponents. With the one-dimensional maps as models, the multidimensional maps cover the same material in higher dimensions. This higher dimensional material is less computational and more conceptual and theoretical. The final chapter on fractals introduces various dimensions which is another computational tool for measuring the complexity of a system. It also treats iterated function systems which give examples of complicated sets. In the second edition of the book, much of the material has been rewritten to clarify the presentation. Also, some new material has been included in both parts of the book. This book can be used as a textbook for an advanced undergraduate course on ordinary differential equations and/or dynamical systems. Prerequisites are standard courses in calculus (single variable and multivariable), linear algebra, and introductory differential equations.

Mathematical Modeling

Mark M. Meerschaert
Mathematical Modeling Book PDF

Author : Mark M. Meerschaert
Publisher : Elsevier
Page : 360 pages
File Size : 47,9 Mb
Release : 2007-06-18
Category : Mathematics
ISBN : 0123708575

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Mathematical Modeling by Mark M. Meerschaert Pdf

Mathematical Modeling, Third Edition is a general introduction to an increasingly crucial topic for today's mathematicians. Unlike textbooks focused on one kind of mathematical model, this book covers the broad spectrum of modeling problems, from optimization to dynamical systems to stochastic processes. Mathematical modeling is the link between mathematics and the rest of the world. Meerschaert shows how to refine a question, phrasing it in precise mathematical terms. Then he encourages students to reverse the process, translating the mathematical solution back into a comprehensible, useful answer to the original question. This textbook mirrors the process professionals must follow in solving complex problems. Each chapter in this book is followed by a set of challenging exercises. These exercises require significant effort on the part of the student, as well as a certain amount of creativity. Meerschaert did not invent the problems in this book--they are real problems, not designed to illustrate the use of any particular mathematical technique. Meerschaert's emphasis on principles and general techniques offers students the mathematical background they need to model problems in a wide range of disciplines. Increased support for instructors, including MATLAB material New sections on time series analysis and diffusion models Additional problems with international focus such as whale and dolphin populations, plus updated optimization problems

Continuous Time Dynamical Systems

B.M. Mohan,S.K. Kar
Continuous Time Dynamical Systems Book PDF

Author : B.M. Mohan,S.K. Kar
Publisher : CRC Press
Page : 250 pages
File Size : 55,5 Mb
Release : 2018-10-08
Category : Technology & Engineering
ISBN : 9781351832236

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Continuous Time Dynamical Systems by B.M. Mohan,S.K. Kar Pdf

Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost functional. This book, Continuous Time Dynamical Systems: State Estimation and Optimal Control with Orthogonal Functions, considers different classes of systems with quadratic performance criteria. It then attempts to find the optimal control law for each class of systems using orthogonal functions that can optimize the given performance criteria. Illustrated throughout with detailed examples, the book covers topics including: Block-pulse functions and shifted Legendre polynomials State estimation of linear time-invariant systems Linear optimal control systems incorporating observers Optimal control of systems described by integro-differential equations Linear-quadratic-Gaussian control Optimal control of singular systems Optimal control of time-delay systems with and without reverse time terms Optimal control of second-order nonlinear systems Hierarchical control of linear time-invariant and time-varying systems

System Theory of Continuous Time Finite Dimensional Dynamical Systems

Yasumichi Hasegawa
System Theory of Continuous Time Finite Dimensional Dynamical Systems Book PDF

Author : Yasumichi Hasegawa
Publisher : Springer Nature
Page : 221 pages
File Size : 45,5 Mb
Release : 2019-09-26
Category : Technology & Engineering
ISBN : 9783030304805

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System Theory of Continuous Time Finite Dimensional Dynamical Systems by Yasumichi Hasegawa Pdf

This book discusses the realization and control problems of finite-dimensional dynamical systems which contain linear and nonlinear systems. The author focuses on algebraic methods for the discussion of control problems of linear and non-linear dynamical systems. The book contains detailed examples to showcase the effectiveness of the presented method. The target audience comprises primarily research experts in the field of control theory, but the book may also be beneficial for graduate students alike.

Stability of Dynamical Systems

Anonim
Stability of Dynamical Systems Book PDF

Author : Anonim
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 49,9 Mb
Release : 2008
Category : Differentiable dynamical systems
ISBN : 9780817644864

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Stability of Dynamical Systems by Anonim Pdf

In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states evolve along continuous time and discrete instants; components whose descriptions may exhibit nonlinearities, time lags, transportation delays, hysteresis effects, and uncertainties in parameters; and components that cannot be described by various classical equations, as in the case of discrete-event systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics. Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models described above. Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model. The book covers the following four general topics: * Representation and modeling of dynamical systems of the types described above * Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces * Specialization of this stability theory to finite-dimensional dynamical systems * Specialization of this stability theory to infinite-dimensional dynamical systems Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics.

Continuous Time Dynamical Systems

B.M. Mohan,S.K. Kar
Continuous Time Dynamical Systems Book PDF

Author : B.M. Mohan,S.K. Kar
Publisher : CRC Press
Page : 247 pages
File Size : 53,7 Mb
Release : 2018-10-08
Category : Technology & Engineering
ISBN : 9781466517301

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Continuous Time Dynamical Systems by B.M. Mohan,S.K. Kar Pdf

Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost functional. This book, Continuous Time Dynamical Systems: State Estimation and Optimal Control with Orthogonal Functions, considers different classes of systems with quadratic performance criteria. It then attempts to find the optimal control law for each class of systems using orthogonal functions that can optimize the given performance criteria. Illustrated throughout with detailed examples, the book covers topics including: Block-pulse functions and shifted Legendre polynomials State estimation of linear time-invariant systems Linear optimal control systems incorporating observers Optimal control of systems described by integro-differential equations Linear-quadratic-Gaussian control Optimal control of singular systems Optimal control of time-delay systems with and without reverse time terms Optimal control of second-order nonlinear systems Hierarchical control of linear time-invariant and time-varying systems

Invitation to Dynamical Systems

Edward R. Scheinerman
Invitation to Dynamical Systems Book PDF

Author : Edward R. Scheinerman
Publisher : Courier Corporation
Page : 408 pages
File Size : 46,6 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9780486275321

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Invitation to Dynamical Systems by Edward R. Scheinerman Pdf

This text is designed for those who wish to study mathematics beyond linear algebra but are unready for abstract material. Rather than a theorem-proof-corollary exposition, it stresses geometry, intuition, and dynamical systems. 1996 edition.

Continuous-Time Markov Jump Linear Systems

Oswaldo Luiz do Valle Costa,Marcelo D. Fragoso,Marcos G. Todorov
Continuous Time Markov Jump Linear Systems Book PDF

Author : Oswaldo Luiz do Valle Costa,Marcelo D. Fragoso,Marcos G. Todorov
Publisher : Springer Science & Business Media
Page : 295 pages
File Size : 48,9 Mb
Release : 2012-12-18
Category : Mathematics
ISBN : 9783642341007

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Continuous-Time Markov Jump Linear Systems by Oswaldo Luiz do Valle Costa,Marcelo D. Fragoso,Marcos G. Todorov Pdf

It has been widely recognized nowadays the importance of introducing mathematical models that take into account possible sudden changes in the dynamical behavior of a high-integrity systems or a safety-critical system. Such systems can be found in aircraft control, nuclear power stations, robotic manipulator systems, integrated communication networks and large-scale flexible structures for space stations, and are inherently vulnerable to abrupt changes in their structures caused by component or interconnection failures. In this regard, a particularly interesting class of models is the so-called Markov jump linear systems (MJLS), which have been used in numerous applications including robotics, economics and wireless communication. Combining probability and operator theory, the present volume provides a unified and rigorous treatment of recent results in control theory of continuous-time MJLS. This unique approach is of great interest to experts working in the field of linear systems with Markovian jump parameters or in stochastic control. The volume focuses on one of the few cases of stochastic control problems with an actual explicit solution and offers material well-suited to coursework, introducing students to an interesting and active research area. The book is addressed to researchers working in control and signal processing engineering. Prerequisites include a solid background in classical linear control theory, basic familiarity with continuous-time Markov chains and probability theory, and some elementary knowledge of operator theory. ​

Hybrid Dynamical Systems

Rafal Goebel,Ricardo G. Sanfelice,Andrew R. Teel
Hybrid Dynamical Systems Book PDF

Author : Rafal Goebel,Ricardo G. Sanfelice,Andrew R. Teel
Publisher : Princeton University Press
Page : 227 pages
File Size : 53,6 Mb
Release : 2012-03-18
Category : Mathematics
ISBN : 9781400842636

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Hybrid Dynamical Systems by Rafal Goebel,Ricardo G. Sanfelice,Andrew R. Teel Pdf

Hybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. Filled with a wealth of examples to illustrate concepts, this book presents a complete theory of robust asymptotic stability for hybrid dynamical systems that is applicable to the design of hybrid control algorithms--algorithms that feature logic, timers, or combinations of digital and analog components. With the tools of modern mathematical analysis, Hybrid Dynamical Systems unifies and generalizes earlier developments in continuous-time and discrete-time nonlinear systems. It presents hybrid system versions of the necessary and sufficient Lyapunov conditions for asymptotic stability, invariance principles, and approximation techniques, and examines the robustness of asymptotic stability, motivated by the goal of designing robust hybrid control algorithms. This self-contained and classroom-tested book requires standard background in mathematical analysis and differential equations or nonlinear systems. It will interest graduate students in engineering as well as students and researchers in control, computer science, and mathematics.

Discrete Dynamics and Difference Equations

Saber N. Elaydi,Henrique Oliveira,Jose Manuel Ferreira
Discrete Dynamics and Difference Equations Book PDF

Author : Saber N. Elaydi,Henrique Oliveira,Jose Manuel Ferreira
Publisher : World Scientific
Page : 438 pages
File Size : 40,8 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814287647

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Discrete Dynamics and Difference Equations by Saber N. Elaydi,Henrique Oliveira,Jose Manuel Ferreira Pdf

This volume holds a collection of articles based on the talks presented at ICDEA 2007 in Lisbon, Portugal. The volume encompasses current topics on stability and bifurcation, chaos, mathematical biology, iteration theory, nonautonomous systems, and stochastic dynamical systems.

Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems

Luis Rodrigues ,Behzad Samadi ,Miad Moarref
Piecewise Affine Control Continuous Time Sampled Data and Networked Systems Book PDF

Author : Luis Rodrigues ,Behzad Samadi ,Miad Moarref
Publisher : SIAM
Page : 224 pages
File Size : 42,9 Mb
Release : 2019-11-06
Category : Mathematics
ISBN : 9781611975901

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Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems by Luis Rodrigues ,Behzad Samadi ,Miad Moarref Pdf

Engineering systems operate through actuators, most of which will exhibit phenomena such as saturation or zones of no operation, commonly known as dead zones. These are examples of piecewise-affine characteristics, and they can have a considerable impact on the stability and performance of engineering systems. This book targets controller design for piecewise affine systems, fulfilling both stability and performance requirements. The authors present a unified computational methodology for the analysis and synthesis of piecewise affine controllers, taking an approach that is capable of handling sliding modes, sampled-data, and networked systems. They introduce algorithms that will be applicable to nonlinear systems approximated by piecewise affine systems, and they feature several examples from areas such as switching electronic circuits, autonomous vehicles, neural networks, and aerospace applications. Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems is intended for graduate students, advanced senior undergraduate students, and researchers in academia and industry. It is also appropriate for engineers working on applications where switched linear and affine models are important.

An Introduction To Mathematical Billiards

Rozikov Utkir A
An Introduction To Mathematical Billiards Book PDF

Author : Rozikov Utkir A
Publisher : World Scientific
Page : 224 pages
File Size : 52,7 Mb
Release : 2018-12-06
Category : Science
ISBN : 9789813276482

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An Introduction To Mathematical Billiards by Rozikov Utkir A Pdf

A mathematical billiard is a mechanical system consisting of a billiard ball on a table of any form (which can be planar or even a multidimensional domain) but without billiard pockets. The ball moves and its trajectory is defined by the ball's initial position and its initial speed vector. The ball's reflections from the boundary of the table are assumed to have the property that the reflection and incidence angles are the same. This book comprehensively presents known results on the behavior of a trajectory of a billiard ball on a planar table (having one of the following forms: circle, ellipse, triangle, rectangle, polygon and some general convex domains). It provides a systematic review of the theory of dynamical systems, with a concise presentation of billiards in elementary mathematics and simple billiards related to geometry and physics.The description of these trajectories leads to the solution of various questions in mathematics and mechanics: problems related to liquid transfusion, lighting of mirror rooms, crushing of stones in a kidney, collisions of gas particles, etc. The analysis of billiard trajectories can involve methods of geometry, dynamical systems, and ergodic theory, as well as methods of theoretical physics and mechanics, which has applications in the fields of biology, mathematics, medicine, and physics.

A Practical Approach to Dynamical Systems for Engineers

Patricia Mellodge
A Practical Approach to Dynamical Systems for Engineers Book PDF

Author : Patricia Mellodge
Publisher : Woodhead Publishing
Page : 292 pages
File Size : 55,7 Mb
Release : 2015-11-19
Category : Mathematics
ISBN : 9780081002247

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A Practical Approach to Dynamical Systems for Engineers by Patricia Mellodge Pdf

A Practical Approach to Dynamical Systems for Engineers takes the abstract mathematical concepts behind dynamical systems and applies them to real-world systems, such as a car traveling down the road, the ripples caused by throwing a pebble into a pond, and a clock pendulum swinging back and forth. Many relevant topics are covered, including modeling systems using differential equations, transfer functions, state-space representation, Hamiltonian systems, stability and equilibrium, and nonlinear system characteristics with examples including chaos, bifurcation, and limit cycles. In addition, MATLAB is used extensively to show how the analysis methods are applied to the examples. It is assumed readers will have an understanding of calculus, differential equations, linear algebra, and an interest in mechanical and electrical dynamical systems. Presents applications in engineering to show the adoption of dynamical system analytical methods Provides examples on the dynamics of automobiles, aircraft, and human balance, among others, with an emphasis on physical engineering systems MATLAB and Simulink are used throughout to apply the analysis methods and illustrate the ideas Offers in-depth discussions of every abstract concept, described in an intuitive manner, and illustrated using practical examples, bridging the gap between theory and practice Ideal resource for practicing engineers who need to understand background theory and how to apply it