Computational Aspects Of Linear Control

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Computational Aspects Of Linear Control

Author : Claude Brezinski
ISBN : 9781461302612
Genre : Mathematics
File Size : 32.68 MB
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Many devices (we say dynamical systems or simply systems) behave like black boxes: they receive an input, this input is transformed following some laws (usually a differential equation) and an output is observed. The problem is to regulate the input in order to control the output, that is for obtaining a desired output. Such a mechanism, where the input is modified according to the output measured, is called feedback. The study and design of such automatic processes is called control theory. As we will see, the term system embraces any device and control theory has a wide variety of applications in the real world. Control theory is an interdisci plinary domain at the junction of differential and difference equations, system theory and statistics. Moreover, the solution of a control problem involves many topics of numerical analysis and leads to many interesting computational problems: linear algebra (QR, SVD, projections, Schur complement, structured matrices, localization of eigenvalues, computation of the rank, Jordan normal form, Sylvester and other equations, systems of linear equations, regulariza tion, etc), root localization for polynomials, inversion of the Laplace transform, computation of the matrix exponential, approximation theory (orthogonal poly nomials, Pad6 approximation, continued fractions and linear fractional transfor mations), optimization, least squares, dynamic programming, etc. So, control theory is also a. good excuse for presenting various (sometimes unrelated) issues of numerical analysis and the procedures for their solution. This book is not a book on control.
Category: Mathematics

Computational Methods For Linear Integral Equations

Author : Prem Kythe
ISBN : 9781461201014
Genre : Mathematics
File Size : 56.44 MB
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This book presents numerical methods and computational aspects for linear integral equations. Such equations occur in various areas of applied mathematics, physics, and engineering. The material covered in this book, though not exhaustive, offers useful techniques for solving a variety of problems. Historical information cover ing the nineteenth and twentieth centuries is available in fragments in Kantorovich and Krylov (1958), Anselone (1964), Mikhlin (1967), Lonseth (1977), Atkinson (1976), Baker (1978), Kondo (1991), and Brunner (1997). Integral equations are encountered in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and mag netism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control sys tems, communication theory, mathematical economics, population genetics, queue ing theory, and medicine. Most of the boundary value problems involving differ ential equations can be converted into problems in integral equations, but there are certain problems which can be formulated only in terms of integral equations. A computational approach to the solution of integral equations is, therefore, an essential branch of scientific inquiry.
Category: Mathematics

Advances In Control Systems

Author : Cornelius T. Leondes
ISBN : UOM:39015001317976
Genre : Automatic control
File Size : 34.49 MB
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Category: Automatic control

Logical And Computational Aspects Of Model Based Reasoning

Author : L. Magnani
ISBN : 9789401005500
Genre : Mathematics
File Size : 82.53 MB
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Information technology has been, in recent years, under increasing commercial pressure to provide devices and systems which help/ replace the human in his daily activity. This pressure requires the use of logic as the underlying foundational workhorse of the area. New logics were developed as the need arose and new foci and balance has evolved within logic itself. One aspect of these new trends in logic is the rising impor tance of model based reasoning. Logics have become more and more tailored to applications and their reasoning has become more and more application dependent. In fact, some years ago, I myself coined the phrase "direct deductive reasoning in application areas", advocating the methodology of model-based reasoning in the strongest possible terms. Certainly my discipline of Labelled Deductive Systems allows to bring "pieces" of the application areas as "labels" into the logic. I therefore heartily welcome this important book to Volume 25 of the Applied Logic Series and see it as an important contribution in our overall coverage of applied logic.
Category: Mathematics

Computational Aspects Of Linear Logic

Author : Patrick Denis Lincoln
ISBN : STANFORD:36105002333081
Genre : Logic, Symbolic and mathematical
File Size : 50.34 MB
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Category: Logic, Symbolic and mathematical

Observers And Macroeconomic Systems

Author : Ric D. Herbert
ISBN : 0792382390
Genre : Business & Economics
File Size : 20.30 MB
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Observers and Macroeconomic Systems is concerned with the computational aspects of using a control-theoretic approach to the analysis of dynamic macroeconomic systems. The focus is on using a separate model for the development of the control policies. In particular, it uses the observer-based approach whereby the separate model learns to behave in a similar manner to the economic system through output-injections. The book shows how this approach can be used to learn the forward-looking behaviour of economic actors which is a distinguishing feature of dynamic macroeconomic models. It also shows how it can be used in conjunction with low-order models to undertake policy analysis with a large practical econometric model. This overcomes some of the computational problems arising from using just the large econometric models to compute optimal policy trajectories. The work also develops visual simulation software tools that can be used for policy analysis with dynamic macroeconomic systems.
Category: Business & Economics

Piecewise Linear Control Systems

Author : Mikael K.-J. Johansson
ISBN : 9783540368014
Genre : Technology & Engineering
File Size : 44.86 MB
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2. Piecewise Linear Modeling . . . . . . . . . . . . . . . . . . . . . 9 2. 1 Model Representation . . . . . . . . . . . . . . . . . . . . . 9 2. 2 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . 2. 3 Uncertainty Models . . . . . . . . . . . . . . . . . . . . . . 2. 4 Modularity and Interconnections . . . . . . . . . . . . . . 26 2. 5 Piecewise Linear Function Representations . . . . . . . . . 28 2. 6 Comments and References . . . . . . . . . . . . . . . . . . 30 3. Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3. 1 Equilibrium Points and the Steady State Characteristic . . 32 3. 2 Constraint Verification and Invariance . . . . . . . . . . . 35 3. 3 Detecting Attractive Sliding Modes on Cell Boundaries 37 3. 4 Comments and References . . . . . . . . . . . . . . . . . . 39 4. Lyapunov Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4. 1 Exponential Stability . . . . . . . . . . . . . . . . . . . . . . 41 4. 2 Quadratic Stability . . . . . . . . . . . . . . . . . . . . . . . 42 4. 3 Conservatism of Quadratic Stability . . . . . . . . . . . . . 46 4. 4 From Quadratic to Piecewise Quadratic . . . . . . . . . . . 48 4. 5 Interlude: Describing Partition Properties . . . . . . . . . 51 4. 6 Piecewise Quadratic Lyapunov Functions . . . . . . . . . 55 4. 7 Analysis of Piecewise Linear Differential Inclusions . . . . 61 4. 8 Analysis of Systems with Attractive Sliding Modes . . . . 63 4. 9 Improving Computational Efficiency . . . . . . . . . . . . 66 4. 10 Piecewise Linear Lyapunov Functions . . . . . . . . . . . 72 4. 11 A Unifying View . . . . . . . . . . . . . . . . . . . . . . . . 77 4. 12 Comments and References . . . . . . . . . . . . . . . . . . 82 5. Dissipativity Analysis . . . . . . . . . . . . . . . . . . . . . . . . 85 5. 1 Dissipativity Analysis via Convex Optimization . . . . . . 86 21 14 Contents Contents 5. 2 Computation of £2 induced Gain . . . . . . . . . . . . . . 88 5. 3 Estimation of Transient Energy . . . . . . . . . . . . . . . . 89 5. 4 Dissipative Systems with Quadratic Supply Rates . . . . . 91 5. 5 Comments and References . . . . . . . . . . . . . . . . . . 95 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6. 1 Quadratic Stabilization of Piecewise Linear" Systems . . . 97 6. 2 Controller Synthesis based on Piecewise Quadratics . . . 98 6. 3 Comments and References . . . . . . . . . . . . . . . . . . 105 7. Selected Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7. 1 Estimation of Regions of Attraction . . . . . . . . . . . . .
Category: Technology & Engineering

Materials Science Research In Japan

Author : DIANE Publishing Company
ISBN : 0788107089
Genre : Fuzzy systems
File Size : 47.76 MB
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Compilation of various summaries, overviews and reports on recent advances in high-technology science research in Japan.
Category: Fuzzy systems

Primer On Optimal Control Theory

Author : Jason L. Speyer
ISBN : 9780898716948
Genre : Mathematics
File Size : 29.26 MB
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A rigorous introduction to optimal control theory, which will enable engineers and scientists to put the theory into practice.
Category: Mathematics

Reduced Order Modelling For Flow Control

Author : Bernd R. Noack
ISBN : 9783709107584
Genre : Science
File Size : 25.45 MB
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The book focuses on the physical and mathematical foundations of model-based turbulence control: reduced-order modelling and control design in simulations and experiments. Leading experts provide elementary self-consistent descriptions of the main methods and outline the state of the art. Covered areas include optimization techniques, stability analysis, nonlinear reduced-order modelling, model-based control design as well as model-free and neural network approaches. The wake stabilization serves as unifying benchmark control problem.
Category: Science

Applied And Computational Control Signals And Circuits

Author : Biswa N. Datta
ISBN : 0817639543
Genre : Computers
File Size : 23.7 MB
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As the first volume in a new annual survey , Applied and Computational Control, Signals, and Circuits is an interdisciplinary publication which provides surveys, expository papers, algorithms, and software reviews. These volumes address significant new developments, applications, and computational methods in control, signal processing, circuit design and analysis. The goal is to provide authoritative and accessible accounts of the rapid development in computational engineering methods, applications, and algorithms. Each volume contains surveys and chapters representing a balance of coverage from the major areas of control, signals, and circuits. The contributions, selected by an editorial board comprised of leading researchers, contain all necessary background information and are extensive presentations of the topics. Topics and Features: Control, filtering, and systems identification Signal and image processing Circuit simulation Linear-control-systems software library, SLICOT Array algorithms Researchers, practitioners, and professionals in computer science, scientific computing, and engineering will find the volume essential for keeping abreast of the latest developments and for critically assessing new software tools. Table of Contents Chapter 1 Discrete Event Systems: The State of the Art and New Directions 1.1 Introduction 1.2 ES Modeling Framework 1.3 Review of the State of the Art in DES Theory 1.4 New Directions in DES Theory 1.5 Decentralized Control and Optimization 1.6 Failure Diagnosis 1.7 Nondeterministic Supervisory Control 1.8 Hybrid Systems and Optimal Control Chapter 2 Array Algorithms for H2 and H-Infinity Estimation 2.1 Introduction 2.2 H2 Square-Root Array Algorithms 2.3 H-Infinity Square-Root Array Algorithms 2.4 H2 Fast Array Algorithms 2.5 H-Infinity Fast Array Algorithms 2.6 Conclusion 2.A Unitary and Hyperbolic Rotations 2.B Krein Spaces Chapter 3 Non-uniqueness, Uncertainty and Complexity in Modeling 3.1 Introduction 3.2 Issues of Models and Modeling 3.3 Non-Uniqueness 3.4 Uncertainty 3.5 Complexity 3.6 Formulation of Model Set Identification 3.7 Learning or Optimization? 3.8 Conclusion Chapter 4 Iterative Learning Control - An Expository Overview 4.1 Introduction 4.2 Generic Description of ILC 4.3 Two Illustrative Examples of ILC Algorithms 4.4 The Literature, Context, Terminology of ILC 4.5 ILC Algorithms and Results 4.6 Example: Combining Some New ILC Approaches 4.7 Conclusion: The Past, Present, and Future of ILC Chapter 5 FIR Filter Design via Spectral Factorization and Convex Optimization 5.1 Introduction 5.2 Spectral factorization 5.3 Convex semi-infinite optimization 5.4 Lowpass filter design 5.5 Log-Chebychev approximation 5.6 Magnitude equalizer design 5.7 Linear antenna array weight design 5.8 Conclusions 5.A Appendix Chapter 6 Algorithms for Subspace State Space System Identification - An Overview 6.1 System identification: To measure is to know! 6.2 Linear subspace identification: an overview 6.3 Comparing PEM with subspace methods 6.4 Statistical consistency results 6.5 Extensions Chapter 7 Iterative Solution Methods for Large Linear Discrete Illposed Problems 7.1 Introduction 7.2 Krylov subspace iterative methods 7.3 Tikhonov regulariztion 7.4 An exponential filter function 7.5 Iterative methods based on implicitly defined filter functions 7.6 Towards a black box 7.7 Computed examples Chapter 8 Wavelet-Based Image Coding: An Overview 8.1 Introduction 8.2 Quantization 8.3 Transform Coding 8.4 Wavelets: A Different Perspective 8.5 A Basic Wavelet Image Coder 8.6 Extending the Transform Coder Paradigm 8.7 Zerotree Coding 8.8 Frequency, space-frequency adaptive coders 8.9 Utilizing Intra-band Dependencies 8.10 Future Trends 8.11 Summary and Conclusion Chapter 9 Reduced-Order Modeling Techniques Based on Krylov Subspaces and their Use in Circuit Simulation 9.1 Introduction 9.2 Reduced-Order Modeling of Linear Dynamical Systems 9.3 Linear Systems in Circuit Simulation 9.4 Krylov Subspaces and Moment Modeling 9.5 The Lanczos Process 9.6 Lanczos-Based Reduced-Order Modeling 9.7 The Arnoldi Process 9.8 Arnoldi-Based Reduced-Order Modeling 9.9 Circuit-Noise Computations 9.10 Concluding Remarks Chapter 10 SLICOT - A Subroutine Library in Systems and Control Theory 10.1 Introduction 10.2 Why Do We Need More Than MATLAB Numerics? 10.3 Retrospect 10.4 The Design of SLICOT 10.5 Contents of SLICOT 10.6 Performance Results 10.7 The Future - NICONET 10.8 Concluding Remarks 10.A Contents of SLICOT Release 3.0 10.B Electronic Access to the Library and Related Literature
Category: Computers

Manoeuvring And Control Of Marine Craft 2003 Mcmc 2003

Author : Joan Batlle
ISBN : 0080440339
Genre : Transportation
File Size : 80.13 MB
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The papers presented in this volume cover recent progress in applications of new theory on manoeuvring-related problems for surface ships and control and sensor problems for underwater vehicles.
Category: Transportation

Nonparametric Kernel Density Estimation And Its Computational Aspects

Author : Artur Gramacki
ISBN : 9783319716886
Genre : Computers
File Size : 64.59 MB
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This book describes computational problems related to kernel density estimation (KDE) – one of the most important and widely used data smoothing techniques. A very detailed description of novel FFT-based algorithms for both KDE computations and bandwidth selection are presented. The theory of KDE appears to have matured and is now well developed and understood. However, there is not much progress observed in terms of performance improvements. This book is an attempt to remedy this. The book primarily addresses researchers and advanced graduate or postgraduate students who are interested in KDE and its computational aspects. The book contains both some background and much more sophisticated material, hence also more experienced researchers in the KDE area may find it interesting. The presented material is richly illustrated with many numerical examples using both artificial and real datasets. Also, a number of practical applications related to KDE are presented.
Category: Computers

Analysis And Design Of Nonlinear Control Systems

Author : Daizhan Cheng
ISBN : 9783642115509
Genre : Science
File Size : 64.99 MB
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"Analysis and Design of Nonlinear Control Systems" provides a comprehensive and up to date introduction to nonlinear control systems, including system analysis and major control design techniques. The book is self-contained, providing sufficient mathematical foundations for understanding the contents of each chapter. Scientists and engineers engaged in the field of Nonlinear Control Systems will find it an extremely useful handy reference book. Dr. Daizhan Cheng, a professor at Institute of Systems Science, Chinese Academy of Sciences, has been working on the control of nonlinear systems for over 30 years and is currently a Fellow of IEEE and a Fellow of IFAC, he is also the chairman of Technical Committee on Control Theory, Chinese Association of Automation.
Category: Science

Optimal Control And Estimation

Author : Robert F. Stengel
ISBN : 9780486134819
Genre : Mathematics
File Size : 43.48 MB
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Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing application of basic concepts to real problems.
Category: Mathematics

Damped Oscillations Of Linear Systems

Author : Krešimir Veselić
ISBN : 9783642213342
Genre : Language Arts & Disciplines
File Size : 62.81 MB
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The theory of linear damped oscillations was originally developed more than hundred years ago and is still of vital research interest to engineers, mathematicians and physicists alike. This theory plays a central role in explaining the stability of mechanical structures in civil engineering, but it also has applications in other fields such as electrical network systems and quantum mechanics. This volume gives an introduction to linear finite dimensional damped systems as they are viewed by an applied mathematician. After a short overview of the physical principles leading to the linear system model, a largely self-contained mathematical theory for this model is presented. This includes the geometry of the underlying indefinite metric space, spectral theory of J-symmetric matrices and the associated quadratic eigenvalue problem. Particular attention is paid to the sensitivity issues which influence numerical computations. Finally, several recent research developments are included, e.g. Lyapunov stability and the perturbation of the time evolution.
Category: Language Arts & Disciplines