Download or read book Computational Methods for Linear Control Systems written by Petko Hr. Petkov and published by . This book was released on 1991-01-01 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Computational Aspects of Linear Control written by Claude Brezinski and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Numerical Methods for Linear Control Systems written by Biswa Datta and published by Elsevier. This book was released on 2004-02-24 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods for Linear Control Systems Design and Analysis is an interdisciplinary textbook aimed at systematic descriptions and implementations of numerically-viable algorithms based on well-established, efficient and stable modern numerical linear techniques for mathematical problems arising in the design and analysis of linear control systems both for the first- and second-order models. Unique coverage of modern mathematical concepts such as parallel computations, second-order systems, and large-scale solutions Background material in linear algebra, numerical linear algebra, and control theory included in text Step-by-step explanations of the algorithms and examples

Download or read book Linear Multivariable Control Systems written by Shankar P. Bhattacharyya and published by Cambridge University Press. This book was released on 2022-01-13 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: This rigorous yet accessible textbook provides broad and systematic coverage of linear multivariable control systems, including several new approaches to design. In addition to standard state space theory, it provides a new measurement-based approach to linear systems, including a generalization of Thevenin's Theorem, a new single-input single-output approach to multivariable control, and analytical design of PID controllers developed by the authors. Each result is rigorously proved and combined with specific control systems applications, such as the servomechanism problem, the fragility of high order controllers, multivariable control, and PID controllers. Illustrative examples solved using MATLAB and SIMULINK, with easily reusable programming scripts, are included throughout. Numerous end-of-chapter homework problems enhance understanding. Based on course-tested material, this textbook is ideal for a single or two-semester graduate course on linear multivariable control systems in aerospace, chemical, electrical and mechanical engineering.

Download or read book Computational Methods for Linear Integral Equations written by Prem Kythe and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Control Systems Design written by Vladimir Zakian and published by Springer Science & Business Media. This book was released on 2005-12-27 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent decades, a comprehensive new framework for the theory and design of control systems has emerged. It treats a range of significant and ubiquitous design problems more effectively than the conventional framework. Control Systems Design brings together contributions from the originators of the new framework in which they explain, expand and revise their research work. It is divided into four parts: - basic principles, including those of matching and inequalities with adjustments for robust matching and matching based on H-infinity methods and linear matrix inequalities; - computational methods, including matching conditions for transient inputs and design of a sampled-data control system; - search methods including search with simulated annealing, genetic algorithms and evaluation of the node array method; - case studies, including applications in distillation, benchmarking critical control of magnetic levitation systems and the use of the principle of matching in cruise control.

Download or read book Computational Methods for Approximation of Large Scale Dynamical Systems written by Mohammad Monir Uddin and published by CRC Press. This book was released on 2019-04-30 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: These days, computer-based simulation is considered the quintessential approach to exploring new ideas in the different disciplines of science, engineering and technology (SET). To perform simulations, a physical system needs to be modeled using mathematics; these models are often represented by linear time-invariant (LTI) continuous-time (CT) systems. Oftentimes these systems are subject to additional algebraic constraints, leading to first- or second-order differential-algebraic equations (DAEs), otherwise known as descriptor systems. Such large-scale systems generally lead to massive memory requirements and enormous computational complexity, thus restricting frequent simulations, which are required by many applications. To resolve these complexities, the higher-dimensional system may be approximated by a substantially lower-dimensional one through model order reduction (MOR) techniques. Computational Methods for Approximation of Large-Scale Dynamical Systems discusses computational techniques for the MOR of large-scale sparse LTI CT systems. Although the book puts emphasis on the MOR of descriptor systems, it begins by showing and comparing the various MOR techniques for standard systems. The book also discusses the low-rank alternating direction implicit (LR-ADI) iteration and the issues related to solving the Lyapunov equation of large-scale sparse LTI systems to compute the low-rank Gramian factors, which are important components for implementing the Gramian-based MOR. Although this book is primarly aimed at post-graduate students and researchers of the various SET disciplines, the basic contents of this book can be supplemental to the advanced bachelor's-level students as well. It can also serve as an invaluable reference to researchers working in academics and industries alike. Features: Provides an up-to-date, step-by-step guide for its readers. Each chapter develops theories and provides necessary algorithms, worked examples, numerical experiments and related exercises. With the combination of this book and its supplementary materials, the reader gains a sound understanding of the topic. The MATLAB® codes for some selected algorithms are provided in the book. The solutions to the exercise problems, experiment data sets and a digital copy of the software are provided on the book's website; The numerical experiments use real-world data sets obtained from industries and research institutes.

Download or read book Optimization of Linear Control Systems written by F A Aliev and published by CRC Press. This book was released on 1998-11-19 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present analytical methods for synthesis of linear stationary and periodical optimal controlled systems, and create effective computational algorithms for synthesis of optimal regulators and filters. The procedures of Youla-Jabr-Bongiorno (1976) and Desoer-Lin-Murray-Saeks (1980) are special cases of this procedure. The monograph also includes original computational algorithms (solutions of usual and generalized Lyapunov and Riccati equations, polynomial matrix factorization) and illustrates the effectiveness of these algorithms by examples in the field of numerical methods for optimization of linear controlled systems.

Download or read book Piecewise Linear Control Systems written by Mikael K.-J. Johansson and published by Springer. This book was released on 2003-07-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 . . . . . . . . . . . . .

Download or read book Computational Methods for Inverse Problems written by Curtis R. Vogel and published by SIAM. This book was released on 2002-01-01 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.

Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.

Download or read book Numerical Methods and Applications written by Todor Boyanov and published by Springer Science & Business Media. This book was released on 2007-02-20 with total page 741 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the 6th International Conference on Numerical Methods and Applications, NMA 2006, held in Borovets, Bulgaria, in August 2006. The 84 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 111 submissions. The papers are organized in topical sections on numerical methods for hyperbolic problems, robust preconditioning solution methods, Monte Carlo and quasi-Monte Carlo for diverse applications, metaheuristics for optimization problems, uncertain/control systems and reliable numerics, interpolation and quadrature processes, large-scale computations in environmental modelling, and contributed talks.

Download or read book Linear State Space Control Systems written by Robert L. Williams, II and published by John Wiley & Sons. This book was released on 2007-02-09 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book blends readability and accessibility common to undergraduate control systems texts with the mathematical rigor necessary to form a solid theoretical foundation. Appendices cover linear algebra and provide a Matlab overivew and files. The reviewers pointed out that this is an ambitious project but one that will pay off because of the lack of good up-to-date textbooks in the area.

Download or read book Computational Methods for Controller Design written by Nicola Elia and published by Springer. This book was released on 2014-03-12 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph is concerned with computational methods for controller design that allow several typical performance specifications to be directly imposed on a system. The general approach proposed, is applicable to a large class of problems; it is based on posing multi-objective control problems as convex infinite dimensional optimization problems. Particularly interesting and useful are the following methodological as pects of the approach proposed in the monograph. These are: A unified way to pose the problems as generalized linear programs. Duality theory results that characterize the duality relationship for the generalized linear programs arising from multi-objective control problems. A set of tools to analyse the convergence properties of the computational method based on the duality relationship. The complete analysis and extension of methods developed for the L1 problem, for several important multi-objective problems. This book is primarily concerned with multi-objective control problems as convex optimizations on the space of the closed loop maps. However, the issue of deriving exact or approximate solutions is similar when the problems are posed as dynamic games in s tate space. Therefore the problem of finding the state feedback controller that minimizes the worst-case peak-to-peak amplification of the closed loop system, is considered in the last chapter. The objective of this work is to propose generic computation methods that can be used to solve a wide range of multi-objective control problems. Infinite dimensional convex optimization problems are considered, giving the book a broader focus than other competitive titles in this field. This non-exclusive approach will have a wide appeal for scientists and graduate students. They will be able to determine and analyse readily implementable computational methods to derive exact or approximate solutions. Key words for the catalogue index: Controller design, multi objective control, computational methods, linear programming, robust control.USPs:Generic computational methods are proposed - these can be used to solve a wide range of multi-objective control p roblems.A new computational method for the L1 problem is suggested, which is superior to existing approaches and is based on the solution of a mixed objective problem.The reader will greatly benefit from the comprehensive treatment of this topic.

Download or read book An Introduction to Linear Control Systems written by Thomas E. Fortmann and published by CRC Press. This book was released on 1977-10-01 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Linear Algebra Techniques for Systems and Control written by IEEE Control Systems Society and published by Piscataway, NJ : IEEE Press. This book was released on 1994 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: A reprint collection of practical papers covering the broad scope of numerical linear algebra in computer-aided control system design software. Between the 35-page introduction and extensive 21-page bibliography, are seven sections: general numerical issues in control; controllability, observability, and realizations; "closeness" problems; frequency response, transfer functions, poles, and zeros; pole assignment and observer design; Riccati, Lyapunov, and Sylvester equations; and some relevant results from numerical linear algebra. Annotation copyright by Book News, Inc., Portland, OR

Download or read book Computational Methods in Optimal Control Problems written by I.H. Mufti and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this modest report is to present in a simplified manner some of the computational methods that have been developed in the last ten years for the solution of optimal control problems. Only those methods that are based on the minimum (maximum) principle of Pontriagin are discussed here. The autline of the report is as follows: In the first two sections a control problem of Bolza is formulated and the necessary conditions in the form of the minimum principle are given. The method of steepest descent and a conjugate gradient-method are dis cussed in Section 3. In the remaining sections, the successive sweep method, the Newton-Raphson method and the generalized Newton-Raphson method (also called quasilinearization method) ar~ presented from a unified approach which is based on the application of Newton Raphson approximation to the necessary conditions of optimality. The second-variation method and other shooting methods based on minimizing an error function are also considered. TABLE OF CONTENTS 1. 0 INTRODUCTION 1 2. 0 NECESSARY CONDITIONS FOR OPTIMALITY •••••••• 2 3. 0 THE GRADIENT METHOD 4 3. 1 Min H Method and Conjugate Gradient Method •. •••••••••. . . . ••••••. ••••••••. • 8 3. 2 Boundary Constraints •••••••••••. ••••. • 9 3. 3 Problems with Control Constraints ••. •• 15 4. 0 SUCCESSIVE SWEEP METHOD •••••••••••••••••••• 18 4. 1 Final Time Given Implicitly ••••. •••••• 22 5. 0 SECOND-VARIATION METHOD •••••••••••••••••••• 23 6. 0 SHOOTING METHODS ••••••••••••••••••••••••••• 27 6. 1 Newton-Raphson Method ••••••••••••••••• 27 6.