Singular Perturbation Methodology in Control Systems

Singular Perturbation Methodology in Control Systems
Author: Desineni S. Naidu
Publisher: IET
Total Pages: 314
Release: 1988
Genre: Technology & Engineering
ISBN: 9780863411076

This book presents the twin topics of singular perturbation methods and time scale analysis to problems in systems and control. The heart of the book is the singularly perturbed optimal control systems, which are notorious for demanding excessive computational costs. The book addresses both continuous control systems (described by differential equations) and discrete control systems (characterised by difference equations).

Singular Perturbation Methods in Control

Singular Perturbation Methods in Control
Author: Petar Kokotovic
Publisher: SIAM
Total Pages: 386
Release: 1999-01-01
Genre: Mathematics
ISBN: 9781611971118

Singular perturbations and time-scale techniques were introduced to control engineering in the late 1960s and have since become common tools for the modeling, analysis, and design of control systems. In this SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications. This book continues to be essential in many ways. It lays down the foundation of singular perturbation theory for linear and nonlinear systems, it presents the methodology in a pedagogical way that is not available anywhere else, and it illustrates the theory with many solved examples, including various physical examples and applications. So while new developments may go beyond the topics covered in this book, they are still based on the methodology described here, which continues to be their common starting point.

Singular Perturbation Theory

Singular Perturbation Theory
Author: Lindsay A. Skinner
Publisher: Springer Science & Business Media
Total Pages: 95
Release: 2011-05-11
Genre: Mathematics
ISBN: 1441999582

This book is a rigorous presentation of the method of matched asymptotic expansions, the primary tool for attacking singular perturbation problems. A knowledge of conventional asymptotic analysis is assumed. The first chapter introduces the theory and is followed by four chapters of applications to ordinary differential equation problems of increasing complexity. Exercises are included as well as several Maple programs for computing the terms of the various asymptotic expansions that arise in solving the problems.

Continuous-Time Markov Chains and Applications

Continuous-Time Markov Chains and Applications
Author: G. George Yin
Publisher: Springer Science & Business Media
Total Pages: 442
Release: 2012-11-14
Genre: Mathematics
ISBN: 1461443466

This book gives a systematic treatment of singularly perturbed systems that naturally arise in control and optimization, queueing networks, manufacturing systems, and financial engineering. It presents results on asymptotic expansions of solutions of Komogorov forward and backward equations, properties of functional occupation measures, exponential upper bounds, and functional limit results for Markov chains with weak and strong interactions. To bridge the gap between theory and applications, a large portion of the book is devoted to applications in controlled dynamic systems, production planning, and numerical methods for controlled Markovian systems with large-scale and complex structures in the real-world problems. This second edition has been updated throughout and includes two new chapters on asymptotic expansions of solutions for backward equations and hybrid LQG problems. The chapters on analytic and probabilistic properties of two-time-scale Markov chains have been almost completely rewritten and the notation has been streamlined and simplified. This book is written for applied mathematicians, engineers, operations researchers, and applied scientists. Selected material from the book can also be used for a one semester advanced graduate-level course in applied probability and stochastic processes.

Perturbation Methods in Optimal Control

Perturbation Methods in Optimal Control
Author: Alain Bensoussan
Publisher: Wiley
Total Pages: 588
Release: 1988-06-23
Genre: Mathematics
ISBN: 9780471919940

Describes, analyzes, and generalizes the principal results concerning perturbation methods in optimal control for systems governed by deterministic or stochastic differential equations. Covers the most important theorems in deterministic and stochastic optimal control, the theory of ergodic control, and the use of control, including regular perturbations and singular perturbations.

Introduction to Perturbation Methods

Introduction to Perturbation Methods
Author: Mark H. Holmes
Publisher: Springer Science & Business Media
Total Pages: 344
Release: 2013-12-01
Genre: Mathematics
ISBN: 1461253470

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.

Design of Nonlinear Control Systems with the Highest Derivative in Feedback

Design of Nonlinear Control Systems with the Highest Derivative in Feedback
Author: Valery D. Yurkevich
Publisher: World Scientific
Total Pages: 374
Release: 2004
Genre: Technology & Engineering
ISBN: 9812388990

This unique book presents an analytical uniform design methodology of continuous-time or discrete-time nonlinear control system design which guarantees desired transient performances in the presence of plant parameter variations and unknown external disturbances. All results are illustrated with numerical simulations, their practical importance is highlighted, and they may be used for real-time control system design in robotics, mechatronics, chemical reactors, electrical and electro-mechanical systems as well as aircraft control systems. The book is easy reading and is suitable for teaching.

Perturbation Methods

Perturbation Methods
Author: E. J. Hinch
Publisher: Cambridge University Press
Total Pages: 178
Release: 1991-10-25
Genre: Mathematics
ISBN: 9780521378970

A textbook presenting the theory and underlying techniques of perturbation methods in a manner suitable for senior undergraduates from a broad range of disciplines.

Feedback Control Theory

Feedback Control Theory
Author: John C. Doyle
Publisher: Courier Corporation
Total Pages: 264
Release: 2013-04-09
Genre: Technology & Engineering
ISBN: 0486318338

An excellent introduction to feedback control system design, this book offers a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems. Its explorations of recent developments in the field emphasize the relationship of new procedures to classical control theory, with a focus on single input and output systems that keeps concepts accessible to students with limited backgrounds. The text is geared toward a single-semester senior course or a graduate-level class for students of electrical engineering. The opening chapters constitute a basic treatment of feedback design. Topics include a detailed formulation of the control design program, the fundamental issue of performance/stability robustness tradeoff, and the graphical design technique of loopshaping. Subsequent chapters extend the discussion of the loopshaping technique and connect it with notions of optimality. Concluding chapters examine controller design via optimization, offering a mathematical approach that is useful for multivariable systems.

Symmetry and Perturbation Theory

Symmetry and Perturbation Theory
Author: Simonetta Abenda
Publisher: World Scientific
Total Pages: 306
Release: 2002
Genre: Mathematics
ISBN: 9812795405

This is the fourth conference on OC Supersymmetry and Perturbation TheoryOCO (SPT 2002). The proceedings present original results and state-of-the-art reviews on topics related to symmetry, integrability and perturbation theory, etc. Contents: An Outline of the Geometrical Theory of the Separation of Variables in the Hamilton-Jacobi and SchrAdinger Equations (S Benenti); Partial Symmetries and Symmetric Sets of Solutions to PDE's (G Cicogna); On the Algebro-Geometric Solution of 3 x 3 Matrix Riemann-Hilbert Problem (V Enolski & T Grava); Bifurcations in Flow-Induced Vibration (S Fatimah & F Verhulst); Steklov-Lyapunov Type Systems (Yu N Fedorov); Renormalization Group and Summation of Divergent Series for Hyperbolic Invariant Tori (G Gentile); On the Linearization of Holomorphic Vector Fields in the Siegel Domain with Linear Parts Having Nontrivial Jordan Blocks (T Gramchev); Smooth Normalization of a Vector Field Near an Invariant Manifold (A Kopanskii); Inverse Problems for SL (2) Lattices (V B Kuznetsov); Some Remarks about the Geometry of Hamiltonian Conservation Laws (J-P Ortega); Janet's Algorithm (W Plesken); Some Integrable Billiards (E Previato); Symmetries of Relative Equilibria for Simple Mechanical Systems (M Rodr guez-Olmos & M E Sousa Dias); A Spectral Sequences Approach to Normal Forms (J A Sanders); Rational Parametrization of Strata in Orbit Spaces of Compact Linear Groups (G Sartori & G Valente); Effective Hamiltonians and Perturbation Theory for Quantum Bound States of Nuclear Motion in Molecules (V G Tyuterev); Generalized Hasimoto Transformation and Vector Sine-Gordon Equation (J P Wang); and other papers. Readership: Researchers and graduate students in mathematical and theoretical physics, and nonlinear science."