Linear Systems : Optimal and Robust Control book cover
1st Edition

Linear Systems
Optimal and Robust Control

ISBN 9780849392177
Published January 31, 2007 by CRC Press
488 Pages 134 B/W Illustrations

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Book Description

Balancing rigorous theory with practical applications, Linear Systems: Optimal and Robust Control explains the concepts behind linear systems, optimal control, and robust control and illustrates these concepts with concrete examples and problems.

Developed as a two-course book, this self-contained text first discusses linear systems, including controllability, observability, and matrix fraction description. Within this framework, the author develops the ideas of state feedback control and observers. He then examines optimal control, stochastic optimal control, and the lack of robustness of linear quadratic Gaussian (LQG) control. The book subsequently presents robust control techniques and derives H control theory from the first principle, followed by a discussion of the sliding mode control of a linear system. In addition, it shows how a blend of sliding mode control and H methods can enhance the robustness of a linear system.

By learning the theories and algorithms as well as exploring the examples in Linear Systems: Optimal and Robust Control, students will be able to better understand and ultimately better manage engineering processes and systems.

Table of Contents

Contents of the Book
State Space Description of a Linear System
Transfer Function of a Single Input/Single Output (SISO) System
State Space Realizations of a SISO System
SISO Transfer Function from a State Space Realization
Solution of State Space Equations
Observability and Controllability of a SISO System
Some Important Similarity Transformations
Simultaneous Controllability and Observability
Multiinput/Multioutput (MIMO) Systems
State Space Realizations of a Transfer Function Matrix
Controllability and Observability of a MIMO System
Matrix-Fraction Description (MFD)
MFD of a Transfer Function Matrix for the Minimal Order of a State Space Realization
Controller Form Realization from a Right MFD
Poles and Zeros of a MIMO Transfer Function Matrix
Stability Analysis
State Feedback Control and Optimization
State Variable Feedback for a Single Input System
Computation of State Feedback Gain Matrix for a Multiinput System
State Feedback Gain Matrix for a Multiinput System for Desired Eigenvalues and Eigenvectors
Fundamentals of Optimal Control Theory
Linear Quadratic Regulator (LQR) Problem
Solution of LQR Problem via Root Locus Plot: SISO Case
Linear Quadratic Trajectory Control
Frequency-Shaped LQ Control
Minimum-Time Control of a Linear Time-Invariant System
Control with Estimated States
Open-Loop Observer
Closed-Loop Observer
Combined Observer–CONTROLLER
Reduced-Order Observer
Response of a Linear Continuous-Time System to White Noise
Kalman Filter: Optimal State Estimation
Stochastic Optimal Regulator in Steady State
Linear Quadratic Gaussian (LQG) Control
Impact of Modeling Errors on Observer-Based Control
Robust Control: Fundamental Concepts and H2, H, and μ Techniques
Important Aspects of Singular Value Analysis
Robustness: Sensitivity and Complementary Sensitivity
Robustness of LQR and Kalman Filter (KF) Feedback Loops
LQG/LTR Control
H2 and HNorms
H2 Control
Well-Posedness, Internal Stability, and Small Gain Theorem
Formulation of Some Robust Control Problems with Unstructured Uncertainties
Formulation of Robust Control Problems with Structured Uncertainties
Loop Shaping
Controller Based on μ Analysis
Robust Control: Sliding Mode Methods
Basic Concepts of Sliding Modes
Sliding Mode Control of a Linear System with Full State Feedback
Sliding Mode Control of an Uncertain Linear System with Full State Feedback: Blending Hand Sliding Mode Methods
Sliding Mode Control of a Linear System with Estimated States
Optimal Sliding Mode Gaussian (OSG) Control
Appendix A: Linear Algebraic Equations, Eigenvalues/Eigenvectors, and Matrix Inversion Lemma
System of Linear Algebraic Equations
Eigenvalues and Eigenvectors
Matrix Inversion Lemma
Appendix B: Quadratic Functions, Important Derivatives, Fourier Integrals, and Parseval’s Relation
Quadratic Functions
Derivative of a Quadratic Function
Derivative of a Linear Function
Fourier Integrals and Parseval’s Theorem
Appendix C: Norms, Singular Values, Supremum, and Infinimum
Vector Norms
Matrix Norms
Singular Values of a Matrix
Singular Value Decomposition (SVD)
Properties of Singular Values
Supremum and Infinimum
Appendix D: Stochastic Processes
Stationary Stochastic Process
Power Spectrum or Power Spectral Density (PSD)
White Noise: A Special Stationary Stochastic Process
Response of a SISO Linear and Time-Invariant System Subjected to a Stationary Stochastic Process
Vector Stationary Stochastic Processes
Appendix E: Optimization of a Scalar Function with Constraints in the Form of a Symmetric Real Matrix Equal to Zero
Appendix F: A Flexible Tetrahedral Truss Structure
Appendix G: Space Shuttle Dynamics during Reentry
Exercises appear at the end of each chapter.

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