488 Pages
134 B/W Illustrations
by
CRC Press
488 Pages
by
CRC Press
Also available as eBook on:
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... Read more
Introduction
Overview
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 H∞ Norms
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
H∞ Control
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 H∞ and Sliding Mode Methods
Sliding Mode Control of a Linear System with Estimated States
Optimal Sliding Mode Gaussian (OSG) Control
REFERENCES
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
INDEX
Exercises appear at the end of each chapter.
Overview
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 H∞ Norms
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
H∞ Control
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 H∞ and Sliding Mode Methods
Sliding Mode Control of a Linear System with Estimated States
Optimal Sliding Mode Gaussian (OSG) Control
REFERENCES
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
INDEX
Exercises appear at the end of each chapter.
Biography
Alok Sinha
