Linear Systems : Optimal and Robust Control

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. 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 o 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 o 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 Front cover; Contents; Chapter 1. Introduction; Chapter 2. State Space Description of a Linear System; Chapter 3. State Feedback Control and Optimization; Chapter 4. Control with Estimated States; Chapter 5. Robust Control: Fundamental Concepts and H, H, and Techniques; Chapter 6. Robust Control: Sliding Mode Methods; References; Appendix A: Linear Algebraic Equations, Eigenvalues/ Eigenvectors, and Matrix Inversion Lemma; Appendix B: Quadratic Functions, Important Derivatives, Fourier Integrals, and Parseval's Relation ; Appendix C: Norms, Singular Values, Supremum, and Infinimum Appendix D: Stochastic ProcessesAppendix E: Optimization of a Scalar Function with Constraints in the Form of a Symmetric Real Matrix Equal to Zero (Zhou et al., 1996); Appendix F: A Flexible Tetrahedral Truss Structure; Appendix G: Space Shuttle Dynamics during Reentry (Doyle et al., 1986); Index; Back cover Appendix G: Space Shuttle Dynamics during Reentry INDEX Exercises appear at the end of each chapter