Cover -- Title Page -- Copyright -- Contents -- Series Preface -- Preface -- Chapter 1 Introduction -- 1.1 Feedback Control of Dynamic Systems -- 1.1.1 Feedback -- 1.1.2 Why Do We Need Feedback? -- 1.2 The Parameter Identification Problem -- 1.2.1 Identifying a System -- 1.3 A Brief Survey on Parameter Identification -- 1.4 The State Estimation Problem -- 1.4.1 Observers -- 1.4.2 Reconstructing the State via Time Derivative Estimation -- 1.5 Algebraic Methods in Control Theory: Differences from Existing Methodologies -- 1.6 Outline of the Book -- References -- Chapter 2 Algebraic Parameter Identification in Linear Systems -- 2.1 Introduction -- 2.1.1 The Parameter-Estimation Problem in Linear Systems -- 2.2 Introductory Examples -- 2.2.1 Dragging an Unknown Mass in Open Loop -- 2.2.2 A Perturbed First-Order System -- 2.2.3 The Visual Servoing Problem -- 2.2.4 Balancing of the Plane Rotor -- 2.2.5 On the Control of the Linear Motor -- 2.2.6 Double-Bridge Buck Converter -- 2.2.7 Closed-Loop Behavior -- 2.2.8 Control of an unknown variable gain motor -- 2.2.9 Identifying Classical Controller Parameters -- 2.3 A Case Study Introducing a "Sentinel'' Criterion -- 2.3.1 A Suspension System Model -- 2.4 Remarks -- References -- Chapter 3 Algebraic Parameter Identification in Nonlinear Systems -- 3.1 Introduction -- 3.2 Algebraic Parameter Identification for Nonlinear Systems -- 3.2.1 Controlling an Uncertain Pendulum -- 3.2.2 A Block-Driving Problem -- 3.2.3 The Fully Actuated Rigid Body -- 3.2.4 Parameter Identification Under Sliding Motions -- 3.2.5 Control of an Uncertain Inverted Pendulum Driven by a DC Motor -- 3.2.6 Identification and Control of a Convey Crane -- 3.2.7 Identification of a Magnetic Levitation System.

3.3 An Alternative Construction of the System of Linear Equations -- 3.3.1 Genesio-Tesi Chaotic System -- 3.3.2 The Ueda Oscillator -- 3.3.3 Identification and Control of an Uncertain Brushless DC Motor -- 3.3.4 Parameter Identification and Self-tuned Control for the Inertia Wheel Pendulum -- 3.3.5 Algebraic Parameter Identification for Induction Motors -- 3.3.6 A Criterion to Determine the Estimator Convergence: The Error Index -- 3.4 Remarks -- References -- Chapter 4 Algebraic Parameter Identification in Discrete-Time Systems -- 4.1 Introduction -- 4.2 Algebraic Parameter Identification in Discrete-Time Systems -- 4.2.1 Main Purpose of the Chapter -- 4.2.2 Problem Formulation and Assumptions -- 4.2.3 An Introductory Example -- 4.2.4 Samuelson's Model of the National Economy -- 4.2.5 Heating of a Slab from Two Boundary Points -- 4.2.6 An Exact Backward Shift Reconstructor -- 4.3 A Nonlinear Filtering Scheme -- 4.3.1 Hénon System -- 4.3.2 A Hard Disk Drive -- 4.3.3 The Visual Servo Tracking Problem -- 4.3.4 A Shape Control Problem in a Rolling Mill -- 4.3.5 Algebraic Frequency Identification of a Sinusoidal Signal by Means of Exact Discretization -- 4.4 Algebraic Identification in Fast-Sampled Linear Systems -- 4.4.1 The Delta-Operator Approach: A Theoretical Framework -- 4.4.2 Delta-Transform Properties -- 4.4.3 A DC Motor Example -- 4.5 Remarks -- References -- Chapter 5 State and Parameter Estimation in Linear Systems -- 5.1 Introduction -- 5.1.1 Signal Time Derivation Through the "Algebraic Derivative Method'' -- 5.1.2 Observability of Nonlinear Systems -- 5.2 Fast State Estimation -- 5.2.1 An Elementary Second-Order Example -- 5.2.2 An Elementary Third-Order Example -- 5.2.3 A Control System Example -- 5.2.4 Control of a Perturbed Third-Order System -- 5.2.5 A Sinusoid Estimation Problem.

5.2.6 Identification of Gravitational Wave Parameters -- 5.2.7 A Power Electronics Example -- 5.2.8 A Hydraulic Press -- 5.2.9 Identification and Control of a Plotter -- 5.3 Recovering Chaotically Encrypted Signals -- 5.3.1 State Estimation for a Lorenz System -- 5.3.2 State Estimation for Chen's System -- 5.3.3 State Estimation for Chua's Circuit -- 5.3.4 State Estimation for Rossler's System -- 5.3.5 State Estimation for the Hysteretic Circuit -- 5.3.6 Simultaneous Chaotic Encoding-Decoding with Singularity Avoidance -- 5.3.7 Discussion -- 5.4 Remarks -- References -- Chapter 6 Control of Nonlinear Systems via Output Feedback -- 6.1 Introduction -- 6.2 Time-Derivative Calculations -- 6.2.1 An Introductory Example -- 6.2.2 Identifying a Switching Input -- 6.3 The Nonlinear Systems Case -- 6.3.1 Control of a Synchronous Generator -- 6.3.2 Control of a Multi-variable Nonlinear System -- 6.3.3 Experimental Results on a Mechanical System -- 6.4 Remarks -- References -- Chapter 7 Miscellaneous Applications -- 7.1 Introduction -- 7.1.1 The Separately Excited DC Motor -- 7.1.2 Justification of the ETEDPOF Controller -- 7.1.3 A Sensorless Scheme Based on Fast Adaptive Observation -- 7.1.4 Control of the Boost Converter -- 7.2 Alternative Elimination of Initial Conditions -- 7.2.1 A Bounded Exponential Function -- 7.2.2 Correspondence in the Frequency Domain -- 7.2.3 A System of Second Order -- 7.3 Other Functions of Time for Parameter Estimation -- 7.3.1 A Mechanical System Example -- 7.3.2 A Derivative Approach to Demodulation -- 7.3.3 Time Derivatives via Parameter Identification -- 7.3.4 Example -- 7.4 An Algebraic Denoising Scheme -- 7.4.1 Example -- 7.4.2 Numerical Results -- 7.5 Remarks -- References -- Appendix A Parameter Identification in Linear Continuous Systems: A Module Approach -- A.1 Generalities on Linear Systems Identification.

A.1.1 Example -- A.1.2 Some Definitions and Results -- A.1.3 Linear Identifiability -- A.1.4 Structured Perturbations -- A.1.5 The Frequency Domain Alternative -- References -- Appendix B Parameter Identification in Linear Discrete Systems: A Module Approach -- B.1 A Short Review of Module Theory over Principal Ideal Ring -- B.1.1 Systems -- B.1.2 Perturbations -- B.1.3 Dynamics and Input-Output Systems -- B.1.4 Transfer Matrices -- B.1.5 Identifiability -- B.1.6 An Algebraic Setting for Identifiability -- B.1.7 Linear identifiability of transfer functions -- B.1.8 Linear Identification of Perturbed Systems -- B.1.9 Persistent Trajectories -- References -- Appendix C Simultaneous State and Parameter Estimation: An Algebraic Approach -- C.1 Rings, Fields and Extensions -- C.2 Nonlinear Systems -- C.2.1 Differential Flatness -- C.2.2 Observability and Identifiability -- C.2.3 Observability -- C.2.4 Identifiable Parameters -- C.2.5 Determinable Variables -- C.3 Numerical Differentiation -- C.3.1 Polynomial Time Signals -- C.3.2 Analytic Time Signals -- C.3.3 Noisy Signals -- References -- Appendix D Generalized Proportional Integral Control -- D.1 Generalities on GPI Control -- D.2 Generalization to MIMO Linear Systems -- References -- Index.