Introduction to Nonlinear Control

Stability, Control Design, and Estimation

Inbunden, Engelska, 2023

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An introductory text on the analysis, control, and estimation of nonlinear systems, appropriate for advanced undergraduate and graduate studentsThis self-contained and accessible introduction to the concepts and techniques used for nonlinear feedback systems offers a holistic treatment suitable for use in both advanced undergraduate and graduate courses; students need only some familiarity with differential equations and linear algebra to understand the material presented. The text begins with an overview of stability and Lyapunov methods for nonlinear systems, with Lyapunov’s second method revisited throughout the book as a connective thread. Other introductory chapters cover linear systems, frequency domain methods, and discrete-time systems. Building on this background material, the book provides a broad introduction to the basic ideas underpinning major themes of research in nonlinear control, including input-to-state stability, sliding mode control, adaptive control, feedback linearization, and robust output regulation. Chapters also cover observer design and estimation for nonlinear systems. The text is notable for its coverage of nonlinear model predictive control and its introduction to the use of linear matrix inequalities and semidefinite programming coupled with their use in modern antiwindup designs.• First text on nonlinear control appropriate for undergraduates• Suitable both for students preparing for rigorous graduate study and for those entering technical fields outside of academia• Unique in its coverage of recent research topics• Pedagogical features including extensive chapter summaries, examples, and appendixes with definitions, results, and MATLAB applications

Produktinformation

Utgivningsdatum2023-06-27
Mått178 x 254 x 37 mm
Vikt1 270 g
FormatInbunden
SpråkEngelska
Antal sidor552
FörlagPrinceton University Press
ISBN9780691240480

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PrefaceGlossaryI Dynamical Systems1 Nonlinear Systems—Fundamentals and Examples1.1 State Space Models1.1.1 Notational Conventions1.1.2 Rescaling1.1.3 Comparison Functions1.2 Control Loops, Controller Design, and Examples1.2.1 The Pendulum on a Cart1.2.2 Mobile Robots—The Nonholonomic Integrator1.3 Exercises1.4 Bibliographical Notes and Further Reading2 Nonlinear Systems—Stability Notions2.1 Stability Notions2.1.1 Local versus Global Properties2.1.2 Time-Varying Systems2.2 Comparison Principle2.3 Stability by Lyapunov’s Second Method2.3.1 Time-Varying Systems2.3.2 Instability2.3.3 Partial Convergence and the LaSalle-Yoshizawa Theorem2.4 Region of Attraction2.5 Converse Theorems2.5.1 Stability2.6 Invariance Theorems2.6.1 Krasovskii-LaSalle Invariance Theorem2.6.2 Matrosov’s Theorem2.7 Exercises2.8 Bibliographical Notes and Further Reading3 Linear Systems and Linearization3.1 Linear Systems Review3.1.1 Stability Properties for Linear Systems3.1.2 Quadratic Lyapunov Functions3.2 Linearization3.3 Time-Varying Systems3.4 Numerical calculation of Lyapunov functions3.4.1 Linear Matrix Inequalities and Semidefinite Programming3.4.2 Global Lyapunov Functions for Polynomial Systems3.4.3 Local Lyapunov Functions for Polynomial Systems3.4.4 Estimation of the Region of Attraction3.5 Systems with Inputs3.5.1 Controllability and Observability3.5.2 Stabilizability and Detectability3.5.3 Pole Placement3.6 Exercises3.7 Bibliographical Notes and Further Reading4 Frequency Domain Analysis4.1 Fundamental Results in the Frequency Domain4.1.1 The Laplace Transform4.1.2 The Transfer Function4.1.3 The ℒ2-, ℒ∞- and ℋ∞-norm4.2 Stability Analysis in the Frequency Domain4.2.1 Bounded-Input, Bounded-Output Stability4.2.2 System Interconnections in the Frequency Domain4.2.3 The Bode Plot4.2.4 The Nyquist Criterion4.3 Exercises4.4 Bibliographical Notes and Further Reading5 Discrete Time Systems5.1 Discrete Time Systems—Fundamentals5.2 Sampling: From Continuous to Discrete Time5.2.1 Discretization of Linear Systems5.2.2 Higher Order Discretization Schemes5.3 Stability Notions5.3.1 Lyapunov Characterizations5.3.2 Linear Systems5.3.3 Stability Preservation of Discretized Systems5.4 Controllability and Observability5.5 Exercises5.6 Bibliographical Notes and Further Reading6 Absolute Stability6.1 A Commonly Ignored Design Issue6.2 Historical Perspective on the Lur’e Problem6.3 Sufficient Conditions for Absolute Stability6.3.1 Circle Criterion6.3.2 Popov Criterion6.3.3 Circle versus Popov Criterion6.4 Exercises6.5 Bibliographical Notes and Further Reading7 Input-to-State Stability7.1 Motivation and Definition7.2 Lyapunov Characterizations7.3 System Interconnections7.3.1 Cascade Connections7.3.2 Feedback Interconnections7.4 Integral-to-Integral Estimates and ℒ2-Gain7.4.1 System interconnections7.5 Integral ISS and Nonlinear ℒ2-Gain7.6 Dissipativity and Passivity7.7 Exercises7.8 Bibliographical Notes and Further ReadingII Controller Design8 LMI-Based Controller and Antiwindup Designs8.1 ℒ2-Gain Optimization for Linear Systems8.1.1 Asymptotic Stability and ℒ2-Gain Optimization8.1.2 Feedback Synthesis8.2 Systems with Saturation8.2.1 LMI-Based Saturated Linear State Feedback Design8.2.2 Global Asymptotic Stability Analysis8.2.3ℒ2-Stability and ℒ2-Gain Optimization8.3 Regional Analysis8.3.1 Local Asymptotic Stability8.3.2ℒ2-Stability and ℒ2-Gain Optimization8.4 Antiwindup Synthesis8.4.1 Global Antiwindup Synthesis8.4.2 Well-Posedness of the Control Law8.4.3 Regional Antiwindup Synthesis8.5 Exercises8.6 Bibliographical Notes and Further Reading9 Control Lyapunov Functions9.1 Control Affine Systems9.2 ISS Redesign via LgV Damping9.3 Sontag’s Universal Formula9.4 Backstepping9.4.1 Avoiding Cancellations9.4.2 Exact Backstepping and a High-Gain Alternative9.4.3 Convergence Structure9.5 Forwarding9.5.1 Forwarding mod LgV9.5.2 Convergence Structure9.5.3 Saturated Control9.6 Stabilizability and Control Lyapunov Functions9.6.1 Existence of Lipschitz Continuous Feedback Laws9.6.2 Nonsmooth Control Lyapunov Functions9.6.3 Robustness and Discontinuous Feedback Laws9.7 Exercises9.8 Bibliographical Notes and Further Reading10 Sliding Mode Control10.1 Finite-Time Stability10.2 Basic Sliding Mode Control10.2.1 Terminology10.2.2 Chattering and Chattering Avoidance10.3 A More General Structure10.4 Estimating the Disturbance10.5 Output Tracking10.6 Exercises10.7 Bibliographical Notes and Further Reading11 Adaptive Control11.1 Motivating Examples and Challenges11.1.1 Limitations of Static Feedback Laws11.1.2 Estimation-Based Controller Designs11.2 Model Reference Adaptive Control11.3 Adaptive Control for Nonlinear Systems11.3.1 Adaptive Backstepping11.3.2 Tuning Function Designs11.3.3 Application: Single Link Manipulator with Flexible Joint11.4 Exercises11.5 Bibliographical Notes and Further Reading12 Introduction to Differential Geometric Methods12.1 Introductory Examples12.2 Zero Dynamics and Relative Degree12.3 Feedback Linearization12.3.1 Nonlinear Controllability12.3.2 Input-to-State Linearization12.4 Exercises12.5 Bibliographical Notes and Further Reading13 Output Regulation13.1 Linear Output Regulation13.2 Robust Linear Output Regulation13.3 Nonlinear Output Regulation13.4 Exercises13.5 Bibliographical Notes and Further Reading14 Optimal Control14.1 Optimal Control—Continuous Time Setting14.1.1 Linear Quadratic Regulator14.1.2 Control-Affine Nonlinear Systems14.1.3 Inverse Optimality14.2 Optimal Control—Discrete Time Setting14.2.1 Definitions and Notations14.2.2 The Linear Quadratic Regulator14.3 From Infinite- to Finite-Dimensional Optimization14.3.1 The Principle of Optimality14.3.2 Constrained Optimal Control for Linear Systems14.3.3 Dynamic Programming and the Backward Recursion14.4 Exercises14.5 Bibliographical Notes and Further Reading15 Model Predictive Control15.1 The Basic MPC Formulation15.2 MPC Closed-Loop Analysis15.2.1 Performance Estimates15.2.2 Closed-Loop Stability Properties15.2.3 Viability and Recursive Feasibility15.2.4 Hard and Soft Constraints15.3 Model Predictive Control Schemes15.3.1 Time-Varying Systems and Reference Tracking15.3.2 Linear MPC versus Nonlinear MPC15.3.3 MPC without Terminal Costs and Constraints15.3.4 Explicit MPC15.3.5 Economic MPC15.3.6 Tube-Based MPC15.4 Implementation Aspects of MPC15.4.1 Warm-Start and Suboptimal MPC15.4.2 Formulation of the Optimization Problem15.5 Exercises15.6 Bibliographical Notes and Further ReadingIII Observer Design and Estimation16 Observer Design for Linear Systems16.1 Luenberger Observers16.2 Minimum Energy Estimator (Continuous Time Setting)16.3 The Discrete Time Kalman Filter16.3.1 Least Squares and Minimum Variance Solution16.3.2 A Prediction-Correction Formulation16.3.3 The Steady-State Kalman Filter16.3.4 A Hybrid Time Kalman Filter16.4 Exercises16.5 Bibliographical Notes and Further Reading17 Extended and Unscented Kalman Filter and Moving Horizon Estimation17.1 Extended Kalman Filter (Continuous Time)17.2 Extended Kalman Filter (Discrete Time)17.3 Unscented Kalman Filter (Discrete Time)17.3.1 Unscented Transformation17.3.2 Unscented Kalman Filter17.4 Moving Horizon Estimation17.5 Exercises17.6 Bibliographical Notes and Further Reading18 Observer Design for Nonlinear Systems18.1 High-Gain Observers18.1.1 Convergence Properties of High-Gain Observers18.1.2 Examples18.1.3 Extension to Multi-Output Systems18.2 Sliding Mode Observers18.2.1 Sliding Mode Observers for Linear Systems18.2.2 Nonlinear Systems18.3 Exercises18.4 Bibliographical Notes and Further ReadingAppendixAppendix A: Fundamental Definitions and ResultsA.1 Norms in Vector and Function SpacesA.2 Auxiliary ResultsA.3 Selection of Comparison Function ResultsA.4 Barbalat’s LemmaA.5 Convexity and Convex OptimizationA.6 Probability TheoryAppendix B: MATLAB ImplementationsB.1 Solving (Nonlinear) Dynamical Systems in MatlabB.2 Linear SystemsB.3 CVXB.3.1 Linear Matrix InequalitiesB.3.2 Convex Optimization ProblemsB.4 SOSTOOLSB.5 CASADIBibliographyIndex