Adaptive Control Tutorial

Transcription

1 Adaptive Control Tutorial Petros loannou University of Southern California Los Angeles, California Baris Fidan National ICT Australia & Australian National University Canberra, Australian Capital Territory, Australia Slam. Society for Industrial and Applied Mathematics Philadelphia

2 Preface Acknowledgments Listof Acronyms xi xiii xv 1 Introduction Adaptive Control: Identifier-Based Adaptive Control: Non-Identifier-Based Gain Scheduling Multiple Models, Search Methods, and Switching Schemes Why Adaptive Control A Brief History 9 2 Parametric Models 13 Problems 22 3 Parameter Identification: Continuous Time Introduction Example: One-Parameter Case Example: Two Parameters Persistence of Excitation and Sufnciently Rieh Inputs Example: Vector Case Gradient Algorithms Based on the Linear Model Gradient Algorithm with Instantaneous Cost Function Gradient Algorithm with Integral Cost Function Least-Squares Algorithms Recursive LS Algonthm with Forgetting Factor Pure LS Algorithm Modified LS Algorithms Parameter Identification Based on DPM Parameter Identification Based on B-SPM Parameter Protection Robust Parameter Identification Instability Example 56 vii

3 VIII Dominantly Rieh Excitation Robust Adaptive Laws Dynamic Normalization Robust Adaptive Laws: cr-modification Parameter Projection DeadZone State-Space Identifiers Adaptive Observers Case Study: Users in a Single Bottleneck Link Computer Network.. 80 Problems 82 4 Parameter Identification: Discrete Time Introduction Discretization of Continuous-Time Adaptive Laws Discrete-Time Parametric Model Sufficiently Rieh Inputs Gradient Algorithms Projection Algorithm Gradient Algorithm Basedon Instantaneous Cost LS Algorithms Pure LS Modified LS Algorithms Parameter Identification Based on DPM Parameter Identification Based on B-SPM Parameter Projection Robust Parameter Identification Dominantly Rieh Excitation Robustness Modifications Parameter Projection Case Study: Online Parameter Estimation of Traffic Flow Characteristics 123 Problems Continuous-Time Model Reference Adaptive Control Introduction Simple MRAC Scheines Scalar Example: Adaptive Regulation Scalar Example: Direct MRAC without Normalization Scalar Example: Indirect MRAC without Normalization Scalar Example: Direct MRAC with Normalization Scalar Example: Indirect MRAC with Normalization VectorCase: Full-State Measurement MRC for SISO Plants Problem Statement MRC Schemes: Known Plant Parameters Direct MRAC with Unnormalized Adaptive Laws 158

4 IX Relative Degree n* = Relative Degree n* = Relative Degree Greater than Direct MRAC with Normalized Adaptive Laws IndirectMRAC Indirect MRAC with Unnormalized Adaptive Laws Indirect MRAC with Normalized Adaptive Law Robust MRAC MRC: Known Plant Parameters Robust Direct MRAC Case Study: Adaptive Cruise Control Design Case Study: Adaptive Attitüde Control ofa Spacecraft 193 Problems Continuous-Time Adaptive Pole Placement Control Introduction Simple APPC Schemes: Without Normalization Scalar Example: Adaptive Regulation Scalar Example: Adaptive Tracking APPC Schemes: Polynomial Approach APPC Schemes: State-Space Approach Adaptive Linear Quadratic Control (ALQC) Stabilizability Issues and Modified APPC Loss of Stabilizability: A Simple Example Modified APPC Schemes Robust APPC Schemes PPC: Known Parameters Robust Adaptive Laws for APPC Schemes Robust APPC: Polynomial Approach Case Study: ALQC Design for an F-16 Fighter Aircraft LQ Control Design with Gain Scheduling Adaptive LQ Control Design Simulations 246 Problems Adaptive Control for Discrete-Time Systems Introduction MRAC Scalar Example General Case: MRC Direct MRAC Indirect MRAC Adaptive Prediction and Control Adaptive One-Step-Ahead Control APPC 272 Problems 275

5 x 8 Adaptive Control of Nonlinear Systems Introduction Feedback Linearization Control Lyapunov Functions Backstepping Adaptive Backstepping with Tuning Functions Adaptive Backstepping with Nonlinear Damping: Modular Design Neuroadaptive Control Neural Networks for Identification Neuroadaptive Control Case Study: Adaptive Nonlinear Control ofa Path-Tracking Vehicle. 310 Problems 314 Appendix 319 A.l Systems Theory 319 A.2 Coprime Polynomials 321 A.3 Norms and C p Spaces 323 A.4 Properties of Functions and Matrices 326 A.5 Input/Output Stability 329 A.6 Bellman-Gronwall Lemma 333 A.7 Lyapunov Stability 334 A.7.1 Definition of Stability 334 A.7.2 Lyapunov's Direct Method 336 A.7.3 Lyapunov-Like Functions 339 A.7.4 Lyapunov's Indirect Method 340 A.8 Stability of Linear Systems 341 A.9 Positivity and Stability 345 A.10 Optimization Techniques 347 A.10.1 Notation and Mathematical Background 348 A.10.2 The Method of Steepest Descent (Gradient Method) A.10.3 Gradient Projection Method 350 A. 11 Swapping Lemmas 352 A.12 Discrete-Time Systems 354 A.12.1 Lyapunov Stability Theory 354 A.12.2 Positive Real Functions 361 A.l2.3 Stability ofperturbed Systems 363 A.12.4 I/O Stability 364 A.12.5 Swapping Lemmas 366 Problems 367 Bibliography 371 Index 385