Direct Adaptive Control Algorithms:

1 Introduction.- 1.1 Definition of the Problem.- 1.2 Prologue to Simple Adaptive Control.- 1.3 Background on Adaptive Control Algorithms.- 1.4 Objectives and Overview.- 1.4.1 Objectives.- 1.4.2 Relation with Other Texts.- 1.4.3 Overview of Text.- 2 Basic Theory of Simple Adaptive Control.- 2.1 Model Following.- 2.2 Output Model Following.- 2.2.1 Command Generator Tracker Description.- 2.2.2 Modifications for the Tracking of A Larger Class of Input Commands.- 2.2.3 The General Tracking Problem.- 2.3 Stability and Positivity Concepts.- 2.3.1 Introduction: Stability with Fixed Controllers Versus Nonlinear Adaptive Controllers.- 2.3.2 Basic Stability Concepts.- 2.3.3 Positive Real Analysis.- 2.4 Adaptive Control Based on CGT.- 2.4.1 Controller Structure.- 2.4.2 Stability Analysis.- 2.4.3 System Constraints.- 2.4.4 An Illustrative Example.- 2.5 The Adaptive Algorithm with General Input Commands 63 2.5.1 Controller Structure.- 2.5.2 Stability Analysis.- 2.5.3 An Illustrative Example.- 2.6 Summary of Adaptive Algorithms.- 2A Proof of Theorem 2.1.- 2B Proof of Theorem 2.2.- 2C Poles, Zeros and Relative Degree in Multivariable Systems.- 3 Extensions of the Basic Adaptive Algorithm.- 3.1 Parallel Feedforward and Stability Considerations.- 3.2 Feedforward Around Plant.- 3.2.1 Adaptive Control with Basic Feedforward Augmentation.- 3.2.2 Summary of MRAC Using Plant Feedforward.- 3.2.3 Illustrative Examples.- 3.3 Feedforward in Both Plant and Model.- 3.3.1 Modifications to Insure Asymptotic Model Following.- 3.3.2 Stability Proof.- 3.3.3 Summary of Constraints and Design Rules Ill.- 3.3.4 Illustrative Examples.- 3.3.5 Conclusions and Recommendations.- 3.4 A Unified Approach to Supplementary Dynamics.- 3.4.1 Theory.- 3.4.2 Summary of Constraints and Design Rules.- 3.4.3 Illustrative Examples.- 3.5 Adaptive Control in the Presence of Nonlinearities.- 3.5.1 Theory.- 3.5.2 Adaptation for Nonlinearity of Known Form.- 3.6 Summary.- 3A Proof of Positivity Lemmas.- 3B Proof of Theorem 3.1.- 3C Proof of Theorem 3.2.- 3D Proof of Theorem 3.3.- 3E Proof of Theorem 3.4.- 4 Robust Design Procedures.- 4.1 Introduction.- 4.2 Robust Redesign of the Basic Adaptive Algorithm.- 4.2.1 Algorithm Description.- 4.2.2 Illustrative Examples.- 4.3 Robustness Considerations with Feedforward in the Reference Model.- 4.3.1 Algorithm Description.- 4.3.2 Illustrative Examples.- 4.4 Robust Redesign for Supplementary Dynamics.- 4.4.1 Algorithm Description.- 4.4.2 Error System Equations.- 4.4.3 Stability Analysis.- 4.4.4 Illustrative Examples.- 4.5 Bursting Phenomena and Their Elimination.- 4.6 Summary.- 4A Proof of Robust Stability, Theorem 1.- 4B Development of Lyapunov Function Derivative.- 4C Proof of Theorem 2.- 5 Adaptive Control of Time—Varying and Nonlinear Systems.- 5.1 Introduction.- 5.2 Passivity and Almost Passivity of Nonstationary Systems.- 5.3 Adaptive Control of ASP Plants.- 5.4 The “Almost Passivity” Lemmas.- 5.5 Adaptive Control of Nonlinear Systems.- 5A Proof of Stability for the Algorithm (5.27)–(5.32).- 5B Strictly Causal Almost Passive Systems.- 5C Proof of Lemma 1.- 6 Design of Model Reference Adaptive Controllers.- 6.1 Algorithm Overview.- 6.2 Constraint Satisfaction.- 6.3 Weight Selection.- 6.4 Reference Model Selection.- 6.5 Digital Implementation.- 6.6 Time Varying Commands.- 6.6.1 Command Generated as Output of Linear System.- 6.6.2 Command Variations Slow Compared with Reference Model.- 7 Case Studies.- 7.1 Direct Model Reference Adaptive Control of a PUMA Manipulator.- 7.1.1 Introduction.- 7.1.2 Puma Model Development.- 7.1.3 Implementation Issues.- 7.1.4 Simulation Results.- 7.1.5 Experimental Results.- 7.1.6 Conclusions and Recommendations.- 7.2 Model Reference Adaptive Control of Large Structures.- 7.2.1 Introduction.- 7.2.2 Large Flexible Structures (LFS) Dynamics.- 7.2.3 The ASPR Condition for Flexible Structures.- 7.2.4 Adaptive Control Algorithm.- 7.2.5 Experimental Set-Up.- 7.2.6 Experiment Results and Discussion.- 7.3 Adaptive Drug Delivery Control.- 7.3.1 Introduction.- 7.3.2 Problem Statement.- 7.3.3 Controller Design.- 7.3.4 Operation of the Complete Hierarchical Controller.- 7.3.5 Experimental Results.- 7.3.6 Conclusions.- 7.4 Adaptive Control for a Relaxed Static Stability Aircraft.- 7.4.1 Introduction.- 7.4.2 Model Development.- 7.4.3 Control Law Development.- 7.4.4 Conclusions.- References.