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.- 1.5 Software Availability for Example Problems.- 2 Basic Theory of Simple Adaptive Control.- 2.1 Model Following.- 2.2 Output Model Following.- 2.3 Stability and Positivity Concepts.- 2.4 Adaptive Control Based on CGT.- 2.5 The Adaptive Algorithm with General Input Commands.- 2.6 Summary of Adaptive Algorithms.- Appendix 2A Proof of Theorem 2.1.- Appendix 2B Proof of Theorem 2.2.- Appendix 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.- 3.3 Feedforward in Both Plant and Model.- 3.4 A Unified Approach to Supplementary Dynamics.- 3.5 Adaptive Control in the Presence of Nonlinearities.- 3.6 Summary.- Appendix 3A Proof of Positivity Lemmas.- Appendix 3B Proof of Theorem 3.1.- Appendix 3C Proof of Theorem 3.2.- Appendix 3D Proof of Theorem 3.3.- Appendix 3E Proof of Theorem 3.4.- Appendix 3F Outline of Proof of Theorem 3.5.- 4 Robust Design Procedures.- 4.1 Introduction.- 4.2 Robust Redesign of the Basic Adaptive Algorithm.- 4.3 Robustness Considerations with Feedforward in the Reference Model.- 4.4 Robust Redesign for Supplementary Dynamics.- 4.5 Bursting Phenomena and Their Elimination.- 4.6 Summary.- Appendix 4A Proof of Robust Stability, Theorem 4.1.- Appendix 4B Development of Lyapunov Function Derivative.- Appendix 4C Proof of Theorem 4.2.- 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 Passivity and Almost Passivity of Nonlinear Systems.- 5.6 Simple Adaptive Control for a Class of Nonlinear Systems.- 5.7 Simple Adaptive Control of Rigid Robotic Manipulators.- 5.8 Summary.- Appendix 5A Proof of Stability for the Algorithm (5.27)-(5.32).- Appendix 5B Strictly Causal Almost Passive Systems.- Appendix 5C Proof of Lemma 5.1.- Appendix 5D Proof of Almost Passivity Lemma in Nonlinear Systems.- Appendix 5E Almost Passivity with Application to Manipulators.- Appendix 5F The Proof of Stability of the Adaptive Control Algorithm.- Appendix 5G Adaptive Control of Strictly Causal Almost Passive Systems.- 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.- Appendix 6A Proof of Theorem 6.1.- Appendix 6B Proof of Theorem 6.2.- Appendix 6C Proof of Lemma 6.1.- Appendix 6D Proof of Theorem 6.3.- 7 Case Studies.- 7.1 Direct Model Reference Adaptive Control of a PUMA Manipulator.- 7.2 Model Reference Adaptive Control of Large Structures.- 7.3 Adaptive Drug Delivery Control.- 7.4 Adaptive Control for a Relaxed Static Stability Aircraft.- 7.5 Liquid Level System Emulation.- References.