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.- 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 63 2.5.1 Controller Structure.- 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.- 3.3 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.- 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.- 4.3 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.- 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.- 6Design 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.- 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.- References.