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E-raamat: Model-Reference Adaptive Control: A Primer

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Model-Reference Adaptive Control: A PrimerSuurem pilt
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This textbook provides readers with a good working knowledge of adaptive control theory through applications. It is intended for students beginning masters or doctoral courses, and control practitioners wishing to get up to speed in the subject expeditiously.

Readers are taught a wide variety of adaptive control techniques starting with simple methods and extending step-by-step to more complex ones. Stability proofs are provided for all adaptive control techniques without obfuscating reader understanding with excessive mathematics.

The book begins with standard model-reference adaptive control (MRAC) for first-order, second-order, and multi-input, multi-output systems. Treatment of least-squares parameter estimation and its extension to MRAC follow, helping readers to gain a different perspective on MRAC. Function approximation with orthogonal polynomials and neural networks, and MRAC using neural networks are also covered.

Robustness issues connected with MRAC are discussed, helping the student to appreciate potential pitfalls of the technique. This appreciation is encouraged by drawing parallels between various aspects of robustness and linear time-invariant systems wherever relevant.

Following on from the robustness problems is material covering robust adaptive control including standard methods and detailed exposition of recent advances, in particular, the author’s work on optimal control modification. Interesting properties of the new method are illustrated in the design of adaptive systems to meet stability margins. This method has been successfully flight-tested on research aircraft, one of various flight-control applications detailed towards the end of the book along with a hybrid adaptive flight control architecture that combines direct MRAC with least-squares indirect adaptive control. In addition to the applications, understanding is encouraged by the use of end-of-chapter exercises and associated MATLAB® files; an electronic solutions manual for instructors can be downloaded from http://extras.springer.com.

Readers will need no more than the standard mathematics for basic control theory such as differential equations and matrix algebra; the book covers the foundations of MRAC and the necessary mathematical preliminaries.

MATLAB® files supplied to assist in working through exercises and examples. Solutions manual pdf.

Arvustused

This book presents the fundamental theories of least-squares function approximation and least-squares adaptive control of systems with unstructured uncertainty. The book is intended for students beginning masters or doctoral courses, and control practitioners wishing to get up to speed in the subject expeditiously. (Vjacheslav Vasiliev, zbMATH 1405.93001, 2019)

1 Introduction 1(16)
1.1 Overview
2(4)
1.2 Verification and Validation Challenges for Adaptive Flight Control Systems
6(3)
1.2.1 Verification by Simulation of Adaptive Flight Control Systems
7(1)
1.2.2 Adaptive Control Metrics
8(1)
1.3 Summary
9(1)
References
9(8)
2 Nonlinear Systems 17(14)
2.1 Equilibrium and Linearization
21(3)
2.2 Local Stability and Phase Plane Analysis
24(3)
2.3 Other Nonlinear Behaviors
27(1)
2.4 Summary
28(1)
2.5 Exercises
29(1)
Reference
30(1)
3 Mathematical Preliminaries 31(16)
3.1 Vector and Matrix Norms
31(6)
3.1.1 Vector Norms
31(4)
3.1.2 Matrix Norms
35(2)
3.2 Compact Set
37(1)
3.3 Existence and Uniqueness
38(3)
3.3.1 Cauchy Theorem
38(1)
3.3.2 Global Lipschitz Condition
39(1)
3.3.3 Local Lipschitz Condition
40(1)
3.4 Positive Definite, Symmetric and Anti-Symmetric Matrices
41(4)
3.4.1 Positive-Definite Matrix and Function
41(2)
3.4.2 Anti-Symmetric Matrix
43(2)
3.5 Summary
45(1)
3.6 Exercises
45(2)
4 Lyapunov Stability Theory 47(36)
4.1 Stability Concepts
48(4)
4.1.1 Stability Definition
49(1)
4.1.2 Asymptotic Stability
50(1)
4.1.3 Exponential Stability
51(1)
4.2 Lyapunov's Direct Method
52(17)
4.2.1 Motivation
52(5)
4.2.2 Lyapunov Theorem for Local Stability
57(3)
4.2.3 Lyapunov Theorem for Exponential Stability
60(1)
4.2.4 Radially Unbounded Functions
61(1)
4.2.5 Barbashin-Krasovskii Theorem for Global Asymptotic Stability
61(2)
4.2.6 LaSalle's Invariant Set Theorem
63(4)
4.2.7 Differential Lyapunov Equation
67(2)
4.3 Stability of Non-Autonomous Systems
69(9)
4.3.1 Uniform Stability
70(1)
4.3.2 Uniform Boundedness
71(3)
4.3.3 Barbalat's Lemma
74(4)
4.4 Summary
78(1)
4.5 Exercises
78(3)
References
81(2)
5 Model-Reference Adaptive Control 83(42)
5.1 Composition of a Model-Reference Adaptive Control System
86(4)
5.1.1 Uncertain Plant
86(2)
5.1.2 Reference Model
88(1)
5.1.3 Controller
89(1)
5.1.4 Adaptive Law
89(1)
5.2 Direct MRAC for First-Order SISO Systems
90(5)
5.2.1 Case I: a and b Unknown but Sign of b Known
90(3)
5.2.2 Case II: a and b Known
93(2)
5.3 Indirect MRAC for First-Order SISO Systems
95(4)
5.4 Direct MRAC for Second-Order SISO Systems
99(7)
5.4.1 Case I: A and B Unknown but Sign of b known
99(6)
5.4.2 Case II: A and B Known
105(1)
5.5 Indirect MRAC for Second-Order SISO Systems
106(4)
5.6 Direct MRAC for MIMO Systems
110(8)
5.6.1 Case I: A and Λ Unknown, but B and Sign of A Known
111(6)
5.6.2 Case II: A, B, Λ = I Known
117(1)
5.7 Indirect MRAC for MIMO Systems
118(2)
5.8 Summary
120(1)
5.9 Exercises
121(2)
References
123(2)
6 Least-Squares Parameter Identification 125(26)
6.1 Least-Squares Regression
126(2)
6.2 Convex Optimization and Least-Squares Gradient Method
128(2)
6.3 Persistent Excitation and Parameter Convergence
130(4)
6.4 Recursive Least-Squares
134(3)
6.5 Indirect Adaptive Control with Least-Squares Parameter Identification
137(9)
6.6 Estimation of Time Derivative Signals
146(1)
6.7 Summary
147(1)
6.8 Exercises
148(1)
References
149(2)
7 Function Approximation and Adaptive Control with Unstructured Uncertainty 151(34)
7.1 Polynomial Approximation by Least-Squares
152(2)
7.2 Neural Network Approximation
154(5)
7.3 Adaptive Control with Unstructured Uncertainty
159(23)
7.3.1 Recursive Least-Squares Direct Adaptive Control with Matrix Inversion
160(4)
7.3.2 Modified Recursive Least-Squares Direct Adaptive Control without Matrix Inversion
164(4)
7.3.3 Least-Squares Gradient Direct Adaptive Control
168(5)
7.3.4 Least-Squares Gradient Direct Adaptive Control with Neural Network Approximation
173(2)
7.3.5 MRAC with Neural Network Approximation
175(7)
7.4 Summary
182(1)
7.5 Exercises
183(1)
References
184(1)
8 Robustness Issues with Adaptive Control 185(24)
8.1 Parameter Drift
186(4)
8.2 Non-minimum Phase Systems
190(3)
8.3 Time-Delay Systems
193(2)
8.4 Unmodeled Dynamics
195(5)
8.5 Fast Adaptation
200(5)
8.6 Summary
205(1)
8.7 Exercises
206(1)
References
207(2)
9 Robust Adaptive Control 209(140)
9.1 Dead-Zone Method
212(1)
9.2 Projection Method
213(7)
9.3 σ Modification
220(8)
9.4 e Modification
228(6)
9.5 Optimal Control Modification
234(27)
9.5.1 Optimal Control
234(6)
9.5.2 Derivation of Optimal Control Modification
240(7)
9.5.3 Lyapunov Stability Analysis
247(7)
9.5.4 Linear Asymptotic Property
254(7)
9.6 Adaptive Loop Recovery Modification
261(6)
9.7 L1 Adaptive Control
267(7)
9.8 Normalization
274(6)
9.9 Covariance Adjustment of Adaptation Rate
280(6)
9.10 Optimal Control Modification for Systems with Control Input Uncertainty
286(5)
9.11 Bi-Objective Optimal Control Modification for Systems with Control Input Uncertainty
291(16)
9.12 Adaptive Control for Singularly Perturbed Systems with First-Order Slow Actuator Dynamics
307(7)
9.13 Optimal Control Modification for Linear Uncertain Systems with Unmodeled Dynamics
314(8)
9.14 Adaptive Control of Non-Minimum Phase Plants with Relative Degree 1
322(17)
9.14.1 Minimum Phase Plant
323(2)
9.14.2 Non-Minimum Phase Plant
325(14)
9.15 Summary
339(1)
9.16 Exercises
340(5)
References
345(4)
10 Aerospace Applications 349(82)
10.1 Inverted Pendulum
351(3)
10.2 Double Pendulum in Robotic Applications
354(5)
10.3 Adaptive Control of Aircraft Longitudinal Dynamics
359(7)
10.4 Recursive Least-Squares and Neural Network Pitch Attitude Adaptive Flight Control
366(8)
10.5 Adaptive Control of Flexible Aircraft
374(11)
10.6 Adaptive Linear Quadratic Gaussian Flutter Suppression Control
385(21)
10.7 Adaptive Flight Control
406(8)
10.8 Hybrid Adaptive Flight Control
414(3)
10.9 Adaptive Flight Control for F-18. Aircraft with Optimal Control Modification
417(8)
10.10 Summary
425(1)
10.11 Exercises
426(1)
References
427(4)
Suggested Exam Questions 431(10)
Index 441
Dr. Nhan Nguyen is a research scientist at NASA Ames Research Center with 29 years of experience. He is the technical group leader of the Advanced Control and Evolvable Systems research group in the Intelligent Systems Division. He directs and leads 20 researchers, half hold Ph.D. degrees. He served as the NASA project scientist of the NASA Integrated Resilient Aircraft Control Project which had an annual budget of $21 million and a 90-person workforce, and funded 24 research grants in adaptive control to leading researchers in the field from 2007 to 2010. He currently leads a 16-person project team to conduct the development of an advanced aircraft control technology. He has published over 160 peer-reviewed technical publications including 120 publications in control theory and applications and three book chapters. He is the reviewer for many journals including IEEE Transaction on Automatic Control, AIAA Journal of Guidance Dynamics and Control, International Journal of Robustand Nonlinear Control, Automatica, and many others. He received several prestigious awards and medals including NASA Exceptional Scientific Achievement Medal, NASA Exceptional Achievement Medal, two-time NASA Ames Honors for Excellence as Engineer, NASA Space Act Award, and 30 other caeer awards. He holds one U.S. patent, and three patents pending. He has 10 other invention disclosures. He developed several innovative adaptive control methods in the 2000s, one of which was peer-reviewed and selected by NASA for flight-testing on NASA F/A-18A research aircraft. NASA only flight-tested two other adaptive control technologies previously: one on NASA X-15 aircraft in the 1960s and the other on NASA F-15 aircraft in the 2000s. He is the incoming chair of the American Institute of Aeronautics and Astronautics (AIAA) Intelligent Systems Technical Committee. He was the conference general chair of AIAA Infotech@Aerospace in 2012. He received an AIAA Distinguished Services Award. He is an adjunct professor at Santa Clara University where he teaches adaptive control, flight dynamics, and advanced dynamics, and aeroelasticity. He received the Lecturer-of-the-Year Award.  
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