Nonlinear H2/H-Infinity Constrained Feedback Control: A Practical Design Approach Using Neural Networks

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Springer Science & Business Media, Aug 2, 2006 - Technology & Engineering - 204 pages
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The series Advances in Industrial Control aims to report and encourage technology transfer in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. New theory, new controllers, actuators, sensors, new industrial processes, computer methods, new applications, new philosophies , new challenges. Much of this development work resides in industrial reports, feasibility study papers and the reports of advanced collaborative projects. The series offers an opportunity for researchers to present an extended exposition of such new work in all aspects of industrial control for wider and rapid dissemination. Almost all physical systems are nonlinear and the success of linear control techniques depends on the extent of the nonlinear system behaviour and the careful attention given to switching linear controllers through the range of nonlinear system operations. In many industrial and process-control applications, good engineering practice, linear control systems and classical PID control can give satisfactory performance because the process nonlinearity is mild and the control system performance specification is not particularly demanding; however, there are other industrial system applications where the requirement for high-performance control can only be achieved if nonlinear control design techniques are used. Thus, in some industrial and technological domains there is a strong justification for more applications of nonlinear methods. One prevailing difficulty with nonlinear control methods is that they are not so easily understood nor are they easy to reduce to formulaic algorithms for routine application.
 

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Contents

Preliminaries and Introduction
1
112 Discretetime Nonlinear Systems
2
12 Stability of Nonlinear Systems
3
121 Lyapunov Stabiltity of Continuoustime Nonlinear Systems
4
13 Dissipativity of Nonlinear Systems
8
131 Dissipativity of Continuoustime Nonlinear Systems
9
132 Dissipativity of Discretetime Nonlinear Systems
12
14 Optimal Control of Nonlinear Systems
14
36 Policy Iterations Without Solving the LEVu
75
37 Bibliographical Notes
76
Policy Iterations and Nonlinear H Constrained State Feedback Control
77
42 Policy Iterations and the Nonlinear Bounded Real Lemma
78
43 L2gain of Nonlinear Control Systems with Input Saturation
83
44 The HJI Equation and the Saddle Point
86
45 Solving the HJI Equation Using Policy Iterations
90
Nearly H Optimal Neural Network Control for ConstrainedInput Systems
95

142 Discretetime HJB Equation
17
15 Policy Iterations and Optimal Control
18
151 Policy Iterations and H2 Optimal Control
19
152 Policy Iterations and the Bounded Real Lemma
21
16 Zerosum Games of Nonlinear Systems
23
162 Linear Quadratic Zerosum Games and H0 Optimal Control
25
163 Discretetime HJI Equation
26
17 Neural Networks and Function Approximation
28
172 Function Approximation Theorems
30
18 Bibliographical Notes
31
Policy Iterations and Nonlinear H2 Constrained State Feedback Control
32
22 Optimal Regulation of Systems with Actuator Saturation
34
23 Policy Iterations for ConstrainedInput Systems
37
24 Nonquadratic Performance Functionals for Minimumtime and Constrained States Control
41
25 Bibliographical Notes
42
Nearly H2 Optimal Neural Network Control for ConstrainedInput Systems
43
32 Convergence of the Method of Least Squares to the Solution of the LEVu
45
33 Convergence of the Method of Least Squares to the Solution of the HJB Equation
52
Introducing a Mesh in Rn
54
35 Numerical Examples
56
352 Nonlinear Oscillator with Constrained Input
62
353 Constrained State Linear System
65
354 Minimumtime Control
68
355 Parabolic Tracker
71
51 Neural Network Representation of Policies
96
52 Stability and Convergence of Least Squares Neural Network Policy Iterations
100
The Nonlinear Benchmark Problem
104
54 Bibliographical Notes
113
Taylor Series Approach to Solving HJI Equation
115
62 Power Series Solution of HJI Equation
118
63 Explicit Expression for Hk
126
64 The Disturbance Attenuation of RTAC System
135
65 Bibliographical Notes
146
An Algorithm to Solve Discrete HJI Equations Arising from Discrete Nonlinear H Control Problems
147
72 Taylor Series Solution of Discrete HamiltonJacobiIsaacs Equation
151
73 Disturbance Attenuation of Discretized RTAC System
164
74 Computer Simulation
172
H Static Output Feedback
176
82 Intermediate Mathematical Analysis
178
83 Coupled HJ Equations for H Static Output Feedback Control
182
84 Existence of Static Output Feedback Game Theoretic Solution
185
85 Iterative Solution Algorithm
187
86 H Static Output Feedback Design for F16 Normal Acceleration Regulator
188
87 Bibliographical Notes
192
References
193
Index
201
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About the author (2006)

Frank Lewis is a Professor of Electrical Engineering at The University of Texas at Arlington, where he was awarded the Moncrief-O'Donnell Endowed Chair in 1990 at the Automation and Robotics Research Institute. He is a Fellow of the IEEE, a member of the New York Academy of Sciences, and a registered Professional Engineer in the State of Texas. He is a Charter Member (2004) of the UTA Academy of Distinguished Scholars. He has served as Visiting Professor at Democritus University in Greece, Hong Kong University of Science and Technology, Chinese University of Hong Kong, National University of Singapore. He is an elected Guest Consulting Professor at both Shanghai Jiao Tong University and South China University of Technology.

Dr. Lewis’s current interests include intelligent control, neural and fuzzy systems, microelectromechanical systems (MEMS), wireless sensor networks, nonlinear systems, robotics, condition-based maintenance, and manufacturing process control. He is the author/co-author of 3 U.S. patents, 157 journal papers, 23 chapters and encyclopedia articles, 239 refereed conference papers, nine books, including Optimal Control, Optimal Estimation, Applied Optimal Control and Estimation, Aircraft Control and Simulation, Control of Robot Manipulators, Neural Network Control, High-Level Feedback Control with Neural Networks and the IEEE reprint volume Robot Control. He was elected to the Editorial Boards of International Journal of Control, Neural Computing and Applications, and Int. J. Intelligent Control Systems. He served as an Editor for the flagship journal Automatica. He is the recipient of an NSF Research Initiation Grant and has been continuously funded by NSF since 1982. Since 1991 he has received $4.8 million in funding from NSF and other government agencies, including significant DoD SBIR and industry funding and his research has won numerous awards and prizes

Doctor Huang is a professor at the Department of Automation and Computer-aided Engineering, The Chinese University of Hong Kong. He is also the director of Applied Control and Computing Laborotory, and the head of the graduate division of Automation and Computer-aided Engineering. He has been advisory/visiting professor at several universities and a Science Advisor to the Leisure and Cultural Services Department of Hong Kong Special Administrative Region. His research interests include control theory and applications, robotics and automation, neural networks and scientific computing, and guidance and control of flight vehicles. His research has led to publications of over 100 technical papers in international journals and conferences, and four book chapters.

Dr. Huang is a member of Editorial Board of Communications in Information and Systems, Control Theory and Applications, and Associate Editor of IEEE Transactions on Automatic Control. He was an Associate Editor of the Asian Journal of Control between 1999 and 2001. He has been Guest Editor for International Journal of Robust and Nonlinear Control, and Asian Journal of Control. He has served in the organizing committee or program committee of various major international conferences including the general chair of 2002 International Conference on Control and Automation, Publicity Chair of 2003 IEEE Conference on Decision and Control, and program committee member of the 1998, and 2002 IEEE Conferences on Decision and Control.

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