Stable Adaptive Neural Network Control

by Ge, S. S.; Hang, Chang C.; Lee, T. H.; Zhang, T.

• ISBN13: 9780792375975
• ISBN10: 0792375971
• Format: Hardcover
• Copyright: 2001-10-01
• Publisher: Kluwer Academic Pub

Summary

While neural network control has been successfully applied in various practical applications, many important issues, such as stability, robustness, and performance, have not been extensively researched for neural adaptive systems. Motivated by the need for systematic neural control strategies for nonlinear systems, Stable Adaptive Neural Network Control offers an in-depth study of stable adaptive control designs using approximation-based techniques, and presents rigorous analysis for system stability and control performance. Both linearly parameterized and multi-layer neural networks (NN) are discussed and employed in the design of adaptive NN control systems for completeness. Stable adaptive NN control has been thoroughly investigated for several classes of nonlinear systems, including nonlinear systems in Brunovsky form, nonlinear systems in strict-feedback and pure-feedback forms, nonaffine nonlinear systems, and a class of MIMO nonlinear systems. In addition, the developed design methodologies are not only applied to typical example systems, but also to real application-oriented systems, such as the variable length pendulum system, the underactuated inverted pendulum system and nonaffine nonlinear chemical processes (CSTR).

Table of Contents

Preface	xiii
Introduction	1	(10)
Introduction	1	(1)
Adaptive Control	2	(1)
Neural Network Control	3	(2)
Instability Mechanisms in Adaptive Neural Control Systems	5	(4)
Outline of the Book	9	(1)
Conclusion	10	(1)
Mathematical Preliminaries	11	(16)
Introduction	11	(1)
Mathematical Preliminaries	11	(5)
Norms for Vectors and Signals	12	(3)
Properties of Matrix	15	(1)
Concepts of Stability	16	(1)
Lyapunov Stability Theorem	17	(2)
Useful Theorems and Formula	19	(7)
Sliding Surface	19	(1)
Mean Value Theorem	20	(1)
Integral Formula	20	(3)
Implicit Function Theorem	23	(2)
Input-Output Stability	25	(1)
Conclusion	26	(1)
Neural Networks and Function Approximation	27	(20)
Introduction	27	(1)
Function Approximation	27	(2)
Linearly Paametrized Neural Networks	29	(6)
Non-linearly Parametrized Networks	35	(9)
Neural Networks for Control Applications	44	(2)
Conclusion	46	(1)
SISO Nonlinear Systems	47	(34)
Introduction	47	(2)
NN Control with Regional Stability	49	(21)
Desired Feedback Control	49	(2)
HONN Controller Design Based on (4.7)	51	(8)
MNN Control Based on (4.10)	59	(11)
VSC --- Semi-Global Stability	70	(9)
VSC-based Adaptive NN Control Design	73	(4)
Elimination for Controller Chattering	77	(2)
Simulation Study	79	(1)
Conclusion	79	(2)
ILF for Adaptive Control	81	(58)
Introduction	81	(1)
Matching SISO Nonlinear Systems	82	(23)
Integral Lyapunov Function	83	(1)
Choice of Weighting Function α(x)	83	(9)
Adaptive NN Control Based on DFCs	92	(13)
Backstepping Adaptive NN Design	105	(22)
Adaptive Design for a First-order System	108	(4)
Design for nth-order Systems	112	(9)
Controller Design with Reduced Knowledge	121	(2)
Simulation Studies	123	(4)
NN Control for MIMO Nonlinear Systems	127	(11)
System Description	128	(2)
Lyapunov Function Design and Control Structure	130	(2)
Adaptive MIMO Control Using MNNs	132	(6)
Conclusion	138	(1)
Non-affine Nonlinear Systems	139	(44)
Introduction	139	(1)
System Description and Properties	140	(7)
Implicit Desired Feedback Control	142	(4)
High-gain Observer	146	(1)
Controller Design Based on LPNN	147	(13)
State Feedback Control	149	(4)
Output Feedback Control	153	(6)
Simulation Study	159	(1)
Controller Design Based on MNN	160	(22)
State Feedback Control	163	(5)
Output Feedback Control	168	(8)
Application to CSTR	176	(6)
Conclusion	182	(1)
Triangular Nonlinear Systems	183	(78)
Introduction	183	(2)
Special Systems in Strict-Feedback Form	185	(16)
Direct Adaptive NN Control	188	(10)
Simulation studies	198	(3)
Partially Known Nonlinear Systems	201	(16)
Adaptive Neural Control Design	203	(12)
Numerical Simulation	215	(2)
Pure-feedback Nonlinear Systems	217	(25)
Direct Adaptive NN Control for Σ1	220	(15)
Direct Adaptive NN Control for Σ2	235	(5)
Simulation studies	240	(2)
MIMO Nonlinear Systems	242	(18)
Conclusion	260	(1)
Conclusion	261	(4)
Conclusion	261	(1)
Design Flexibility	262	(1)
Further Research	263	(2)
References	265	(16)
Index	281