Deterministic Learning Theory For Identification – Cong Wang

The indirect ANC approach, on the other hand, uses NNs to identify the system nonlinearities f1(x1) and f2(x1, x2) (e.g., see [181]). For ANC of general nonlinear systems, it is nor- mally considered that the direct approach provides a better solution than the indirect approach [269]. However, the learning issue in both approaches, that is, accurate learning of either h(x, v) or fi(·) (i = 1, 2), has not previously been fully studied.

4.3.2 Direct ANC Design For the control of strict-feedback system (4.41), the direct ANC approach de- veloped in [65] is applicable. At each recursive step i (i = 1, 2), a desired feed- back control α∗ i is first shown to exist. Then, a stabilizing function αi (u = α2) is designed, where a localized RBF network is employed to approximate the unknown nonlinearity in α∗ i (i = 1, 2).

Define z1 = x1 −xd1. Its derivative is ˙z1 = f1(x1) + x2 −˙xd1. By viewing x2 as a virtual control input, it is clear that there exists a desired virtual control α∗ △= x2, α∗ 1 = −c1z1 −f1(x1) + ˙xd1 where c1 > 0 is a design constant.

Denote h1(Z1) △= f1(x1), where Z1 △= [x1]T ∈1 ⊂R. By employing an RBF neural network WT 1 S1(Z1) to approximate h1(Z1) in a compact set 1, we have h1(Z1) = W∗T 1 S1(Z1) + ϵ1, (4.43) where W∗ 1 denotes the ideal constant weights, and |ϵ1| ≤ϵ∗ 1 is the approxima- tionerrorwithconstantϵ∗ 1 > 0.Let W1 betheestimateof W∗ 1 and !

1 . Define z2 = x2 −α1 and let α1 = −c1z1 − 1 S1(Z1) + ˙xd1 (4.44) where W1 is updated by ˙ W1 = 1S1(Z1)z1 −σ11 (4.45) with 1 = T 1 > 0 and σ1 > 0 being a small constant. Then, the dynamics of z1 are governed by ˙z1 = f1(x1) + (z2 + α1) −˙xd1 = −c1z1 + z2 −!

12. Actuator Saturation Control, edited by Vikram Kapila and Karolos M. Grigoriadis 13. Nonlinear Control Systems, Zoran Vukiç, Ljubomir Kuljaãa, Dali Donlagiã, and Sejid Tesnjak 14. Linear Control System Analysis & Design: Fifth Edition, John D’Azzo, Constantine H. Houpis and Stuart Sheldon 15. Robot Manipulator Control: Theory & Practice, Second Edition, Frank L.

Lewis, Darren M. Dawson, and Chaouki Abdallah 16. Robust Control System Design: Advanced State Space Techniques, Second Edition, Chia-Chi Tsui 17. Differentially Flat Systems, Hebertt Sira-Ramirez and Sunil Kumar Agrawal FRANK L. LEWIS, PH.D., FELLOW IEEE, FELLOW IFAC Professor Automation and Robotics Research Institute The University of Texas at Arlington SHUZHI SAM GE, PH.D., FELLOW IEEE Professor Interactive Digital Media Institute The National University of Singapore 18. Chaos in Automatic Control, edited by Wilfrid Perruquetti and Jean-Pierre Barbot 19. Fuzzy Controller Design: Theory and Applications, Zdenko Kovacic and Stjepan Bogdan 20.

Quantitative Feedback Theory: Fundamentals and Applications, Second Edition, Constantine H. Houpis, Steven J. Rasmussen, and Mario Garcia-Sanz 21. Neural Network Control of Nonlinear Discrete-Time Systems, Jagannathan Sarangapani 22. Autonomous Mobile Robots: Sensing, Control, Decision Making and Applications, edited by Shuzhi Sam Ge and Frank L. Lewis 23. Hard Disk Drive: Mechatronics and Control, Abdullah Al Mamun, GuoXiao Guo, and Chao Bi 24.

Stochastic Hybrid Systems, edited by Christos G. Cassandras and John Lygeros 25. Wireless Ad Hoc and Sensor Networks: Protocols, Performance, and Control, Jagannathan Sarangapani 26. Modeling and Control of Complex Systems, edited by Petros A. Ioannou and Andreas Pitsillides 27. Intelligent Freight Transportation, edited by Petros A. Ioannou 28. Feedback Control of Dynamic Bipedal Robot Locomotion, Eric R. Westervelt, Jessy W.

Grizzle, Christine Chevallereau, Jun Ho Choi, and Benjamin Morris 29. Optimal and Robust Estimation: With an Introduction to Stochastic Control Theory, Second Edition, Frank L. Lewis; Lihua Xie and Dan Popa 30. Intelligent Systems: Modeling, Optimization, and Control, Yung C. Shin and Chengying Xu 31. Optimal Control: Weakly Coupled Systems and Applications, Zoran Gajic´, Myo-Taeg Lim, Dobrila Skataric´, Wu-Chung Su, and Vojislav Kecman 32.

Deterministic Learning Theory for Identification, Recognition, and Control, Cong Wang and David J. Hill 33. Linear Control Theory: Structure, Robustness, and Optimization, Shankar P. Bhattacharyya, Aniruddha Datta, and Lee H. Keel v CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2010 by Taylor and Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S.

This is a short excerpt from the opening of “” by Unknown, quoted for review and introduction purposes. All rights belong to the copyright holders.

Book Information

• Unique ID: 748ba3262fa3465d
• File Extension: .pdf
• File Size: 11,585,546 bytes (11.049 MB)
• Title: –
• Author: Unknown
• ISBN: 9780849375538
• Pages: 219
• Language: English (en)

Reading & Word Statistics

• Estimated Reading Time: 390.15 minutes
• Total Words: 78,031
• Total Characters: 458,494
• Average Words per Page: 356.31
• Average Characters per Page: 2093.58

Most Frequent Words

control (868), system (711), dynamical (591), learning (586), pattern (576), recognition (389), patterns (366), systems (354), dynamics (341), identification (324), deterministic (306), nonlinear (282), adaptive (242), rbf (239), state (223), training (223), approximation (218), neural (212), time (208), test (199), using (195), theory (194), networks (192), orbit (189), vol (173), closed-loop (162), network (160), trajectory (152), small (151), along (150), function (149), condition (137), error (128), stability (126), convergence (123), accurate (121), tracking (120), periodic (118), knowledge (112), recurrent (110), problem (109), achieved (108), representation (104), similarity (104), equation (102), model (101), constant (101), design (98), observer (97), unknown (96), figure (96), chaotic (94), following (93), controller (92), set (92), shown (90), similar (88), seconds (88), rapid (85), ieee (84), partial (82), reference (80), observation (78), also (78), obtained (77), chapter (77), based (76), theorem (76), process (75), parameter (73), two (73), dynamic (70), single-variable (70), thus (70), region (69), locally (68), new (68), bounded (68), form (67), corresponding (67), given (67), weights (64), without (63), space (62), seen (62), intelligent (61), information (61), used (61), achieve (61), local (61), within (61), section (61), input (61), transactions (61), analysis (60), one (60), models (60), states (59), temporal (59), pattern-based (59).

PDF Download