|
|
|
Chaotic system optimal tracking using data-based synchronous method with unknown dynamics and disturbances |
| Ruizhuo Song(宋睿卓)1, Qinglai Wei(魏庆来)2 |
1 School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China;
2 The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China |
|
|
|
|
Abstract We develop an optimal tracking control method for chaotic system with unknown dynamics and disturbances. The method allows the optimal cost function and the corresponding tracking control to update synchronously. According to the tracking error and the reference dynamics, the augmented system is constructed. Then the optimal tracking control problem is defined. The policy iteration (PI) is introduced to solve the min-max optimization problem. The off-policy adaptive dynamic programming (ADP) algorithm is then proposed to find the solution of the tracking Hamilton-Jacobi-Isaacs (HJI) equation online only using measured data and without any knowledge about the system dynamics. Critic neural network (CNN), action neural network (ANN), and disturbance neural network (DNN) are used to approximate the cost function, control, and disturbance. The weights of these networks compose the augmented weight matrix, and the uniformly ultimately bounded (UUB) of which is proven. The convergence of the tracking error system is also proven. Two examples are given to show the effectiveness of the proposed synchronous solution method for the chaotic system tracking problem.
|
Received: 09 October 2016
Revised: 18 December 2016
Accepted manuscript online:
|
|
PACS:
|
05.45.Gg
|
(Control of chaos, applications of chaos)
|
|
| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61304079, 61673054, and 61374105), the Fundamental Research Funds for the Central Universities, China (Grant No. FRF-TP-15-056A3), and the Open Research Project from SKLMCCS, China (Grant No. 20150104). |
Corresponding Authors:
Qinglai Wei
E-mail: qinglai.wei@ia.ac.cn
|
Cite this article:
Ruizhuo Song(宋睿卓), Qinglai Wei(魏庆来) Chaotic system optimal tracking using data-based synchronous method with unknown dynamics and disturbances 2017 Chin. Phys. B 26 030505
|
| [1] |
Shen Z and Li J 2016 Mathematics and Computers in Simulation
|
| [2] |
Wang G, Cai B, Jin P and Hu T 2016 Chin. Phys. B 25 010503
|
| [3] |
Wang W, Zhang X, Chang Y, Wang X, Wang Z, Chen X and Zheng L 2016 Chin. Phys. B 25 010202
|
| [4] |
Zhang Z Y, Feng X Q, Yao Z H and Jia H Y 2015 Chin. Phys. B 24 110503
|
| [5] |
Wu J, Wang L, Chen G and Duan S 2016 Chaos Soliton. Fract. 92 20
|
| [6] |
Lü J H and Chen G R 2002 International Journal of Bifurcation and Chaos 12 659
|
| [7] |
Ma T, Zhang H and Fu J 2008 Chin. Phys. B 17 4407
|
| [8] |
Ma T and Fu J 2011 Chin. Phys. B 20 050511
|
| [9] |
Yang D 2014 Chin. Phys. B 23 010504
|
| [10] |
Song R, Xiao W and Wei Q 2014 Chin. Phys. B 23 050504
|
| [11] |
Wei Q, Song R, Xiao W and Sun Q 2015 Chin. Phys. B 24 090504
|
| [12] |
Wei Q, Liu D and Lin H 2016 IEEE Transactions on Cybernetics 46 840
|
| [13] |
Zhang H, Feng T, Yang G H and Liang H 2015 IEEE Transactions on Cybernetics 45 1315
|
| [14] |
Wei Q, Wang F, Liu D and Yang X 2014 IEEE Transactions on Cybernetics 44 2820
|
| [15] |
Modares H and Lewis F L 2014 IEEE Transactions on Automatic Control 59 3051
|
| [16] |
Liu D and Wei Q 2013 IEEE Transactions on Cybernetics 43 779
|
| [17] |
Nguyen T L 2016 Neurocomputing
|
| [18] |
Song R, Xiao W, Zhang H and Sun C 2014 IEEE Transactions on Neural Networks and Learning Systems 25 1733
|
| [19] |
Song R, Lewis F L, Wei Q, Zhang H and Jiang Z P 2015 IEEE Transactions on Neural Networks and Learning Systems 26 851
|
| [20] |
Song R, Lewis F L, Wei Q and Zhang H 2016 IEEE Transactions on Cybernetics 46 1041
|
| [21] |
Wang W, Li L, Peng H, Xiao J and Yang Y 2014 Nonlinear Dynamics 76 591
|
| [22] |
Wang W, Li L, Peng H, Xiao J and Yang Y 2014 Neural Networks 53 8
|
| [23] |
Li L, Li W, Kurths J, Luo Q, Yang Y and Li S 2015 Chaos Soliton. Fract. 72 20
|
| [24] |
Song R, Xiao W, Sun C and Wei Q 2013 Chin. Phys. B 22 090502
|
| [25] |
Basar T and Bernard P 1995 H∞ Optimal Control and Related Minimax Design Problems (Boston: Birkhauser)
|
| [26] |
Basar T and Olsder G J 1999 Dynamic Noncooperative Game Theory (2nd Edn.) Vol. 23
|
| [27] |
Devasia S, Chen D and Paden B 1996 IEEE Transactions of Automatic Control 14 930
|
| [28] |
Zhang H, Wei Q and Liu D 2011 Automatica 47 207
|
| [29] |
Wei Q, Song R and Yan P 2016 IEEE Transactions on Neural Networks and Learning Systems 27 444
|
| [30] |
Liu D and Wei Q 2014 International Journal of Adaptive Control and Signal Processing 28 205
|
| [31] |
Song R, Lewis F L and Wei Q 2016 IEEE Transactions on Neural Networks and Learning Systems
|
| [32] |
Zhang F, Liao X and Zhang G 2016 Applied Mathematics and Computation 284 332
|
| [33] |
Chen G and Ueta T 1999 International Journal of Bifurcation and Chaos 9 1465
|
| [34] |
Leonov G A and Kuznetsov N V 2015 Applied Mathematics and Computation 256 334
|
| [35] |
Lorenz E 1963 Journal of the Atmospheric Sciences 20 130
|
| [36] |
Leonov G A, Kuznetsov N V, Korzhemanova N A and Kusakin D V 2016 Communications in Nonlinear Science and Numerical Simulation 41 84
|
| [37] |
Chua L, Komuro M and Matsumoto T 1986 IEEE Transactions on Circuits and Systems 33 1072
|
| [38] |
Alkahtani B S T 2016 Chaos Soliton. Fract. 89 547
|
| [39] |
Wiggins S 1987 Phys. Lett. A 124 138
|
| [40] |
Simo H and Woafo P 2016 Optik-International Journal for Light and Electron Optics 127 8760
|
| [41] |
Vargas J A R, Grzeidak E and Gularte K H M 2016 Neurocomputing 174 1038
|
| [42] |
Lü J, Chen G and Zhang S 2002 International Journal of Bifurcation and Chaos 12 1001
|
| [43] |
Lü J, Chen G and Zhang S 2002 Chaos Soliton. Fract. 14 669
|
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
