Consensus of multiple autonomous underwater vehicles with double independent Markovian switching topologies and timevarying delays

doi:10.1088/1674-1056/26/4/040203

Abstract A new method in which the consensus algorithm is used to solve the coordinate control problems of leaderless multiple autonomous underwater vehicles (multi-AUVs) with double independent Markovian switching communication topologies and time-varying delays among the underwater sensors is investigated. This is accomplished by first dividing the communication topology into two different switching parts, i.e., velocity and position, to reduce the data capacity per data package sent between the multi-AUVs in the ocean. Then, the state feedback linearization is used to simplify and rewrite the complex nonlinear and coupled mathematical model of the AUVs into a double-integrator dynamic model. Consequently, coordinate control of the multi-AUVs is regarded as an approximating consensus problem with various time-varying delays and velocity and position topologies. Considering these factors, sufficient conditions of consensus control are proposed and analyzed and the stability of the multi-AUVs is proven by Lyapunov-Krasovskii theorem. Finally, simulation results that validate the theoretical results are presented.

Keywords: multiple autonomous underwater vehicles consensus control Markovian switching topology time-varying delay

Received: 19 November 2016
Revised: 19 January 2017
Accepted manuscript online:

PACS:	02.30.Yy	(Control theory)
	05.10.-a	(Computational methods in statistical physics and nonlinear dynamics)
	05.65.+b	(Self-organized systems)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 51679057, 51309067, and 51609048), the Outstanding Youth Science Foundation of Heilongjiang Providence of China (Grant No. JC2016007), and the Natural Science Foundation of Heilongjiang Province, China (Grant No. E2016020).

Corresponding Authors: Yi-Bo Liu
E-mail: liuyibo8888@126.com

Cite this article:

Zhe-Ping Yan(严浙平), Yi-Bo Liu(刘一博), Jia-Jia Zhou(周佳加), Wei Zhang(张伟), Lu Wang(王璐) Consensus of multiple autonomous underwater vehicles with double independent Markovian switching topologies and timevarying delays 2017 Chin. Phys. B 26 040203

[1]	Yang H, Wang C and Zhang F 2013 IET Contor. Theor. 7 1950
[2]	Zhang L, Zhao J, Qi X and Jia H 2013 Int. J. Control 86 1008
[3]	Yan Z P, Yu H M and Li B Y 2014 J. Cent. South Univ. 22 4193
[4]	Zhang L, Qi X and Pang Y 2009 Ocean Eng. 36 716
[5]	Lapierre L and Jouvencel B 2008 IEEE J. Oceanic Eng. 33 89
[6]	Lee P M, Hong S W, Lin Y K, Lee C M, Joem B H and Park J W 1999 IEEE Oceanic Eng. 24 38
[7]	Zhu D Q and Sun B 2013 Eng. Appl. Artif. Intell. 26 2260
[8]	Wang J S and Lee C S 2003 IEEE Trans. Robotics Automat. 19 283
[9]	Refenes J E, Sorensen A J and Petterson K Y 2008 IEEE Trans. Control Syst. Technol. 16 930
[10]	Li J H and Lee P M 2005 Ocean Eng. 32 2165
[11]	Jia H M, Zhang L J, Bian X Q, Yan Z P, Cheng X Q and Zhou J J 2012 J. Cent. South Univ. 19 1240
[12]	Qi X 2014 Ocean Eng. 91 84
[13]	Cui R X, Ge S S, How B V E and Choo Y S 2010 Ocean Eng. 37 1491
[14]	Yang E F and Gu D B 2007 IEEEASME Trans. Mechatron 12 164
[15]	Wang R S, Gao L X, Chen W H and Dai D M 2016 Chin. Phys. B 25 100202
[16]	Cao J, Wu Z H and Li P 2016 Chin. Phys. B 25 058902
[17]	Li S H and Wang X Y 2013 Automatica 49 3359
[18]	Zhou F, Wang Z J and Fan N J 2015 Chin. Phys. B 24 020203
[19]	Hu J P and Lin Y S 2010 IET Control Theor. Appl. 4 109
[20]	Tang Z J, Huang T Z, Shao J J and Hu J P 2012 Neurocomputing 97 410
[21]	Shang Y L 2015 J. Frankl. Inst. 352 4826
[22]	Xie D M and Cheng Y L 2015 Int. J. Robust Nonlinear Control 25 252
[23]	Shojaei K and Arefi M M 2015 IET Control Appl. 9 1264
[24]	Qin J H and Yu C B 2013 IEEE Trans. Neural Networks Learn. Syst. 24 1588
[25]	Olfati-Saber R and Murray R M 2004 IEEE Trans. Automat. Control 49 1520
[26]	Park M J, Kwon O M, Park J H, Lee S M and Cha EJ 2012 Chin. Phys. B 21 110508
[27]	Ren W and Beard R W 2005 IEEE Trans. Automat. Control 50 655
[28]	Fossen T I 2011 Handbook of marine craft hydrodynamics and motion control (New York: John Wiley & Sons Ltd) pp. 52-70
[29]	Fossen T I 1994 Guidance and control of ocean vehicles (New York: John Wiley & Sons Ltd) p. 75
[30]	Body S, Ghaoui L E, Feron E and Balakrishnan V 1994 Linear matrix inequalities in system and control theory (Philadelphia: Society for Industrial and Applied Mathematics) p. 102
[31]	Fragoso M and Costa O 2005 SIAM J. Control Optim. 44 1165
[32]	Gu K 2000 Proceeding of 39th IEEE Conference on Decision and Control, December 12-15, 2000, Sydney, Australia, p. 2805
[33]	Ming P S, Liu J C, Tan S B, Wang G, Shang L L and Jia C Y 2015 J. Frankl. Inst. 352 3682
[34]	Shang Y L 2016 Appl. Math. Comput. 273 1234
[35]	Ogata K 2010 Modern Control Engineering (New Jersey: Prentice Hall) p. 150

[1]	Robust H_∞ control of uncertain systems with two additive time-varying delays M. Syed Ali, R. Saravanakumar. Chin. Phys. B, 2015, 24(9): 090202.
[2]	Exponential synchronization of chaotic Lur'e systems with time-varying delay via sampled-data control R. Rakkiyappan, R. Sivasamy, S. Lakshmanan. Chin. Phys. B, 2014, 23(6): 060504.
[3]	Stability analysis of Markovian jumping stochastic Cohen–Grossberg neural networks with discrete and distributed time varying delays M. Syed Ali. Chin. Phys. B, 2014, 23(6): 060702.
[4]	Robust H_∞ cluster synchronization analysis of Lurie dynamical networks Guo Ling (郭凌), Nian Xiao-Hong (年晓红), Pan Huan (潘欢), Bing Zhi-Tong (邴志桐). Chin. Phys. B, 2014, 23(4): 040501.
[5]	Exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and mode-dependent probabilistic time-varying delays R. Rakkiyappan, N. Sakthivel, S. Lakshmanan. Chin. Phys. B, 2014, 23(2): 020205.
[6]	Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays M. Syed Ali, R. Saravanakumar. Chin. Phys. B, 2014, 23(12): 120201.
[7]	Cluster exponential synchronization of a class of complex networks with hybrid coupling and time-varying delay Wang Jun-Yi (王军义), Zhang Hua-Guang (张化光), Wang Zhan-Shan (王占山), Liang Hong-Jing (梁洪晶). Chin. Phys. B, 2013, 22(9): 090504.
[8]	Leader–following consensus control for networked multi-teleoperator systems with interval time-varying communication delays M. J. Park, S. M. Lee, J. W. Son, O. M. Kwon, E. J. Cha. Chin. Phys. B, 2013, 22(7): 070506.
[9]	H_∞ synchronization of chaotic neural networks with time-varying delays O. M. Kwon, M. J. Park, Ju H. Park, S. M. Lee, E. J. Cha. Chin. Phys. B, 2013, 22(11): 110504.
[10]	Pinning synchronization of time-varying delay coupled complex networks with time-varying delayed dynamical nodes Wang Shu-Guo(王树国) and Yao Hong-Xing(姚洪兴) . Chin. Phys. B, 2012, 21(5): 050508.
[11]	Cluster projective synchronization of complex networks with nonidentical dynamical nodes Yao Hong-Xing (姚洪兴), Wang Shu-Guo (王树国 ). Chin. Phys. B, 2012, 21(11): 110506.
[12]	Robust stability analysis of Takagi–Sugeno uncertain stochastic fuzzy recurrent neural networks with mixed time-varying delays M. Syed Ali . Chin. Phys. B, 2011, 20(8): 080201.
[13]	New results on stability criteria for neural networks with time-varying delays O.M. Kwon, J.W. Kwon, and S.H. Kim. Chin. Phys. B, 2011, 20(5): 050505.
[14]	New synchronization analysis for complex networks with variable delays Zhang Hua-Guang(张化光), Gong Da-Wei(宫大为), and Wang Zhan-Shan(王占山) . Chin. Phys. B, 2011, 20(4): 040512.
[15]	Pinning impulsive synchronization of stochastic delayed coupled networks Tang Yang(唐漾), Wong W K(黃偉強), Fang Jian-An(方建安), and Miao Qing-Ying(苗清影) . Chin. Phys. B, 2011, 20(4): 040513.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Consensus of multiple autonomous underwater vehicles with double independent Markovian switching topologies and timevarying delays

Cite this article:

Online attention