**Page description appears here**

“Global Practical Stabilization and Tracking for an Underactuated Ship - A Combined Averaging and Backstepping Approach”

Authors: Kristin Y. Pettersen and Henk Nijmeijer,
Affiliation: NTNU, Department of Engineering Cybernetics and University of Twente, Netherlands
Reference: 1999, Vol 20, No 4, pp. 189-200.

     Valid XHTML 1.0 Strict

Keywords: Time-varying control, exponential convergence, underactuated surface vessels

Abstract: We solve both the global practical stabilization and tracking problem for an underactuated ship, using a combined integrator backstepping and averaging approach. Exponential convergence to an arbitrarily small neighbourhood of the origin and of the reference trajectory, respectively, is proved. Simulation results are included.

PDF PDF (1358 Kb)        DOI: 10.4173/mic.1999.4.1

DOI forward links to this article:
  [1] Wenjing Xie and Baoli Ma (2013), doi:10.1002/rnc.3129
  [2] Lutao Liu, Zhilin Liu and Jun Zhang (2013), doi:10.1155/2013/846389
  [3] Yaswanth Siramdasu and Farbod Fahimi (2013), doi:10.1080/00207179.2013.813646
  [4] Farbod Fahimi and Chris Van Kleeck (2013), doi:10.1017/S0263574712000070
  [5] Farshad Mahini, Leonard DiWilliams, Kevin Burke and Hashem Ashrafiuon (2013), doi:10.1017/S0263574712000720
  [6] R. Yu, Q. Zhu, G. Xia and Z. Liu (2012), doi:10.1049/iet-cta.2011.0176
  [7] E. Fredriksen and K.Y. Pettersen (2006), doi:10.1016/j.automatica.2005.12.020
  [8] Anna Witkowska and Roman S mierzchalski (2009), doi:10.1007/s11633-009-0277-2
  [9] Chaker Jammazi and Maâli Zaghdoudi (2013), doi:10.1016/j.amc.2013.03.096
  [10] Wenjing Xie, Hailing Sun and Baoli Ma (2013), doi:10.1007/s11768-013-2258-9
  [11] Mohamed Harmouche, Salah Laghrouche and Yacine Chitour (2014), doi:10.1080/00207179.2014.898188
  [12] Xie Wen-Jing and Ma Bao-Li (2014), doi:10.1002/asjc.968
  [13] Anna Witkowska, Miroslaw Tomera and Roman mierzchalski (2007), doi:10.2478/v10006-007-0007-2
  [14] Changzhong Pan, Xuzhi Lai, Simon X. Yang and Min Wu (2015), doi:10.1007/s00521-015-1839-6
  [15] Hongyan Chu, Chunjiang Qian, Rongjie Liu and Liming Di (2015), doi:10.1080/00207179.2015.1022796
  [16] K.Y. Pettersen and H. Nijmeijer (2000), doi:10.1109/CDC.2000.914112
  [17] A. Behal, D.M. Dawson, W.E. Dixon and Y. Fang (2000), doi:10.1109/CDC.2000.914113
  [18] K.Y. Pettersen and H. Nijmeijer (1998), doi:10.1109/CDC.1998.762046
  [19] A.P. Aguiar and A.M. Pascoal (2002), doi:10.1109/CDC.2002.1184375
  [20] G. Indiveri, M. Aicardi and G. Casalino (2000), doi:10.1109/CDC.2000.914114
  [21] A.P. Aguiar, L. Cremean and J.P. Hespanha (2003), doi:10.1109/CDC.2003.1271751
  [22] I. Fantoni, R. Lozano, F. Mazenc and K.Y. Pettersen (1999), doi:10.1109/CDC.1999.831309
  [23] Lin Zhuang Guo Zhiqun, Yang Qiang and Liu Zhilin (2012), doi:10.1109/ICCSNT.2012.6526146
  [24] Kilsoo Kim, Young-Ki Lee, Sehwan Oh, David Moroniti, Dimitri Mavris, George J. Vachtsevanos, Nikos Papamarkos and George Georgoulas (2013), doi:10.1109/MED.2013.6608750
  [25] Zhuang Lin, Benjie Dong and Zhiqun Guo (2013), doi:10.1109/ICICIP.2013.6568176
  [26] E. Fredriksen and K.Y. Pettersen (2004), doi:10.1109/CDC.2004.1429660
  [27] Chang-Zhong Pan, Simon X. Yang, Xu-Zhi Lai and Lan Zhou (2014), doi:10.1109/CCDC.2014.6852744
  [28] A. Behal, D.M. Dawson, B. Xian and P. Setlur (2001), doi:10.1109/CCA.2001.973940
  [29] Hongyan Chu, Chunjiang Qian, Rongjie Liu, Shihua Li and Hongqing Gao (2015), doi:10.1109/ACC.2015.7171137
  [30] Brigitte d Andréa-Novel and Sylvain Thorel (2016), doi:10.1051/cocv/2016047

[1] Brockett, R.W. (1983). Asymptotic stability and feedback stabilization, In: Differential Geometric Control Theory.R. W. Brockett, R. S. Millman and H. J. Sussmann, Eds.. pp. 181-191. Birkhäuser.
[2] Coron, J.-M. L. Rosier (1994). A relation between continuous time-varying and discontinuous feedback stabilization, J. of Math. Syst. Estimation, and Control .1, 67-84.
[3] Fossen, T. I. (1994). Guidance and Control of Ocean Vehicles, John Wiley and Sons Ltd. Chichester.
[4] Godhavn, J.-M. (1996). Nonlinear tracking of underactuated surface vessels, In: Proc. 35th IEEE Conf. on Decision and Control. Kobe, Japan. pp. 987-991.
[5] Jiang, Z.-P. H. Nijmeijer (1997). A recursive technique for tracking control of nonholonomic systems in chained form, Technical Report 1397. Univ. of Twente.
[6] Kanayama, Y., Y. Kimura, F. Miyazaki T. Noguchi (1990). A stable tracking control method for an autonomous mobile robot, In: Proc. 1990 IEEE Int. Conf. on Robotics and Automation. Cincinnati, Ohio. pp. 384-389.
[7] Krstic, M., I. Kanellakopoulos P. Kokotovic (1995). Nonlinear and Adaptive Control Design, Wiley. NY.
[8] Marino, R. P. Tomei (1995). Nonlinear Control Design, Prentice Hall, Europe.
[9] Nakamura, Y. S. Savant (1992). Nonlinear tracking control of autonomous underwater vehicle, In: Proc. 1992 IEEE Int. Conf. on Robotics and Automation. Nice, France. pp. A4-A9.
[10] Pettersen, K. Y. O. Egeland (1996). Exponential stabilization of an underactuated surface vessel, In: Proc. 35th IEEE Conf. on Decision and Control. Kobe, Japan. pp. 967-971.
[11] Reyhanoglu, M. (1996). Control and stabilization of an underactuated surface vessel, In: Proc. 35th IEEE Conf. on Decision and Control. Kobe, Japan. pp. 2371-2376.
[12] Sanders, J.A. F. Verhulst (1985). Averaging Methods in Nonlinear Dynamical Systems, Springer-Verlag, New York.
[13] Zabczyk, J. (1989). Some comments on stabilizability, Appl. Math. and Optimization 19, 1-9 doi:10.1007/BF01448189

  title={{Global Practical Stabilization and Tracking for an Underactuated Ship - A Combined Averaging and Backstepping Approach}},
  author={Pettersen, Kristin Y. and Nijmeijer, Henk},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}


May 2016: MIC reaches 2000 DOI Forward Links. The first 1000 took 34 years, the next 1000 took 2.5 years.

July 2015: MIC's new impact factor is now 0.778. The number of papers published in 2014 was 21 compared to 15 in 2013, which partially explains the small decrease in impact factor.

Aug 2014: For the 3rd year in a row MIC's impact factor increases. It is now 0.826.

Dec 2013: New database-driven web-design enabling extended statistics. Article number 500 is published and MIC reaches 1000 DOI Forward Links.

Jan 2012: Follow MIC on your smartphone by using the RSS feed.


July 2011: MIC passes 1000 ISI Web of Science citations.

Mar 2010: MIC is now indexed by DOAJ and has received the Sparc Seal seal for open access journals.

Dec 2009: A MIC group is created at LinkedIn and Twitter.

Oct 2009: MIC is now fully updated in ISI Web of Knowledge.