“Tutorial on nonlinear backstepping: Applications to ship control”

Authors: Thor I. Fossen and Jan P. Strand,
Affiliation: NTNU, Department of Engineering Cybernetics and ABB
Reference: 1999, Vol 20, No 2, pp. 83-135.

Keywords: Nonlinear control, backstepping, feedback linearization

Abstract: The theoretical foundation of nonlinear backstepping designs is presented in a tutorial setting. This includes a brief review of integral backstepping, extensions to SISO and MIMO systems in strict feedback form and physical motivated case studies. Parallels and differences to feedback linearization where it is shown how so-called 'good nonlincarities' can be exploited in the design are also made.

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[1] (2011), doi:10.1002/9781119994138.refs
[2] Gerasimos Rigatos and Spyros Tzafestas (2006), doi:10.1016/j.mechatronics.2006.01.003
[3] Anna Witkowska and Roman S mierzchalski (2009), doi:10.1007/s11633-009-0277-2
[4] Francesco Bullo (2000), doi:10.1016/S0005-1098(00)00115-1
[5] Nassim Khaled and Nabil G. Chalhoub (2013), doi:10.1007/s11071-013-0840-9
[6] Guoqing Xia, Huiyong Wu and Xingchao Shao (2014), doi:10.1155/2014/218585
[7] Junsheng Ren and Lu Liu (2013), doi:10.3923/jas.2013.1691.1697
[8] H.M. Morishita and C.E.S. Souza (2014), doi:10.1016/j.conengprac.2014.08.012
[9] Thor Fossen and Tristan Perez (2009), doi:10.1109/MCS.2009.934408
[10] S. Mojtaba Tabatabaeipour and Roberto Galeazzi (2015), doi:10.1016/j.ifacol.2015.09.551
[11] Swarup Das, Aditi Bhatt and S. E. Talole (2015), doi:10.1109/IIC.2015.7150778
[12] Feng Yi-wei and Feng Ping (2014), doi:10.1109/WCICA.2014.7053431
[13] Mikkel Eske, Norgaard Sorensen and Morten Breivik (2015), doi:10.1016/j.ifacol.2015.10.295
[14] Edoardo I. Sarda, Ivan R. Bertaska, Ariel Qu and Karl D. von Ellenrieder (2015), doi:10.1109/OCEANS-Genova.2015.7271425
[15] Arsit Boonyaprapasorn, Eakachai Pengwang, Thavida Maneewarn, Parinya Sa Ngiamsunthorn, Chadchawarn Pongsomboon, Wishanuruk Wechsathol and Rardchawadee Silapunt (2015), doi:10.1109/ICCAS.2015.7364582
[16] Defeng Wu and Fengkun Ren (2015), doi:10.1109/ChiCC.2015.7260536
[17] Huajin Qu, Edoardo I. Sarda, Ivan R. Bertaska and Karl D. von Ellenrieder (2015), doi:10.1109/OCEANS-Genova.2015.7271438
[18] Thor I. Fossen, Karl-Petter Lindegaard and Roger Skjetne (2002), doi:10.3182/20020721-6-ES-1901.01282
[19] Swarup Das and S.E. Talole (2016), doi:10.1016/j.oceaneng.2016.05.027
[20] Ramy Rashad, Ahmed Aboudonia and Ayman El-Badawy (2016), doi:10.1016/j.jfranklin.2016.07.017
[21] Ya-nan Song, Rong-hua Xu and Qin-ruo Wang (2016), doi:10.1109/ChiCC.2016.7554919
[22] Edoardo I. Sarda, Huajin Qu, Ivan R. Bertaska and Karl D. von Ellenrieder (2016), doi:10.1016/j.oceaneng.2016.09.037
[23] Swarup Das and Sanjay E. Talole (2016), doi:10.1109/JOE.2016.2518256
[24] Mikkel Eske Nørgaard Sørensen and Morten Breivik (2016), doi:10.1016/j.ifacol.2016.10.359
[25] Mikkel Eske Norgaard Sorensen, Elias S. Bjorne and Morten Breivik (2016), doi:10.1109/CCA.2016.7587926
[26] Yang Qu, Haixiang Xu, Wenzhao Yu, Hui Feng and Xin Han (2017), doi:10.1007/s11804-017-1410-1
[27] N. Khaled and NG Chalhoub (2011), doi:10.1177/1077546309346245
[28] Wilhelm B. Klinger, Ivan R. Bertaska, Karl D. von Ellenrieder and M. R. Dhanak (2017), doi:10.1109/JOE.2016.2571158
[29] Thor I. Fossen (2000), doi:10.1016/S1474-6670(17)37044-1
[30] Soulaymen Kammoun, Souhir Sallem and Mohamed Ben Ali Kammoun (2017), doi:10.1007/s13369-017-2606-z
[31] Gabriel H. Negri, Mariana S. M. Cavalca, José de Oliveira, Celso J. F. Araújo and Luiz A. Celiberto (2017), doi:10.1007/s40313-017-0327-x
[32] Jun Yuan, Zhengxing Wu, Junzhi Yu and Min Tan (2017), doi:10.1109/TIE.2017.2674606
[33] Nabil G Chalhoub and Nassim Khaled (2014), doi:10.1177/1077546312461026
[34] Defeng Wu, Fengkun Ren, Lei Qiao and Weidong Zhang (2017), doi:10.1016/j.isatra.2017.10.010
[35] Hafiz Zeeshan Iqbal Khan, Jahanzeb Rajput, Shakil Ahmed, Muhammad Sarmad and Muhammad Sharjil (2018), doi:10.1109/IBCAST.2018.8312235
[36] Lili Wan, Yixin Su, Huajun Zhang, Yongchuan Tang and Binghua Shi (2018), doi:10.1177/1687814018795523
[37] Peng Wang, Xiaobing Zhang and Jihong Zhu (2018), doi:10.1016/j.fss.2018.12.002
[38] Aditi Bhatt, Swarup Das and S. E. Talole (2018), doi:10.1080/20464177.2018.1550030
[39] Anna Witkowska and Roman Smierzchalski (2007), doi:10.1007/978-0-387-73137-7_14
[40] Nassim Khaled and Nabil G. Chalhoub (2009), doi:10.1007/978-3-642-00629-6_14
[41] Anna Witkowska, Miroslaw Tomera and Roman mierzchalski (2007), doi:10.2478/v10006-007-0007-2
[42] Chunyue Li, Jiajia Jiang, Fajie Duan, Wei Liu, Xianquan Wang, Lingran Bu, Zhongbo Sun and Guoliang Yang (2019), doi:10.3390/s19092051
[43] Shasha Wang, Mingyu Fu and Yuanhui Wang (2019), doi:10.1002/acs.3030
[44] Wei Guan, Haotian Zhou, Zuojing Su, Xianku Zhang and Chao Zhao (2019), doi:10.1155/2019/3821048
[45] Xin Wang and Carlos Guedes Soares (2020), doi:10.1109/ACCESS.2019.2962604
[46] Yuanqiao Wen, Wei Tao, Man Zhu, Jie Zhou and Changshi Xiao (2020), doi:10.1016/j.apor.2020.102293
[47] V Petrov (2020), doi:10.1088/1757-899X/878/1/012002
[48] Zhizun Xu, Maryam Haroutunian, Alan J. Murphy, Jeff Neasham and Rose Norman (2020), doi:10.1016/j.oceaneng.2020.107822
References:
[1] BARBALAT (1959). Systèmes d´Équations Différentielles d´Oscillations Non Linéaires, Revue de Mathématiques Pures et Appliquées, Vol. 4(2), 267-270. Académie de la République Populaire Roumaine (in French).
[2] BECH, M.I. WAGNER SMITH, L. (1969). Analogue Simulation of Ship Maneuvers, Technical Report Hy-14, Hydro- and Aerodynamics Laboratory, Lyngby, Denmark.
[3] BYRNES C.I. ISIDORI, A. (1989). New Results and Examples in Nonlinear Feedback Stabilization, Systems and Control Letters, Vol. 12, 437-442 doi:10.1016/0167-6911(89)90080-7
[4] BYRNES, C.I., ISIDORI, A. WILLEMS, J.C. (1991). Passivity, Feedback Equivalence, and the Global Stabilization of Minimum Phases Nonlinear Systems, IEEE Transactions on Automatic Control, TAC-36, 1228-1240 doi:10.1109/9.100932
[5] EZAL, K., PAN, Z. KOKOTOVIC, P.V. (1998). Locally Optimal Backstepping Design, Proceedings of 36th IEEE Conference on Decision and Control.CDC´97, San Diego, December 1997, pp, 1767-1773.
[6] EZAL, K. (1998). Disturbance Attenuating Control of Nonlinear Systems with Local Optimality, PhD thesis, University of California, Santa Barbara.
[7] FOSSEN, T.I. (1994). Guidance and Control of Ocean Vehicles, John Wiley and Sons, Ltd., Chichester, England.
[8] FOSSEN, T.I. (1999). Nonlinear Backstepping Designs: Applications to Mechanical Systems and Ship Control, in progress.
[9] FOSSEN, T.I. BERGE, S. (1997). Nonlinear Vectorial Backstepping Design for Global Exponential Tracking of Marine Vessels in the Presence of Actuator Dynamics, Proceedings of IEEE Conference on Decision and Control.CDC 97, San Diego, December 1997, pp. 4237-4242.
[10] FOSSEN, T.I. FJELLSTAD, O.-E (1995). Nonlinear Modelling of Marine Vehicles in 6 Degrees of Freedom, International Journal of Mathematical Modelling of Systems, JMMS-.1, 17-28.
[11] FOSSEN, T.I. GRØVLEN, Å. (1998). Nonlinear Output Feedback Control of Dynamically Positioned Ships Using Vectorial Observer Backstepping, IEEE Transactions on Control Systems Technology, TCST-.1, January, 121-128 doi:10.1109/87.654882
[12] FOSSEN, T.I., LORIA, A. TEEL, A. (1998). UGAS/ULES when Backstepping with Integral Action: Applications to Mechanical Systems and Ships, Submitted to the Journal of Nonlinear and Robust Control.
[13] FOSSEN, T.I. STRAND, J.P. (1999). Passive Nonlinear Observer Design for Ships Using Lyapunov Methods: Experimental Results with a Supply Vessel, Automatica, AUT-3.1, January.
[14] GODHAVN, J.-M., FOSSEN, T.I. BERGE, S.P. (1998). Nonlinear and Adaptive Backstepping Designs for Tracking Control of Ships, International Journal of Adaptive Control and Signal Processing, Special Issue on Marine Systems Control.to appear.
[15] GRAVDAHL, J.T. EGELAND, O. (1998). Two Results on Compressor Surge Control with Disturbance Rejection, Proceedings of the 37th IEEE Conference on Decision and Control.CDC´98, Tampa, Florida.
[16] GRAVDAHL, J.T. (1998). Surge and Rotating Stall in Compressors, Modeling and Control, Advances in Industrial Control, Springer-Verlag, London.
[17] GREITZER, E.M. (1976). Surge and Rotating Stall in Axial Flow Compressors, Part 1: Theoretical Compression System Model, Journal of Engineering for Power, JEP-98, 190-198.
[18] KANELLAKOPOULOS, I., KOKOTOVIC, P.V. MORSE, A.S. (1992). A Toolkit for Nonlinear Feedback Design, Systems and Control Letters, Vol. 18, 83-92 doi:10.1016/0167-6911(92)90012-H
[19] KHALIL, H.K. (1996). Nonlinear Systems, Macmillan, New York.
[20] KODITSCHEK, D.E. (1987). Adaptive Techniques for Mechanical Systems, Proceedings of the 5th Yale Workshop on Adaptive Systems, New Haven, CT, 259-265.
[21] KOKOTOVIC, P.V. SUSSMANN, H.J. (1989). A Positive Real Condition for Global Stabilization of Nonlinear Systems, Systems and Control Letters, Vol. 13, 125-133 doi:10.1016/0167-6911(89)90029-7
[22] KOKOTOVIC, P.V. (1991). The Joy of Feedback: Nonlinear and Adaptive, 1991 Bode Price Lecture, IEEE Control Systems Magazine, Vol. 12,7-17 doi:10.1109/37.165507
[23] KRSTIC, M. DENG, H. (1998). Stabilization of Nonlinear Uncertain Systems, Springer Verlag.
[24] KRSTIC, M., KANELLAKOPOULOS, I. KOKOTOVIC, P.V. (1995). Nonlinear and Adaptive Control Design, John Wiley and Sons Ltd., New York.
[25] LANDAU, Y.D. (1977). Adaptive Control, Marcel Dekker, New York.
[26] LASALLE, J.P. (1966). Stability Theory for Ordinary Differential Equations, Journal of Differential Equations, Vol. 4,57-65 doi:10.1016/0022-0396(68)90048-X
[27] LOZANO, R., BROGLIATO, B. LANDAU, I.D. (1992). Passivity and Global Stabilization of Cascaded Nonlinear Systems, IEEE Transactions on Automatic Control, TAC-37, 1386-1388 doi:10.1109/9.159577
[28] NARENDRA, K.S. ANNASWAMY, A.M. (1989). Stable Adaptive Systems, Prentice Hall, Englewood Cliffs, NJ.
[29] NORRBIN, N.H. (1963). On the Design and Analyses of the Zig-Zag test on Base of Quasi Linear Frequency Response, Technical Report B 104-3, The Swedish State Shipbuilding Experimental Tank.SSPA, Gothenburg, Sweden.
[30] ORTEGA, R. (1991). Passivity Properties for Stabilization of Cascaded Nonlinear Systems, Automatica, AUT-27, 423-424 doi:10.1016/0005-1098(91)90094-I
[31] PARKS, P.C. (1966). Lyapunov Redesign of Model Reference Adaptive Control Systems, IEEE Transactions on Automatic Control, TAC-11, 362-367 doi:10.1109/TAC.1966.1098361
[32] SABERI, A., KOKOTOVIC, P.V. SUSSMANN, H.J. (1990). Global Stabilization of Partially Linear Composite Systems, SIAM J. Control Opt, Vol. 28, 1491-1503 doi:10.1137/0328079
[33] SCIAVICCO, L. SICILIANO, B. (1996). Modelling and Control of Robot Manipulators, McGraw-Hill Companies.
[34] SEPULCHRE, R., JANKOVIC, M. KOKOTOVIC, P. (1997). Constructive Nonlinear Control, Springer Verlag, Berlin.
[35] SLOTINE, J.J.E. LI, W. (1987). Adaptive Manipulator Control: A Case Study, Proceedings of the 1987 IEEE Robotics and Automation, Raleigh, North Carolina, pp. 1392-1400.
[36] SONNTAG, E.D. SUSSMANN, H.J. (1988). Further Comments on the Stabilizability of the Angular Velocity of a Rigid Body, Systems and Control Letters, Vol. 12, 437-442.
[37] STRAND, J.P. (1999). Nonlinear Position Control Systems Design for Marine Vessels, Doctoral Dissertation, Dept. of Eng. Cybernetics, Norwegian Univ. of Sci. and Techn.
[38] STRAND, J.P., EZAL., K., FOSSEN, T.I. KOKOTOVIC, P.V. (1998). Nonlinear Control of Ships: A Locally Optimal Design, Proceedings of the !PAC NOLCOS´98, Enschede, The Netherlands, 1-3 July 1998.
[39] STRAND, J. P., EZAL, K., FOSSEN, T.I. KOKOTOVIC, P. V. (1999). Nonlinear Output Feedback and Locally Optimal Control of Free-Floating and Moored Ships: Experimental Results with a Model Ship, submitted to Automatica.
[40] TSINIAS, J. (1989). Sufficient Lyapunov-Like Conditions for Stabilization, Mathematics of Control, Signals and Systems, Vol. 2, 343-357 doi:10.1007/BF02551276
[41] YOSHIZAWA, T. (1968). Stability Theory by Lyapunov´s Second Method, The Mathematical Society of Japan.
[42] ZHANG, Y., IOANNOU, P.A. CHIEN, C.-C. (1996). Parameter Convergence of a new Class of Adaptive Controllers, IEEE Transactions on Automatic Control, TAC-4.10, 1489-1493 doi:10.1109/9.539430


BibTeX:
@article{MIC-1999-2-3,
  title={{Tutorial on nonlinear backstepping: Applications to ship control}},
  author={Fossen, Thor I. and Strand, Jan P.},
  journal={Modeling, Identification and Control},
  volume={20},
  number={2},
  pages={83--135},
  year={1999},
  doi={10.4173/mic.1999.2.3},
  publisher={Norwegian Society of Automatic Control}
};