Global uniform asymptotic stabilization of an underactuated surface vessel

IEEE Transactions on Automatic Control

Volumn 47, Issue 10, 2002, Pages 1759-1762

  Mazenc, Frédéric ^a   Pettersen, Kristin ^b   Nijmeijer, Henk ^c  

^a INRIA   (France)

^b NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

^c EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Global stability; Lyapunov function; Time varying feedback; Underactuated system

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTATIONAL METHODS; FUNCTIONS; LYAPUNOV METHODS; TIME VARYING CONTROL SYSTEMS;

UNDERACTUATED SURFACE VESSELS;

FEEDBACK CONTROL;

EID: 0036806352     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2002.803554     Document Type: Article

References (34)

1. S.P. Berge, K. Ohtsu, and T.I. Fossen, "Nonlinear control of ships minimizing the position tracking errors," in Proc. IFAC Conf. Control Applications in Marine Systems, Fukuoka, Japan, Oct. 1998, pp. 141-147.
2. A.M. Bloch, "Stabilizability of nonholonomic control systems," Automatica, vol. 28, no. 2, pp. 431-435, 1992.
3. A.M. Bloch and N.H. McClamroch, "Control of mechanical systems with classical nonholonomic constraints," in Proc. 28th IEEE Conf. Decision and Control, Tampa, FL, 1989, pp. 201-205.
4. N.H. McClamroch, "Asymptotic stability and feedback stabilization," in Differential Geometric Control Theory, R.W. Brockett, R.S. Millman, and H.J. Sussmann, Eds. Boston, MA: Birkhauser.
5. F. Bullo, "Stabilization of relative equilibria for underactuated systems on Riemannian manifolds," Automatica, vol. 36, no. 12, pp. 1819-1834, Dec. 2000.
6. F. Bullo, N.E. Leonard, and A.D. Lewis, "Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups," IEEE Trans. Automat. Contr., vol. 45, pp. 1437-1454, Aug. 2000.
7. J.M. Coron, "Global asymptotic stabilization for controllable systems without drift," Math, Control Signals Syst., vol. 5, pp. 295-312, 1992.
8. _, "On the stabilization in finite time of locally controllable systems by means of continuous time-varying feedback law," SIAM J. Control Optim., vol. 33, no. 3, pp. 804-833, 1995.
9. J.M. Coron and L. Praly, "Adding an integrator for the stabilization problem," Syst. Control Lett., vol. 17, pp. 89-104, 1991.
10. J.M. Coron and L. Rosier, "A relation between continuous time-varying and discontinuous feedback stabilization," J. Math. Syst. Estimat. Control, vol. 4, no. 1, pp. 67-84, 1994.
11. I. Fantoni, R. Lozano, F. Mazenc, and K.Y. Pettersen, "Stabilization of a nonlinear underactuated hovercraft," Int. J. Robust Nonlinear Control, vol. 10, no. 8, pp. 645-654, 2000.
12. T.I. Fossen, Guidance and Control of Ocean Vehicles. New York: Wiley, 1994.
13. T.I. Fossen, J.M. Godhavn, S.P. Berge, and K.P. Lindegaard, "Nonlinear control of underactuated ships with forward speed compensation," in Proc, 1998 IFAC Symp. Nonlinear Control Systems Design, Enschede, The Netherlands, pp. 121-126.
14. T.I. Fossen and J.P. Strand, "Passive nonlinear observer design for ships using Lyapunov methods: Experimental results with a supply vessel," Automatica, vol. 35, no. 1, pp. 3-16, 1999.
15. R.A. Freeman and P.V. Kokotovic, Robust Nonlinear Control Design. Boston, MA: Birkhauser, 1996.
16. J.M. Godhavn, "Nonlinear tracking of underactuated surface vessels," in Proc. 35th IEEE Conf. Decision and Control, Kobe, Japan, 1996, pp. 987-991.
17. H. Khalil, Nonlinear Systems, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1996.
18. I. Kolmanovsky and N.H. McClamroch, "Developments in nonholonomic control problems," IEEE Contr. Syst. Mag., vol. 15, pp. 20-36, June 1995.
19. M. Kristic, I. Kanellakopoulos, and P.V. Kokotovic, Nonlinear and Adaptive Control Design. New York: Wiley, 1995.
20. F. Mazenc, "Strict Lyapunov functions for time-varying systems," Automatica, 2002, to be published.
21. _, "Interconnected nonlinear systems, local and global stabilization," Syst. Control Lett., no. 35, pp. 317-323, 1998.
22. P. Morin and C. Samson, "Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics," ESAIM: Control, Optim., Calc. Variat., vol. 4, pp. 1-3, Apr. 1999.
23. K.Y. Pettersen and O. Egeland, "Exponential stabilization of an underactuated surface vessel," in Proc. 35th IEEE Conf. Decision and Control, Kobe, Japan, 1996, pp. 967-971.
24. K.Y. Pettersen and T.I. Fossen, "Underactuated ship stabilization using integral control: Experimental results with Cybership I," in Proc. 1998 IFAC Symp. Nonlinear Control Systems Design, Enschede, The Netherlands, July 1998, pp. 127-132.
25. K.Y. Pettersen and H. Nijmeijer, "Tracking control of an underactuated surface vessel," in Proc. 37th IEEE Conf. Decision and Control, Tampa, FL, 1998, pp. 4561-4566.
26. _, "Global practical stabilization and tracking for an underactuated ship-A combined averaging and backstepping approach," in Proc. IFAC Conf. Systems Structure Control, Nantes, France, 1998, pp. 59-64.
27. M. Reyhanoglu, "Control and stabilization of an underactuated surface vessel," in Proc. 35th IEEE Conf. Decision and Control, Kobe, Japan, 1996, pp. 2371-2376.
28. C. Samson, "Velocity and torque feedback control of a nonholonomic cart," in Proc. Int. Workshop Nonlinear Adaptive Control: Issues Robotics, Grenoble, France, 1990.
29. R. Sepulchre, M. Jankovic, and P.V. Kokotovic, Constructive Nonlinear Control. New York: Springer-Verlag, 1996.
30. H. Sira-Ramirez, "On the control of the underactuated ship: A trajectory planning approach," in Proc. 38th IEEE Conf. Decision and Control, Phoenix, AZ, 1999, pp. 1658-1663.
31. E.D. Sontag, "Smooth stabilization implies coprime factorization," IEEE Trans. Automat. Contr., vol. 34, pp. 435-443, Apr. 1989.
32. K.Y. Wichlund, O.J. Sørdalen, and O. Egeland, "Control of vehicles with second-order nonholonomic constraints: Underactuated vehicles," in Proc. 3rd Eur. Control Conf., Rome, Italy, 1995, pp. 3086-3091.
33. J. Zabczyk, "Some comments on stabilizability," Appl. Math. Optim., vol. 19, pp. 1-9, 1989.
34. C. Samson, "Velocity and torque feedback control of a nonholonomic cart," in International Workshop in Adaptive and Nonlinear Control: Issues in Robotics, ser. Lectrue Notes in Control and Information Sciences. New York: Springer-Verlag, 1991, pp. 125-151.