Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one

IEEE Transactions on Automatic Control

Volumn 50, Issue 12, 2005, Pages 1936-1955

  Acosta, José Ángel ^a   Ortega, Romeo ^b   Astolfi, Alessandro ^c   Mahindrakar, Arun D ^b  

^a UNIVERSIDAD DE SEVILLA   (Spain)

^b UNIV PARIS SUD   (France)

^c IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Energy shaping; Hamiltonian systems; Nonlinear control; Passivity; Underactuated mechanical systems

Indexed keywords

CONTROL SYSTEM SYNTHESIS; FEEDBACK CONTROL; HAMILTONIANS; LYAPUNOV METHODS; PARTIAL DIFFERENTIAL EQUATIONS; ROBUSTNESS (CONTROL SYSTEMS); STATE ESTIMATION; SYSTEM STABILITY;

ENERGY SHAPING; HAMILTONIAN SYSTEMS; PASSIVITY; UNDERACTUATED MECHANICAL SYSTEMS;

NONLINEAR CONTROL SYSTEMS;

EID: 30344458173     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2005.860292     Document Type: Article

References (41)

1. J. A. Acosta, "Underactuated nonlinear control systems," Ph.D. dissertation, Dept. Autom. Control Syst. Eng., Univ. Seville, Seville, Spain, 2004.
2. J. A. Acosta, R. Ortega, and A. Astolfi, "Position feedback stabilization of mechanical systems with underactuation degree one," in Proc. 6th IFAC Symp. Nonlinear Control Systems, NOLCOS'04, Stuttgart, Germany, Sep. 1-3, 2004.
3. J. A. Acosta, R. Ortega, "Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one," in Proc. Amer. Control Conf.(ACC04), Boston, MA, Jun. 30-Jul. 2, 2004.
4. A. Ailon and R. Ortega, "An observer-based controller for robot manipulators with flexible joints:" Syst. Control Lett., vol. 21, pp. 329-335, 1993.
5. A. Astolfi and R. Ortega, "Energy based stabilization of the angular velocity of a rigid body operating in failure configuration," J. Guid. Control Dyna., vol. 25, no. 1, pp. 184-187, Jan.-Feb. 2002.
6. A. Astolfi and R. Ortega, "Immersion and invariance: A new tool for stabilization and adaptive control of nonlinear systems:" IEEE Trans. Autom. Control, vol. 48, no. 4, pp. 590-606, Apr. 2003.
7. R. Akmeliawati and I. Mareels, "Passivity-based-control for flight control systems;" in Proc. Inform. Decision Control, 1999, pp. 15-20.
8. D. Auckly, L. Kapitanski, and W. White, "Control of nonlinear underactuated systems:" Comm. Pure Appl. Math., vol. 3, pp. 354-369, 2000.
9. D. Auckly and L. Kapitanski, "On the λ-equations for matching control laws," SIAM J. Control Optim., vol. 41, no. 5, pp. 1372-1388, 2002.
10. P. Berg and J. McGregor, Elementary Partial Differential Equations. New York: McGraw-Hill, 1966.
11. G. Blankenstein, R. Ortega, and A. J. van der Schaft, "The matching conditions of controlled Lagrangians and interconnection assigment passivity based control:" Int. J. Control, vol. 75, no. 9, pp. 645-665, 2002.
12. A. Bloch, N. Leonard, and J. Marsden, "Controlled lagrangians and the stabilization of mechanical systems,IEEE Trans. Autom. Control, vol., 45, no. 12, Dec. 2000.
13. A. M. Bloch, D. E. Chang, N. Leonard, and J. E. Marsden, "Controlled lagrangians and the stabilization of mechanical systems II: Potential shaping," IEEE Trans. Autom. Control, vol. 46, pp. 1556-1571, 2001.
14. D. E. Chang and J. E. Marsden, "Reduction of controlled lagrangian and hamiltonian systems with symmetry," SIAM J. Control Optim., vol. 43, pp.277-300, 2004.
15. A. M. Bloch, Nonoholonomic Mechanics and Control. New York: Springer-Verlag, 2003.
16. D. E. Chang, A. M. Bloch, N. E. Leonard, J. E. Marsden, and C. A. Woolsey, "The equivalence of controlled lagrangian and controlled hamiltonian systems for simple mechanical systems;" ESAIM. Control, Optim., Calc. Variations, vol. 8, pp. 393-422, 2002.
17. D. Mclean, Automatic Flight Control Systems. Upper Saddle River, NJ: Prentice-Hall, 1990.
18. F Gomez-Estern, R. Ortega, F. Rubio, and J. Aracil, "Stabilization of a class of underactuated mechanical systems via total energy shaping:" in Proc. IEEE Conf. Decision and Control, Orlando', FL, Dec. 4-7, 2001.
19. J. W. Grizzle, C. H. Moog, and C. Chevallereau, "Nonlinear control of mechanical systems with an unactuated cyclic variable:" IEEE Trans. Autom. Control, vol. 50, no. 5, pp. 559-576, May 2005.
20. J. Hauser, S. Sastry, and G. Meyer, "Nonlinear control design for slightly nonminimum phase systems: Application to V/STOL aircraft," Automatica', vol. 28, no. 4, pp. 665-679, July 1992.
21. Z. P. Jiang and I. Kanellakopoulos, "Global output feedback tracking for a benchmark nonlinear system," IEEE Trans. Autom. Control, vol. 45, no. 5, pp. 1023-1027, May 2000.
22. D. Karagiannis, A. Astolfi, and R. Ortega, "Two results for adaptive output feedback stabilization of nonlinear systems:" Automatica, vol. 39, no. 5, pp. 857-866, May 2003.
23. A. Lewis, "Notes on energy shaping:" in Proc. 43rd IEEE Conf. Decision and Control, Bahamas, Dec. 14-17, 2004.
24. A. D. Mahindrakar, A. Astolfi, R. Ortega, and J. A. Acosta, "Further constructive results on IDA-PBC of mechanical systems:" LSS, LSS Internal Report, Mar. 2005.
25. P. Martin, S. Devasia, and B. Paden, "A different look at output tracking: Control of a VTOL aircraft," Automatica, vol. 32, no. 1, pp. 101-107, 1996.
26. R. Olfati-Saber, "Global configuration for the VTOL aircraft with strong input coupling," IEEE Trans. Autom. Control, vol. 47, no. 11, pp. 1949-1952, Nov. 2002.
27. R. Olfati-Saber, "Normal forms for underactuated mechanical systems with symmetry," IEEE Trans. Autom. Control, vol. 47, no. 2, pp. 305-308, Feb. 2002.
28. R. Ortega, J. A. Acosta, and A. Astolfi, "On energy functions assignable to mechanical systems: Conditions for invariance under partial feedback linearization," LSS, LSS Internal Report, Mar. 2005.
29. R. Ortega and E. Garcia-Canseco, "Interconnection and damping assignment passivity-based control: A survey," Eur. J. Control, vol. 10, pp. 432-450, 2004.
30. R. Ortega, A. van der Schaft, B. Maschke, and G. Escobar, "Interconnection and damping assignment passivity-based control of port-controlled hamiltonian systems," Automatica, vol. 38, no. 4, Apr. 2002.
31. R. Ortega, M. Spong, F. Gomez, and G. Blankenstein, "Stabilization of underactuated mechanical systems via interconnection and damping assignment," IEEE Trans. Autom. Control, vol. 47, no. 8, pp. 1218-1233, Aug. 2002.
32. R. Ortega, A. Loria, P. J. Nicklasson, and H. Sira-Ramirez, "Passivity-based control of Euler-Lagrange systems," in Communications and Control Engineering. Berlin, Germany: Springer-Verlag, Sept. 1998.
33. H. Rodriguez, A. Astolfi, and R. Ortega, "On the construction of static stabilizers and static output trackers for dynamically linearizable systems, related results and applications," in Proc. IEEE 2004 Conf. Decision and Control, Paradise Island, Bahamas, Dec. 14-17, 2004.
34. N. Rouche and J. Mawhin, Ordinary Differential Equations. London, U.K.: Pitman, 1980, vol. II.
35. S. Sastry, Nonlinear Systems. Analisys, Stability and Control. New York: Springer-Verlag, 1999.
36. R. Sepulchre, M. Janković, and P. Kokotoviacc, Constructive Nonlinear ControL. London, U.K.: Springer-Verlag, 1997.
37. M. W. Spong, "Underactuated mechanical systems," in Control Problems in Robotics and Automation, B. Siciliano and K. Valavanis, Eds. New York: Springer-Verlag, 1998, vol. 230. LNICS.
38. E. D. Sontag, "On stability of perturbed asymptotically stable systems," IEEE Trans. Autom. Control, vol. 48, no. 2, pp. 313-314, Feb. 2003.
39. A. R. Teel, "A nonlinear small gain theorem for analysis of systems with saturation:" IEEE Trans. Autom. Control, vol. 41, no. 9, pp. 1256-1270, Sep. 1996.
40. 2 -Gain and Passivity Techniques in Nonlinear Control. Berlin, Germany: Springer-Verlag, 1999.
41. C. Woolsey, C. Reddy, A. Bloch, D. Chang, N. Leonard, and J. Marsden, "Controlled lagrangian systems with gyroscopic forcing and dissipation," Eur. J. Control, vol. 10, no. 5, pp. 478-496, 2004.