Ball on a beam: Stabilization under saturated input control with large basin of attraction

Multibody System Dynamics

Volumn 21, Issue 1, 2009, Pages 71-89

  Aoustin, Yannick ^a   Formal'Skii, Alexander ^b  

^a INSTITUT DE RECHERCHE EN COMMUNICATIONS ET CYBERNÉTIQUE DE NANTES   (France)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Basin of attraction; Controllability domain; Jordan form; Saturated control; Stabilization

Indexed keywords

BIPED LOCOMOTION; CONTROLLABILITY; NEURAL NETWORKS; NONLINEAR SYSTEMS; SPHERES; STABILIZATION;

BASIN OF ATTRACTION; CIRCULAR BEAMS; CONTROL LAWS; EQUILIBRIUM POINTS; GAIN PARAMETERS; JORDAN FORM; NONLINEAR CONTROL LAWS; PLANAR SYSTEMS; SATURATED CONTROL; SATURATED INPUTS; SIMULATION RESULTS; UNDER ACTUATED; UNSTABLE MODES;

NONLINEAR CONTROL SYSTEMS;

EID: 63049086306     PISSN: 13845640     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11044-008-9128-0     Document Type: Article

References (27)

1. J. Hauser S. Sastry G. Meyer 1992 Nonlinear control design for slightly nonminimum phase systems. Application to V/STOL aircraft Automatica 28 4 665 679
2. M. Alimir F. Boyer 2003 Fast generation of attractive trajectories for an under-actuated satellite. Application to feedback control design J. Optim. Eng. 4 225 244
3. W.J. Book M. Majette 1983 Controller design for flexible, distributed parameter mechanical arms via combined state space and frequency domain techniques Trans. ASME, J. Dyn. Syst. Meas. Control 105 245 254
4. A. De Luca B. Siciliano 1991 Closed-form dynamic model of planar multi-link lightweight robots IEEE Trans. Syst. Man Cybern. 21 4 826 839
5. K.J. Astrom K. Furuta 2000 Swinging up a pendulum by energy control Automatica 36 2 287 295
6. A.A. Grishin A.V. Lenskii D.E. Okhotsimsky D.A. Panin A.M. Formal'sky 2002 A control synthesis for an unstable object. An inverted pendulum J. Comput. Syst. Sci, Int. 41 5 685 694
7. M.W. Spong 1995 The swing up control problem for the acrobot IEEE Control Syst. Mag. 14 1 49 55
8. J.W. Grizzle C.M. Moog C. Chevallereau 2005 Nonlinear control of mechanical systems with an unactuated cyclic variable IEEE Trans. Autom. Control 50 5 559 576
9. Aoustin, Y., Formal'sky, A.M.: Design of reference trajectory to stabilize desired nominal cyclic gait of a biped. In: Proceedings International Workshop on Robot Motion and Control, ROMOCO'99, pp. 159-165 (1999)
10. Y. Aoustin A.M. Formal'sky 2003 Control design for a biped reference trajectory based on driven angles as functions of the undriven angle J. Comput. Syst. Sci. Int. 42 4 159 176
11. F. Plestan J.W. Grizzle W. Westervelt G. Abba 2003 Stable walking of a 7-dof biped robot IEEE Trans. Robot. Autom. 19 653 668
12. Acosta, J., Ortega, R., Astolfo, A.: Position feedback stabilization of mechanical systems with underactuation degree one. In: Proceedings of the 6th IFAC Symposium Nonlinear Control Systems, NOCOLS'04 (2004)
13. Fantoni, I., Lozano, R.: Non Linear Control for Underactuated Mechanical Systems. Communications and Control Engineering Series. Springer, London (2002)
14. Olfati-Saber, R.: Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles. PhD thesis, Massachusetts Institute of Technology (2001)
15. J. Hauser S. Sastry P. Kokotović 1992 Nonlinear control via approximate input-output linearization IEEE Trans. Autom. Control 37 392 398
16. A.R. Teel L. Praly 1995 Tools for semiglobal stabilization by partial state and output feedback SIAM J. Control Optim. 33 1443 1488
17. Teel, A.R.: Using saturation to stabilize a class of single-input partially linear composite systems. In: IFAC NOLCOS'92 Symposium, May 1992, pp. 369-374 (1992)
18. Sepulchre, R., Janković, M., Kokotović, P.: Constructive Nonlinear Control. Springer, Berlin (1997)
19. Y. Aoustin A.M. Formal'sky 2005 On the stabilization of biped vertical posture in single support using internal torques Robotica 23 1 65 74
20. Y. Aoustin A.M. Formal'sky Y. Martynenko 2006 Stabilisation of unstable equilibrium postures of a two-link pendulum using a flywheel J. Comput. Syst. Sci. Int. 2 16 23
21. Formal'skii, A.M.: Controllability and Stability of Systems with Limited Resources. Nauka, Moscow (1974) (in Russian)
22. T. Hu Z. Lin L. Qiu 2001 Stabilization of exponentially unstable linear systems with saturating actuators IEEE Trans. Autom. Control 46 6 973 979
23. Gorinevsky, D.M., Formal'sky, A.M., Schneider, A.Yu.: Force Control of Robotics Systems. CRC Press, New York (1997)
24. Kalman, R.E., Falb, P.L., Arbib, M.A.: Topics in Mathematical System Theory. McGraw-Hill, New York (1969)
25. Korn, G.A., Korn, T.M.: Mathematical Handbook for Engineers and Scientists. McGraw-Hill, New York (1968)
26. Khalil, H.K.: Nonlinear System. Prentice Hall, New Jersey (2002)
27. Boltyansky, V.G.: Mathematical Methods of Optimal Control. Nauka, Moscow (1966) (in Russian)