Lyapunov stability control of inverted pendulums with general base point motion

International Journal of Non-Linear Mechanics

Volumn 33, Issue 5, 1998, Pages 801-818

  Wu, Q ^a   Thornton Trump, A B ^a   Sepehri, N ^a  

^a UNIVERSITY OF MANITOBA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000863735     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0020-7462(97)00052-8     Document Type: Article

References (25)

1. Q. Wu and A. B. Thornton-Trump, Stabilization of a base-excited inverted pendulum with two degrees of rotational freedom. J. Inst. Franklin: Engng Appl. Math. 334B, 63 (1996).
2. C. K. Chow and D. H. Jacobson, Further studies of human locomotion: postural stability and control. Math. Biosci. 15, 63 (1972).
3. H. Hemami and A. Katbab, Constrained inverted pendulum model for evaluating upright postural stability. ASME J. Dynamic Systems, Measurement Control 111, 343 (1982).
4. K. Iqbal, H. Hemami and S. Simon, Stability and control of a frontal four-link biped system. IEEE Trans. Biomed. Engng 40, 1007 (1993).
5. J. S. Yang, A control study of a kneeless biped locomotion system. J. Inst. Franklin: Engng Appl. Math. 125, (1994).
6. A. F. Filippov, Differential equations with discontinuous right-hand side. Math. Sbornik 51, 99 (1960). [English Translation: American Mathematical Society Translations 42, 191 (1964)].
7. A. F. Filippov, Differential equations with discontinuous right-hand side. Math. Sbornik 51, 99 (1960). [English Translation: American Mathematical Society Translations 42, 191 (1964)].
8. A. F. Filippov, Differential equations with second members discontinuous on intersecting surfaces. Differentsial'nye Uravneniya 15, 1814 (1979). (English Translation: Differential Equations 15, 1292 (1980)].
9. A. F. Filippov, Differential equations with second members discontinuous on intersecting surfaces. Differentsial'nye Uravneniya 15, 1814 (1979). (English Translation: Differential Equations 15, 1292 (1980)].
10. J. J. Slotine and S. S. Sastry, Tracking control of nonlinear systems using sliding surfaces, with application to robot manipulators. Int. J. Control 38, 465 (1983).
11. B. E. Paden and S. S. Sastry, A calculus for computing Filippov's differential inclusion with application to the variable structure control of robot manipulators. IEEE Trans. Cire. Systems 34, 73 (1987).
12. R. A. DeCarlo, S. H. Zak and P. Matthews, Variable structure control of nonlinear multivariable systems: a tutorial. Proc. IEEE 76, 212 (1988).
13. S. C. Southward, C. J. Radcliffe and C. R. MacCluer, Robust nonlinear stick-slip friction compensation. ASME J. Dynamic Systems Measurement Control 113, 639 (1991).
14. M. Corless, Control of uncertain nonlinear systems. ASME J. Dynamic Systems Measurement Control 115, 362 (1993).
15. D. Shevitz and B. Paden, Lyapunov stability theory of nonsmooth systems. IEEE Trans. Automat. Control 39, 1910 (1994).
16. W. Hahn, Theory and Application of Lyapunov's Direct Method. Prentice Hall, Englewood Cliffs, NJ (1963).
17. Q. Wu, Lyapunov stability control of a base-excited inverted pendulum and its application to locomotion systems. Ph.D. thesis, The University of Manitoba, Winnipeg, Manitoba, Canada (1996).
18. J. J. Slotine and W. Li, Applied Nonlinear Control. Prentice Hall, Englewood Cliffs, NJ (1991).
19. V. I. Utkin, Variable structure systems with sliding modes. IEEE Trans. Automat. Control 22, 212 (1977).
20. V. I. Utkin, Sliding Modes in Control and Optimization. Springer, Berlin (1992).
21. R. M. Murray, Z. Li and S. S. Sastry, A Mathematical Introduction to Robot Manipulation. CRC Press, Boca Raton, FL (1994).
22. L. Cai and G. Song, A smooth robust nonlinear controller for robot manipulators with joint stick-slip friction. Proc. IEEE Internat. Conf. on Robotics Automation, Atlanta, GA, p. 449 (1993).
23. Q. Wu, N. Sepehri, A. B. Thornton-Trump and S. Onyshko, An extended integral method to derive Lyapunov functions for nonlinear systems. Int. J. Control 62, 717 (1995).
24. M. Vidyasagar, Nonlinear Systems Analysis. Prentice-Hall, Englewood Cliffs, NJ (1993).
25. Q. Wu, A. B. Thornton-Trump and M. Alexander, Stability and control of human trunk movement during walking, preprint. Proc. 4th Int. Symp. on 3-D Analysis of Human Movement. Granoble, France (1996).