Integral manifolds of singularity perturbed systems with application to rigid-link flexible-joint multibody systems

International Journal of Non-Linear Mechanics

Volumn 35, Issue 1, 2000, Pages 133-155

  Ghorbel, Fathi ^a   Spong, Mark W ^b  

^a Rice University   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEM ANALYSIS; DIFFERENTIAL EQUATIONS; DYNAMICS; LYAPUNOV METHODS; MATRIX ALGEBRA; SYSTEM STABILITY;

INTEGRAL MANIFOLDS; RIGID LINK FLEXIBLE JOINT MULTIBODY SYSTEMS; SINGULARLY PERTURBED SYSTEMS;

NONLINEAR EQUATIONS;

EID: 0033684426     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(98)00092-4     Document Type: Article

References (29)

1. [1] V.A. Sobolev, Integral manifolds and decomposition of singularly perturbed systems, Systems Control Lett. 5 (1984) 169-179.
2. [2] H.W. Knobloch, B. Aulback, Singular perturbations and integral manifolds, J. Math. Phys. Sci. 18 (5) (1984).
3. [3] K.V. Zadiraka, On the integral manifold of a system of differential equations containing a small parameters, Dokl. Akad. Nauk. SSSR 115 (1957) 646-649 (in Russian).
4. [4] K.V. Zadiraka, On a nonlocal integral manifold of a nonregularly perturbed differential system, Ukrain. Math. Z. 17 (1965) 47-63 (in Russian). Translated in AMS Transl., Ser. 2, 89 (1970) 29-49.
5. [4] K.V. Zadiraka, On a nonlocal integral manifold of a nonregularly perturbed differential system, Ukrain. Math. Z. 17 (1965) 47-63 (in Russian). Translated in AMS Transl., Ser. 2, 89 (1970) 29-49.
6. [5] J.S. Baris, On an integral manifold of a nonregularly perturbed differential system, Usp. Mat. Nauk 20 (1968) 439-448 (in Russian).
7. [6] N. Fenichel, Geometric singular perturbation theory for ordinary differential equations, J. Differential Equations 31 (1979) 53-98.
8. [7] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol. 840, Springer, Berlin, New York, 1981.
9. [8] H.W. Knobloch, Dichotomy and integral manifolds I: general principles, Results Math. 14 (1988) 93-124.
10. [9] H.W. Knobloch, Dichotomy and integral manifolds II: proof of the continuation principle, Results Math. 16 (1989) 107-135.
11. [10] H.W. Knobloch, Invariant manifolds for ordinary differential equations, in: C. Bennewitz (Ed.), Differential Equations and Mathematical Physics, Mathematics in Science and Engineering, vol. 186, Academic Press, New York, 1992.
12. [11] A.R. Hausrath, Stability in the critical case of purely imaginary roots for neutral functional differential equations, J. Differential Equations 13 (1973) 329-357.
13. [12] J. Carr, Applications of Center Manifold Theory, Applied Mathematical Sciences, Vol. 35, Springer, New York, 1981.
14. [13] F. Ghorbel, R. Abaza, Integral manifolds of singularly perturbed differential equations, Internal Report, Dynamic Systems and Control Laboratory, Department of Mechanical Engineering, Rice University, December, 1997 (in French).
15. [14] A. Saberi, H.K. Khalil, Quadratic-type Lyapunov functions for singularly perturbed systems, IEEE Trans. Automat. Control AC-29 (6) (1984) 542-550.
16. [15] P.V. Kokotović, H.K. Khalil, J. O'Reilly, Singular Perturbation Methods in Control: Analysis and Design, Academic Press, London, 1986.
17. [16] M.W. Spong, Modeling and control of elastic joint manipulators, J. Dyn. System Meas. Control 109 (1987) 310-319.
18. [17] M.W. Spong, Adaptive control of flexible joint manipulators, Systems Controls Lett. 13 (1989) 15-21.
19. [18] F. Ghorbel, M.W. Spong, Robustness of adaptive control of robots, J. Intell. Robot. Systems 6 (1992) 3-15.
20. [19] K. Khorasani, P.V. Kokotović, Invariant manifolds and their application to robot manipulators with flexible joints, Proc. IEEE Int. Conf. Robot. Automat., St. Louis, MO, 1985.
21. [20] K. Khorasani, M.W. Spong, Invariant manifolds and their application to robot manipulators with flexible joints, Proc. IEEE Int. Conf. Robot. Automat., St. Louis, MO, 1985.
22. [21] M.W. Spong, K. Khorasani, P.V. Kokotović, An integral manifold approach to feedback control of flexible joint robots, IEEE J. Robot. Automat. 3 (4) (1987) 291-300.
23. [22] M. Vidyasagar, Nonlinear Systems Analysis, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1993.
24. [23] J.-J.E. Slotine, W. Li, On the adaptive control of robot manipulators, Int. J. Robot. Res. 6 (3) (1987) 49-59.
25. [24] R. Bellman, Introduction to Matrix Analysis, McGraw-Hill, New York, 1970.
26. [25] L.S. Shieh, M.M. Mehio, H.M. Dib, Stability of the second-order matrix polynomial, IEEE Trans. Automat. Control AC-32 (1987) 231-233.
27. [26] V.V. Strygin, V.A. Sobolev, Effect of geometric and kinetic parameters and energy dissipation on the orientation stability of satellites with double spin, Kosmicheskye Issle-dovaniya 14 (3) (1976) 366-371 (in Russian).
28. [27] C. Desoer, M. Vidyasagar, Feedback Systems: Input-Output Properties, Academic Press, New York, 1975.
29. [28] F. Ghorbel, M.W. Spong, Integral manifold corrective control of flexible joint robot manipulators: the known parameter case, Modeling and Control of Compliant and Rigid Motion Systems, DSV-vol. 31, ASME Winter Annual Meeting, Atlanta, GA, 1-6 December 1991, pp. 81-93.