On local transverse feedback linearization

SIAM Journal on Control and Optimization

Volumn 47, Issue 5, 2008, Pages 2227-2250

  Nielsen, Christopher ^a   Maggiore, Manfredi ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

Controlled invariant sets; Feedback linearization; Multi input systems; Nonlinear geometric control; Set stabilization; Zero dynamics

Indexed keywords

CONTROL SYSTEMS; DYNAMICS; FEEDBACK; LINEARIZATION;

CONTROLLED INVARIANT SETS; MULTI-INPUT SYSTEMS; NONLINEAR GEOMETRIC CONTROL; SET STABILIZATION; ZERO DYNAMICS;

FEEDBACK LINEARIZATION;

EID: 55549120219     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/070682125     Document Type: Article

References (31)

1. J. P. AUBIN, Viability Theory, Birkhäuser, Boston, 1991.
2. A. BANASZUK AND J. HAUSER, Feedback linearization of transverse dynamics for periodic orbits, Systems Control Lett., 26 (1995), pp. 95-105.
3. R. W. BROCKETT, Feedback invariants for nonlinear systems, in Proceedings of the IFAC World Congress, Helsinki, 1978, pp. 1115-1120.
4. P. BRUNOVSKÝ, A classification of linear controllable systems, Kybernetika, 3 (1970), pp. 173-187.
5. V. GUILLEMIN AND A. POLLACK, Differential Topology, Prentice-Hall, Englewood Cliffs, NJ, 1974.
6. M. W. HIRSCH, Differential Topology, Graduate Texts in Math. 33, Springer-Verlag, New York, 1976.
7. R. M. HIRSCHORN, (A, B)-invariant distributions and disturbance decoupling of nonlinear systems, SIAM J. Control Optim., 19 (1981), pp. 1-19.
8. L. R. HUNT, R. SU, AND G. MEYER, Design for multi-input nonlinear systems, in Differential Geometric Control Theory, R. W. Brockett, R. S. Millman, and H. Sussmann, eds., Birkhäuser, Boston, 1983, pp. 268-298.
9. A. ISIDORI, Nonlinear Control Systems, 3rd ed., Springer, New York, 1995.
10. A. ISIDORI AND A. J. KRENER, On feedback equivalence of nonlinear systems, Systems Control Lett., 2 (1982), pp. 118-121.
11. A. ISIDORI, A. J. KRENER, C. GORI-GIORGI, AND S. MONACO, Nonlinear decoupling via feedback: A differential geometric approach, IEEE Trans. Automat. Control, 26 (1981), pp. 331-345.
12. B. JAKUBCZYK AND W. RESPONDEK, On linearization of control systems, Bull. Acad. Polon. Sci. Sér. Sci. Math., 28 (1980), pp. 517-522.
13. A. J. KRENER, A. ISIDORI, AND W. RESPONDEK, Partial and robust linearization by feedback, in Proceedings of the 22nd IEEE Conference on Decision and Control, San Antonio, 1983, pp. 126-130.
14. A. J. KRENER, On the equivalence of control systems and the linearization of nonlinear systems, SIAM J. Control Optim., 11 (1973), pp. 670-676.
15. R. MARINO, On the largest feedback linearizable subsystem, Systems Control Lett., 6 (1986), pp. 345-351.
16. R. MARINO, W. M. BOOTHBY, AND D. L. ELLIOTT, Geometric properties of linearizable control systems, Math. Systems Theory, 18 (1985), pp. 97-123.
17. R. MARINO AND P. TOMEI, Nonlinear Control Design, Prentice-Hall, Toronto, 1995.
18. C. NIELSEN AND M. MAGGIORE, Maneuver regulation via transverse feedback linearization: Theory and examples, in Proceedings of the IFAC Symposium on Nonlinear Control Systems (NOLCOS), Stuttgart, Germany, 2004, pp. 59-66.
19. C. NIELSEN AND M. MAGGIORE, Output stabilization and maneuver regulation: A geometric approach, Systems Control Lett., 55 (2006), pp. 418-427.
20. H. NIJMEIJER, Controlled invariance for affine control systems, Internat. J. Control, 34 (1981), pp. 825-833.
21. H. NIJMEIJER AND A. VAN DER SCHAFT, Nonlinear Dynamical Control Systems, Springer-Verlag, New York, 1990.
22. H. POINCARÉ, Sur les propérties des fonctions définies par les équations aux différences partielles, in Œuvres, Vol. 1, Gauthier-Villars, Paris, 1929, pp. xcix-cx.
23. W. RESPONDEK, Partial linearization, decompositions and fibre linear systems, in Theory and Applications of Nonlinear Control Systems, C. I. Byrnes and A. Lindquist, eds., North-Holland, Amsterdam, 1986, pp. 137-154.
24. A. SHIRIAEV, J. W. PERRAM, AND C. CANUDAS de WIT, Constructive tool for orbital stabilization of underactuated nonlinear systems: Virtual constraints approach, IEEE Trans. Automat. Control, 50 (2005), pp. 1164-1176.
25. M. SPIVAK, A Comprehensive Introduction to Differential Geometry, Vol. 1, 3rd ed., Publish or Perish, Houston, 2005.
26. R. SU, On the linear equivalents of nonlinear systems, Systems Control Lett., 2 (1982), pp. 48-52.
27. R. SU AND L. R. HUNT, A canonical expansion for nonlinear systems, IEEE Trans. Automat. Control, 31 (1986), pp. 670-673.
28. W. M. WONHAM, Linear Multivariable Control: A Geometric Approach, 3rd ed., Springer-Verlag, New York, 1985.
29. W. M. WONHAM AND A. S. MORSE, Feedback invariants of linear multivariable systems, Automatica, 8 (1972), pp. 93-100.
30. Z. XU AND L. R. HUNT, On the largest input-output linearizable subsystem, IEEE Trans. Automat. Control, 41 (1996), pp. 128-132.
31. Z. XU AND L. R. HUNT, Finding maximal linear subsystems of nonlinear systems with outputs, IEEE Trans. Automat. Control, 45 (2000), pp. 1701-1704.