Limit sets, zero dynamics, and internal models in the problem of nonlinear output regulation

IEEE Transactions on Automatic Control

Volumn 48, Issue 10, 2003, Pages 1712-1723

  Byrnes, Christopher I ^a   Isidori, Alberto ^a,b  

^a WASHINGTON UNIVERSITY   (United States)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Internal model; Limit sets; Nonlinear control; Regulation; Tracking; Zero dynamics

Indexed keywords

ASYMPTOTIC STABILITY; CONTROL SYSTEM SYNTHESIS; MATHEMATICAL MODELS; SYSTEM STABILITY;

INTERNAL MODEL; LIMIT SETS; ZERO DYNAMICS;

NONLINEAR CONTROL SYSTEMS;

EID: 0242334020     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2003.817926     Document Type: Article

References (25)

1. J. P. Aubin, Viability Theory, Boston, MA: Birkhaüser, 1991.
2. J. P. Aubin and A. Cellina, Differential Inclusions. New York: Springer-Verlag, 1984.
3. G. D. Birkhoff, Dynamical Systems. Providence, RI: Amer. Math. Soc., 1927.
4. C. I. Byrnes, F. Delli Priscoli, A. Isidori, and W. Kang, "Structurally stable output regulation of nonlinear systems," Automatica, vol. 33, pp. 369-385, 1997.
5. C. I. Byrnes and A. Isidori, "Asymptotic stabilization of minimum phase nonlinear systems," IEEE Trans. Automat. Control, vol. 36, pp. 1122-1137, Oct. 1991.
6. C. I. Byrnes, A. Isidori, and L. Praly, "On the asymptotic properties of a system arising in non-equilibrium theory of output regulation," Mittag-Leffler Institute, Stockholm, Sweden, 2003.
7. E. J. Davison, "The robust control of a servomechanism problem for linear time-invariant multivariable systems," IEEE Trans. Automat. Contr., vol. AC-21, pp. 25-34, Feb. 1976.
8. B. A. Francis, "The linear multivariable regulator problem," SIAM J. Control Optim., vol. 14, pp. 486-505, 1977.
9. B. A. Francis and W. M. Wonham, "The internal model principle of control theory," Automatica, vol. 12, pp. 457-465, 1976.
10. C. I. Byrnes, D. Gilliam, A. Isidori, and J. Ramsey, "On the steady-state behavior of forced nonlinear systems," in New Trends in Nonlinear Dynamics and Control, and their Applications. ser. Lecture Notes in Control and Information Sciences, W. Kang, M. Xiao, and C. Borges, Eds. Heidelberg, Germany: Springer-Verlag, 2003, vol. 295.
11. J. K. Hale, L. T. Magalhães, and W. M. Oliva, Dynamics in Infinite Dimensions. New York: Springer-Verlag, 2002.
12. R. Hermann and A. J. Krener, "Nonlinear controllability and observability," IEEE Trans. Automat. Contr., vol. AC-22, pp. 25-34, Oct. 1977.
13. J. Huang and C. F. Lin, "On a robust nonlinear multivariable servomechanism problem," IEEE Trans. Automat. Contr., vol. 39, pp. 1510-1513, July 1994.
14. J. Huang and W. J. Rugh, "On a nonlinear multivariable servomechanism problem," Automatica, vol. 26, pp. 963-972, 1990.
15. A. Isidori, Nonlinear Control Systems, 3rd ed. New York: Springer-Verlag, 1995.
16. ____, Nonlinear Control Systems II, 1st ed. New York: Springer-Verlag, 1999.
17. A. Isidori and C. I. Byrnes, "Output regulation of nonlinear systems," IEEE Trans. Automat. Contr., vol. 35, pp. 131-140, Jan. 1990.
18. Y. Lin, E. D. Sontag, and Y. Wang, "A smooth converse Lyapunov theorem for robust stability," SIAM J. Control Optim., vol. 34, pp. 124-160, 1996.
19. V. O. Nikiforov, "Adaptive nonlinear tracking with complete compensation of unknown disturbances," Eur. J. Control, vol. 4, pp. 132-139, 1998.
20. A. Serrani, A. Isidori, and A. Marconi, "Semiglobal nonlinear output regulation with adaptive internal model," IEEE Trans. Automat. Contr., vol. 46, pp. 1178-1194, Aug. 2001.
21. E. D. Sontag, "Further facts about input to state stabilization," IEEE Trans. Automat. Contr., vol. 35, pp. 473-476, Apr. 1990.
22. ____, "Adaptation implies internal model," Syst. Control Lett., vol. 50, pp. 119-126, 2003.
23. A. R. Teel and L. Praly, "Tools for semiglobal stabilization by partial state and output feedback," SIAM J. Control Optim., vol. 33, pp. 1443-1485, 1995.
24. F. W. Wilson, "Smoothing derivatives of functions and applications," Trans. Amer. Math. Soc., vol. 139, pp. 413-428.
25. W. Boothby and R. Marino, "Feedback stabilization of planar linear systems," Syst. Control Lett., vol. 12, pp. 89-92, 1989.