Rejection of persistent ℒ ∞-bounded disturbances for nonlinear systems

IEEE Transactions on Automatic Control

Volumn 43, Issue 12, 1998, Pages 1692-1702

  Lu, Wei Min ^a,b  

^a IEEE   (United States)

^b IBM   (United States)

Author keywords

optimal control; Controlled invariance; Disturbance rejection; Nonlinear systems; Robust control

Indexed keywords

DISCRETE TIME CONTROL SYSTEMS; INVARIANCE; OPTIMAL CONTROL SYSTEMS; ROBUSTNESS (CONTROL SYSTEMS); STATE SPACE METHODS;

CONTINUOUS TIME SYSTEMS; CONTROL PROBLEM; DISTURBANCE REJECTION;

NONLINEAR CONTROL SYSTEMS;

EID: 0032290883     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.736066     Document Type: Article

References (39)

1. J.-P. Aubin, Viability Theory. Boston, MA: Birkhauser, 1991.
2. J.-P. Aubin, C. I. Byrnes, and A. Isidori, "Viability kernels, controlled invariance, and zero dynamics for nonlinear systems," in Analysis and Optimization of Systems, A. Bensoussan and J. L. Lions, Eds. Berlin, Germany: Springer-Verlag, 1990.
3. J.-P. Aubin and A. Cellina, Differential Inclusions: Set-Valued Maps and Viability Theory. Berlin, Germany: Springer-Verlag, 1984.
4. J.-P. Aubin and H. Frankowska, Set-Valued Analysis. Boston, MA: Birkhauser, 1990.
5. D. P. Bertsekas, "Infinite-time reachability of state-space regions by using feedback control," IEEE Trans. Automat. Contr., vol. AC-17, pp. 604-613, 1972.
6. D. P. Bertsekas and I. B. Rhodes, "On the minimax reachability of target sets and target tubes," Automatica, vol. 7, pp. 233-247, 1971.
7. G. Bitsoris and E. Gravalou, "Comparison principle, positive invariance and constrained regulation of nonlinear systems," Automatica, vol. 31, pp. 217-222, 1995.
8. F. Blanchini, "Feedback control for linear time-invariant systems with state and control bounds in the presence of disturbances," IEEE Trans. Automat. Contr., vol. 35, pp. 1231-1235, 1990.
9. _, "Non-quadratic Lyapunov functions for robust control," Automatica, vol. 31, pp. 451-461, 1995.
10. ⊥-suboptimal compensators for continuous-time systems," IEEE Trans. Automat. Contr., vol. 39, pp. 1487-1492, 1994.
11. _, "Persistent disturbance rejection via static state feedback," in Proc. IEEE Conf. Decision and Control, Orlando, FL, 1994, pp. 3159-3164.
12. M. A. Dahleh and I. J. Diaz-Bobillo, Control of Uncertain Systems: A Linear Programming Approach. Englewood Cliffs, NJ: Prentice-Hall, 1994.
13. ⊥-Optimal feedback controllers for MIMO discrete-time systems," IEEE Trans. Automat. Contr., vol. 32, pp. 314-322, 1987.
14. ⊥-Optimal compensators for continuous-time systems," IEEE Trans. Automat. Contr., vol. 32, pp. 889-895, 1987.
15. M. A. Dahleh and J. S. Shamma, "Rejection of persistent bounded disturbances: Nonlinear controllers," Syst. Contr. Lett., vol. 18, pp. 245-252, 1992.
16. M. C. Delfour and S. K. Mitter, "Reachability of perturbed systems and min-sup problems," SIAM J. Contr., vol. 7, pp. 521-533, 1969.
17. R. J. P. de Figueiredo and G. Chen, "Optimal disturbance rejection for nonlinear control systems," IEEE Trans. Automat. Contr., vol. 34, pp. 1242-1248, 1989.
18. ⊥-optimal controllers can be dynamic," Syst. Contr. Lett., vol. 19, pp. 87-93, 1992.
19. A. F. Filippov, "Classical solutions of differential equations with multivalued right-hand side," SIAM J. Contr., vol. 5, pp. 609-621, 1967.
20. E. G. Gilbert and K. T. Tan, "Linear systems with state and control constraints: The theory and application of maximal output admissible sets," IEEE Trans. Automat. Contr., vol. 36, pp. 1008-1020, 1991.
21. J. D. Glover and F. C. Scheppe, "Control of linear dynamical systems with set constrained disturbances," IEEE Trans. Automat. Contr., vol. AC-16, pp. 411-423, 1971.
22. F.-O. Gutman and M. Cwikel, "Admissible sets and feedback control for discrete-time linear dynamical systems with bounded controls and states," IEEE Trans. Automat. Contr., vol. AC-31, pp. 373-376, 1986.
23. P. Hartman, Ordinary Differential Equations New York: Wiley, 1964.
24. A. Isidori, Nonlinear Control Systems: An Introduction, 2nd ed. Berlin, Germany: Springer-Verlag, 1989.
25. S. S. Keerthi and E. G. Gilbert, "Computation of minimum-time feedback control laws for discrete-time systems with state-control constraints," IEEE Trans. Automat. Contr., vol. AC-32, pp. 432-435, 1987.
26. ∞-bounded disturbances for nonlinear systems," Caltech CDS Tech. Memo. CIT-CDS-95-002.
27. W.-M. Lu and A. Packard, "Asymptotic disturbance rejection of persistent bounded disturbances," in Proc. IEEE Conf. Decision and Control, Kobe, Japan, Dec. 1996.
28. Y. Lin, E. D. Sontag, and Y. Wang, "Recent results on Lyapunov-theoretic techniques for nonlinear stability," Rutgers Univ., SYCON Tech. Rep. SYCON-93-09, Nov. 1993.
29. H. Nijmeijer and A. J. van der Schaft, Nonlinear Dynamical Control Systems. New York: Springer-Verlag, 1990.
30. W. Rudin, Real and Complex Analysis. New York: McGraw-Hill, 1987.
31. ⊥ optimal control," Syst. and Contr. Lett., vol. 21, pp. 265-270, 1993.
32. ∞-induced norm under full state feedback," IEEE Trans. Automat. Contr., to be published.
33. ⊥-optimal controllers for linear systems," in Proc. 1994 IEEE Conf. Decision and Control, Orlando, FL, 1994, pp. 3151-3152.
34. P. Tallos, "Viability problems for nonautonomous differential inclusions," SIAM J. Contr. Optim., vol. 29, pp. 253-263, 1991.
35. M. Vidyasagar, "Optimal rejection of persistent bounded disturbances," IEEE Trans. Automat. Contr., vol. 31, pp. 527-534, 1986.
36. _, Nonlinear Systems Analysis, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 1993.
37. H. S. Witsenhausen, "A minimax control problem for sampled linear systems," IEEE Trans. Automat. Contr., vol. AC-13, pp. 5-21, 1968.
38. W. M. Wonham, Linear Multivariable Control: A Geometric Approach. New York: Springer-Verlag, 1985.
39. J. A. Yorke, "Invariance for ordinary differential equations," Math. Syst. Theory, vol. 1, pp. 353-372, 1967.