l∞-Bounded Robustness for Nonlinear Systems: Analysis and Synthesis

IEEE Transactions on Automatic Control

Volumn 48, Issue 11, 2003, Pages 1875-1891

  Huang, Shoudong ^a   James, Matthew R ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Controller synthesis; Dissipative systems; Dynamic programming; Information states; l criteria; Nonlinear robust control

Indexed keywords

APPROXIMATION THEORY; CLOSED LOOP CONTROL SYSTEMS; CONTROL EQUIPMENT; DYNAMIC PROGRAMMING; NONLINEAR CONTROL SYSTEMS; OPTIMAL CONTROL SYSTEMS; SPURIOUS SIGNAL NOISE;

DISSIPATIVE SYSTEMS;

ROBUSTNESS (CONTROL SYSTEMS);

EID: 0344395581     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2003.819072     Document Type: Article

References (31)

1. ∞-Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach, 2nd ed. Boston, MA: Birkhaüser, 1995.
2. E. N. Barron and H. Ishii, "The Bellman equation for minimizing the maximum cost," Nonlinear Anal., Theory, Meth., Applicat., vol. 13, no. 9, pp. 1067-1090, 1989.
3. D. P. Bertsekas and I. B. Rhodes, "On the minimax reachability of target sets and target tubes," Automatica, vol. 7, pp. 233-247, 1971.
4. _, "Recursive state estimation for a set-membership description of uncertainty," IEEE Trans. Automat. Contr., vol. AC-16, pp. 117-128, Apr. 1971.
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, Oct. 1972.
6. _, Dynamic Programming and Optimal Control. Belmont, MA: Athena, 1995.
7. E. N. Barron, "Differential games with maximum cost," Nonlinear Anal., Theory, Meth., Applicat., vol. 14, no. 11, pp. 971-989, 1990.
8. M. A. Dahleh and I. J. Diaz-Bobillo, "Minimization of the maximum peak-to-peak gain: The general multiblock problem," IEEE Trans. Automat. Contr., vol. 38, pp. 1459-1482, Oct. 1993.
9. _, Control of Uncertain Systems: A Linear Programming Approach. Upper Saddle River, NJ: Prentice-Hall, 1995.
10. 1-optimal feedback controllers for MIMO discrete-time systems," IEEE Trans. Automat. Contr., vol. AC-32, pp. 314-322, Apr. 1987.
11. _, "Optimal rejection of persistent disturbances, robust stability, and mixed sensitivity minimization," IEEE Trans. Automat. Contr., vol. 33, pp. 722-731, Aug. 1988.
12. N. Elia and M. A. Dahleh, "Minimization of the worst case peak-to-peak gain via dynamic programming: State feedback case," IEEE Trans. Automat. Contr., vol. 45, pp. 687-701, Apr. 2000.
13. I. J. Fialho and T. T. Georgiou, "Worst case analysis of nonlinear systems," IEEE Trans. Automat. Contr., vol. 44, pp. 1180-1196, June 1999.
14. M. Green and D. J. N. Limebeer, Linear Robust Control. Upper Saddle River, NJ: Prentice-Hall, 1995.
15. ∞ control to nonlinear systems: Control of systems to achieve performance objectives," in SIAM Advances Design Control. Philadelphia, PA: SIAM, 1999.
16. D. J. Hill and P. J. Moylan, "The stability of nonlinear dissipative systems," IEEE Trans. Automat. Contr., vol. AC-21, pp. 708-711, Oct. 1976.
17. _, "Dissipative dynamical systems: Basic input-output and state space properties," J. Franklin Inst., vol. 309, pp. 327-357, 1980.
18. S. Huang, M. R. James, D. Nesic, and P. M. Dower, "Analysis of input to state stability for discrete-time nonlinear systems via dynamic programming," Automatica, 2003, submitted for publication.
19. _, "On input to state stabilization for nonlinear discrete-time systems: A dynamic programming approach," presented at the Eur. Control Conf., 2003.
20. ∞ bounded robustness: State feedback analysis and design," presented at the NOLCOS, 2001.
21. M. R. James, J. S. Baras, and R. J. Elliott, "Risk-sensitive control and dynamic games for partially observed discrete-time nonlinear systems," IEEE Trans. Automat. Contr., vol. 39, pp. 780-792, Apr. 1994.
22. ∞ output feedback control for nonlinear systems," IEEE Trans. Automat. Contr., vol. 40, pp. 1007-1017, June 1995.
23. J. P. Lasalle, The Stability of Dynamical Systems. Philadelphia, PA: SIAM, 1976.
24. ∞-bounded disturbances for non-linear systems," IEEE Trans. Automat. Contr., vol. 43, pp. 1692-1702, Dec. 1998.
25. ∞ disturbance attenuation and global stabilization of linear systems with bounded control," Int. J. Robust Nonlinear Control, vol. 9, pp. 659-675, 1999.
26. 1 optimal control," Syst. Control Lett., vol. 21, pp. 265-270, 1993.
27. ∞-induced norm under full state feedback," IEEE Trans. Automat. Contr., vol. 41, pp. 533-544, Feb. 1996.
28. J. S. Shamma and K.-Y. Tu, "Set-valued observers and optimal disturbance rejection," IEEE Trans. Automat. Contr., vol. 44, pp. 253-264, Feb. 1999.
29. M. Vidyasagar, "Optimal rejection of persistent bounded disturbances," IEEE Trans. Automat. Contr., vol. AC-31, pp. 527-534, June 1986.
30. 2-Gain and Passivity Techniques in Nonlinear Control New York: Springer-Verlag, 1996.
31. J. C. Willems, "Dissipative dynamical systems, Part I: General theory," Arch. Rational Mech. Anal., vol. 45, pp. 321-351, 1972.