Worst case analysis of nonlinear systems

IEEE Transactions on Automatic Control

Volumn 44, Issue 6, 1999, Pages 1180-1196

  Fialho, Ian J ^b   Georgiou, Tryphon T ^a,c  

^a IEEE   (United States)

^b University of Minnesota   (United States)

^c UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDED DISTURBANCES; HAMILTON-JACOBI EQUATIONS; INDUCED GAINS;

ALGORITHMS; APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; DYNAMIC PROGRAMMING; NONLINEAR CONTROL SYSTEMS; OPTIMAL CONTROL SYSTEMS; ROBUSTNESS (CONTROL SYSTEMS); VARIATIONAL TECHNIQUES;

CONTROL SYSTEM ANALYSIS;

EID: 0032628514     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.769372     Document Type: Article

References (35)

1. J. P. Aubin, Viability Theory. Boston, MA: Birkhauser, 1991.
2. J. P. Aubin and A. Cellina, "A series of comprehensive studies in mathematics," in Differential Inclusions: Set-Valued Maps and Viability Theory, vol. 264. New York: Springer-Verlag, 1984.
3. G. Barles and B. Perthame, "Discontinuous solutions of deterministic optimal stopping time problems," Math. Modeling and Numerical Anal., vol. 21, no. 4, pp. 557-579, 1987.
4. G. Barles and P. E. Souganidis, "Convergence of approximation schemes for fully nonlinear second order equations," Asymptotic Anal., vol. 4, pp. 271-283, 1991.
5. E. N. Barron and H. Ishii, "The Bellman equation for minimizing the maximum cost," Nonlinear Anal., Theory, Methods and Applicat., vol. 13, no. 9, pp. 1067-1090, 1989.
6. E. N. Barron, "Differential games with maximum cost," Nonlinear Anal., Theory Methods and Applicat., vol. 14, no. 11, pp. 971-989, 1990.
7. R. Bellman, Dynamic Programming. Princeton, NJ: Princeton Univ. Press, 1957.
8. I. C. Dolcetta and M. Falcone, "Discrete dynamic programming and viscosity solutions of the Bellman equation," Ann. Inst. H. Poincare, Anal. Non Lin., vol. 6 (supplement), pp. 161-183, 1989.
9. I. C. Dolcetta and H. Ishii, "Approximate solutions of the Bellman equation of deterministic control theory," Appl. Math. Optim., vol. 11, pp. 161-181, 1984.
10. M. G. Crandall, L. C. Evans, and P. L. Lions, "Some properties of viscosity solutions of Hamilton-Jacobi equations," Trans. Amer. Math. Soc., vol. 282, no. 2, pp. 487-502, 1984.
11. M. G. Crandall, H. Ishii, and P. L. Lions, "User's guide to viscosity solutions of second order partial differential equations," Bull. Amer. Math. Soc., vol. 27, no. 1, pp. 1-67, 1992.
12. M. Falcone, "A numerical approach to the infinite horizon problem of deterministic control theory," Appl. Math. Optim., vol. 15, pp. 1-13, 1987.
13. ⊥ norm of uncertain linear systems," IEEE Trans. Automat. Contr., vol. 40, pp. 1142-1147, 1995.
14. ⊥ state feedback control with a prescribed rate of exponential convergence," IEEE Trans. Automat. Contr., 1996.
15. I. J. Fialho, "Worst-case analysis and design of nonlinear feedback systems," Ph.D. dissertation, Univ. Minnesota, 1996.
16. W. H. Fleming and H. M. Soner, "Controlled Markov processes and viscosity solutions," in Applications of Mathematics, vol. 25. New York: Springer-Verlag, 1993.
17. I. Fialho, G. Balas, A. Packard, J. Renfrow, and C. Mullaney, "Linear fractional transformation control of the F-14 aircraft lateral-directional axis during powered approach landing," in Proc. Amer. Contr. Conf., June 1997.
18. T. T. Georgiou and M. C. Smith, "Robustness analysis of nonlinear feedback systems: An input-output approach," IEEE Trans. Automat. Contr., vol. 42, pp. 1200-1221, Sept. 1997.
19. P. Henrici, Discrete Variable Methods in Ordinary Differential Equations. New York: Wiley, 1962.
20. R. Isaacs, Differential Games. Huntington, NY: Kruger, 1965.
21. H. Ishii, "Uniqueness of unbounded viscosity solution of Hamilton-Jacobi equations," Indiana Univ. Math. J., vol. 33, no. 5, pp. 721-748.
22. _, "A simple direct proof of uniqueness for solutions of the Hamilton-Jacobi equations of the Eikonal type," in Proc. Amer. Math. Soc., 1987, vol. 100, no. 2, pp. 247-251.
23. ∞ norm for nonlinear systems," Automatica, vol. 31, no. 8, pp. 1075-1085, 1995.
24. H. K. Khalil, Nonlinear Systems. New York: Macmillan, 1992.
25. H. J. Kushner and P. G. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time. New York: Springer-Verlag, 1992.
26. ∞ bounded disturbances for nonlinear systems," IEEE Trans. Automat. Contr., vol. 43, pp. 1692-1702, Dec. 1998.
27. P. L. Lions, Generalized Solutions of Hamilton-Jacobi Equations. London, U.K.: Pitman, 1982.
28. ∞-induced norm under full state feedback," IEEE Trans. Automat. Contr., vol. 41, pp. 533-544, 1996.
29. E. D. Sontag, "State-space and I/O stability for nonlinear systems," Feedback Control, Nonlinear Systems, and Complexity, Lecture Notes in Control and Information Sciences, vol. 202, B. A. Francis and A. R. Tannenbaum, Eds. New York: Springer-Verlag, 1995, pp. 215-235.
30. J. E. Tierno, R. M. Murray, and J. C. Doyle, "An efficient algorithm for performance analysis of nonlinear control systems," in Proc. American Control Conf., 1995.
31. J. E. Tierno, R. M. Murray, J. C. Doyle, and I. M. Gregory, "Numerically efficient robustness analysis of trajectory tracking for nonlinear systems," Nov. 1995.
32. J. E. Tierno and R. M. Murray, "Robust performance analysis for a class of uncertain nonlinear systems," in Proc. IEEE Conf. Decision and Control, 1995, pp. 1684-1689.
33. J. Warga, " Relaxed variational problems," J. Math. Anal. Applicat., vol. 4, pp. 111-128, 1962.
34. _, Optimal Control of Differential and Functional Equations. New York: Academics, 1972.
35. K. Zhou, J. Doyle, and K. Glover, Robust and Optimal Control. Englewood Cliffs, NJ: Prentice-Hall, 1996.