Set simulations for quadratic systems

IEEE Transactions on Automatic Control

Volumn 48, Issue 5, 2003, Pages 800-805

  Calafiore, Giuseppe ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Domain of attraction; Nonlinear systems; Quadratic systems; Semidefinite relaxations; Set simulations

Indexed keywords

DIFFERENTIAL EQUATIONS; DISCRETE TIME CONTROL SYSTEMS; LINEAR CONTROL SYSTEMS; MATHEMATICAL MODELS; POLYNOMIAL APPROXIMATION;

NONLINEAR QUADRATIC SYSTEMS;

NONLINEAR CONTROL SYSTEMS;

EID: 0037955654     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2003.811257     Document Type: Article

References (24)

1. B. R. Barmish and J. Sankaran, "The propagation of parametric uncertainty via polytopes," IEEE Trans. Automat. Contr., vol. AC-24, pp. 346-349, Apr. 1979.
2. A. Ben-Tal and A. Nemirovski, On Ellipsoidal Approximations of Sums of Ellipsoids. Philadelphia, PA: SIAM, 2001.
3. D. P. Bertsekas and I. B. Rhodes, "Recursive state estimation with a set-membership description of the uncertainty," IEEE Trans. Automat. Contr., vol. AC-16, pp. 117-128, Feb. 1971.
4. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, ser. Studies in Applied Mathematics. Philadelphia, PA: SIAM, June 1994, vol. 15.
5. A. C. Brooms, B. Kouvaritakis, and Y. I. Lee, "Constrained MPC for uncertain linear systems with ellipsoidal target sets," Syst. Control Letters, vol. 44, pp. 157-166, 2001.
6. G. Chesi, A. Tesi, and A. Vicino, "Computing optimal quadratic Lyapunov functions for polynomial nonlinear systems via LMIs," presented at the 15th IFAC World Congress, Barcelona, Spain, July 2002.
7. C. Durieu, E. Walter, and B. Polyak, "Trace versus determinant in ellipsoidal outer-bounding with application to state estimation," in Proc. 13th IFAC World Congress, San Francisco, CA, 1996, pp. 43-48.
8. L. El Ghaoui and G. Calafiore, "Worst-case simulation of uncertain systems," in Lecture Notes in Control and Information Sciences. London, U.K.: Springer-Verlag, 1999, vol. 245, pp. 134-146.
9. _, "Robust filtering for discrete-time systems with bounded noise and parametric uncertainty," IEEE Trans. Automat. Contr., vol. 46, pp. 1084-1089, July 2001.
10. M. X. Goemans and D. P. Williamson, "Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming," J. ACM, vol. 42, pp. 1115-1145, 1995.
11. D. Henrion, S. Tarbouriech, and D. Arzelier, "LMI approximations for the radius of the intersection of ellipsoids," J.Optim. Theory Applicat., vol. 108, no. 1, pp. 1-28, 2001.
12. L. Jaulin, M. Kieffer, O. Didrit, and E. Walter, Applied Interval Analysis. London, U.K.: Springer-Verlag, 2001.
13. O. N. Kiselev and B. T. Polyak, "Ellipsoidal estimation with respect to a generalized criterion," Automat. Remote Control, vol. 52, pp. 1281-1292, 1992.
14. D. E. Koditschek and K. S. Narendra, "The stability of second-order quadratic differential equations," IEEE Trans. Automat. Contr., vol. AC-27, pp. 783-798, Aug. 1982.
15. A. B. Kurzhanski and I. Valyi, Ellipsoidal Calculus for Estimation and Control. Boston, MA: Birkhauser, 1996.
16. J. B. Lasserre, "Global optimization with polynomials and the problem of moments," SIAM J. Optim., vol. 11, no. 3, pp. 796-817, 2001.
17. R. R. Mohler, Bilinear Control Processes. New York: Academic, 1973.
18. A. Nemirovski, C. Roos, and T. Terlaky, "On maximization of quadratic form over intersection of ellipsoids with common center," Math. Program., vol. 86, no. 3, pp. 463-473, 1999.
19. Y.Yu Nesterov, "Semidefinite relaxation and nonconvex quadratic optimization," Optim. Meth. Software, vol. 12, pp. 1-20, 1997.
20. J. P. Norton and S. M. Veres, "Developments in parameter bounding," in Topics in Stochastic Systems: Modeling, Estimation and Adaptive Control, L. Gerencser and P. E. Caines, Eds. Berlin, Germany: Springer-Verlag, 1991, pp. 1137-1158.
21. P. A. Parrilo, "Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization," Ph.D. dissertation, California Inst. Technol., Pasadena, CA, 2000.
22. F. C. Schweppe, "Recursive state estimation: unknown but bounded errors and system inputs," IEEE Trans. Automat. Contr., vol. AC-13, pp. 22-28, 1968.
23. A. Tesi, F. Villoresi, and R. Genesio, "On the stability domain estimation via a quadratic Lyapunov function: convexity and optimality properties for polynomial systems," IEEE Trans. Automat. Contr., vol. 41, pp. 1650-1656, Nov. 1996.
24. L. Vandenberghe and S. Boyd, "Semidefinite programming," SIAM Rev., vol. 38, no. 1, pp. 49-95, March 1996.