Linearized analysis versus optimization-based nonlinear analysis for nonlinear systems

Proceedings of the American Control Conference

Volumn , Issue , 2009, Pages 790-795

  Topcu, Ufuk ^a   Packard, Andrew ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYSIS TOOLS; ASYMPTOTICALLY STABLE EQUILIBRIUM; DIRECT USE; EQUILIBRIUM POINT; FINITE SIZE; GAIN ANALYSIS; INPUT-OUTPUT; INPUT-OUTPUT PROPERTIES; LINEARIZED ANALYSIS; LINEARIZED DYNAMICS; NONLINEAR SYSTEMS STABILITY; REACHABILITY; S-PROCEDURES; SUM OF SQUARES; SUM-OF-SQUARES PROGRAMMING;

LIFE SUPPORT SYSTEMS (SPACECRAFT); LINEARIZATION; NONLINEAR SYSTEMS; SYSTEM STABILITY;

NONLINEAR ANALYSIS;

EID: 70449636033     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACC.2009.5160528     Document Type: Conference Paper

References (24)

1. J. C. Willems, "Dissipative dynamical systems I: Genaral theory," Archive for Rational Mechanics and Analysis, vol. 45, pp. 321-343, 1972.
2. nd ed. Prentice Hall, 1993.
3. rd ed. Prentice Hall, 2002.
4. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory. Philadelphia: SIAM, 1994.
5. Z. Jarvis-Wloszek, R. Feeley, W. Tan, K. Sun, and A. Packard, "Control applications of sum of squares programming," in Positive Polynomials in Control, D. Henrion and A. Garulli, Eds. Springer-Verlag, 2005, pp. 3-22.
6. P. Parrilo, "Semidefinite programming relaxations for semialgebraic problems," Mathematical Programming Series B, vol. 96, no. 2, pp. 293-320, 2003.
7. U. Topcu and A. Packard, "Local stability analysis for uncertain nonlinear systems," 2007, to appear in IEEE Transaction on Automatic Control.
8. T.-C. Wang, S. Lall, and M. West, "Polynomial level-set methods for nonlinear dynamical systems analysis," in Proc. Allerton Conf. on Communication, Control, and Computing, Allerton, IL, 2005.
9. J. Lasserre, "Global optimization with polynomials and the problem of moments," SIAM Journal on Optimization, vol. 11, no. 3, pp. 796-817, 2000.
10. E. M. Aylward, P. A. Parrilo, and J. E. Slotine, "Stability and robustness analysis of nonlinear systems via contraction metrics and SOS programming," 2008, doi:10.1016/j.automatica.2007.12.012.
11. A. Papachristodoulou and S. Prajna, "On the construction of Lyapunov functions using the sum of squares decomposition," in Proceedings of the IEEE Conference on Decision and Control, 2002, pp. 3482-3487.
12. P. Parrilo, "Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization," Ph.D. Dissertation, California Institute of Technology, May 2000.
13. S. Prajna, "Barrier certificates for nonlinear model validation," vol. 3, 2003, pp. 2884-2889.
14. U. Topcu, A. Packard, and P. Seiler, "Local stability analysis using simulations and sum-of-squares programming," DOI: 10.1016/j.automatica. 2008.03.010.
15. W. Tan, "Nonlinear control analysis and synthesis using sum-ofsquares programming," Ph.D. Dissertation, UC, Berkeley, May 2006.
16. G. Chesi, A. Garulli, A. Tesi, and A. Vicino, "LMI-based computation of optimal quadratic Lyapunov functions for odd polynomial systems," Int. J. Robust Nonlinear Control, vol. 15, pp. 35-49, 2005.
17. G. Chesi, "On the estimation of the domain of attraction for uncertain polynomial systems via lmis," in Proc. Conf. on Decision and Control, Bahamas, 2004, pp. 881-886.
18. C. Ebenbauer and F. Allgower, "A dissipation inequality for the minimum phase property," IEEE Transactions on Automatic Control, vol. 53, pp. 821-826, 2008.
19. V. A. Yakubovich, "The S-procedure in non-linear control theory," Vestnik Leningrad Univ. Math., vol. 4, pp. 73-93, 1977.
20. W. Tan and A. Packard, "Stability region analysis using sum of squares programming," in Proc. American Control Conf., Minneapolis, MN, 2006, pp. 2297-2302.
21. W. Tan, U. Topcu, P. Seiler, G. Balas, and A. Packard, "Simulationaided reachability and local gain analysis for nonlinear dynamical systems," in Proc. Conf. on Decision and Control, Cancun, Mexico, 2008.
22. W. Tan, A. Packard, and T. Wheeler, "Local gain analysis of nonlinear systems," in Proc. American Control Conf., Minneapolis, MN, 2006, pp. 92-96.
23. P. A. Ioannou and J. Sun, Robust Adaptive Control. Prentice Hall, Inc, 1996.
24. U. Topcu, A. Packard, P. Seiler, and G. Balas, "Robust region-of-attraction estimation," 2008, submitted to IEEE Transaction on Automatica Control.