Stability region analysis using simulations and sum-of-squares programming

Proceedings of the American Control Conference

Volumn , Issue , 2007, Pages 6009-6014

  Topcu, Ufuk ^a   Packard, Andrew ^a   Seiler, Peter ^b   Wheeler, Timothy ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b HONEYWELL TECHNOLOGY CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; LIFE SUPPORT SYSTEMS (SPACECRAFT); LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; OPTIMIZATION; POLYNOMIAL APPROXIMATION; POLYNOMIALS; TELECOMMUNICATION NETWORKS;

(MIN ,MAX ,+) FUNCTIONS; BILINEAR CONSTRAINTS; COMPUTING BOUNDS; FINITE DIMENSIONAL; INVARIANT SETS; LYAPUNOV; NECESSARY CONDITIONS; OPTIMIZ ATION PROBLEMS; PARAMETERIZATIONS; POLYNOMIAL VECTOR FIELDS; SEARCH STRATEGIES; STABILITY REGIONS; SUM OF SQUARES (SOS); SUM OF SQUARES PROGRAMMING;

SET THEORY;

EID: 46449114370     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACC.2007.4283013     Document Type: Conference Paper

References (16)

1. H.-D. Chiang and J. S. Thorp. "Stability regions of nonlinear dynamical systems: A constructive methodology," IEEE Transaction on Automatic Control, vol. 34, no. 12, pp. 1229-1241, 1989.
2. R. Genesio, M. Tarlaglia, and A. Vicino, "On the estimation of asymptotic stability regions: State of the art and new proposals," IEEE Transaction on Automatic Control, vol. 30, no. 8, pp. 747-755, 1985.
3. E. J. Davison and E. M. Kurak, "A computational method for determining quadratic Lyapunov functions for nonlinear systems," Automatica, vol. 7, pp. 627-636, 1971.
4. A. Papachristodoulou, "Scalable analysis of nonlinear systems using convex optimization," Ph.D. Dissertation, Caltech, Jan. 2005.
5. A. Vannelli and M. Vidynsagar, "Maximal Lyapunov functions and domains of attraction for autonomous nonlinear systems." Automatica. vol. 21, no. 1, pp. 69-80, 1985.
6. 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.
7. W. Tan and A. Packard, "Stability region analysis using sum of squares programming," in Proc. American Control Conf. Minneapolis, MN. 2006, pp. 2297-2302.
8. P. Parrilo, "Semidetinitc: programming relaxations for semialgebraic problems," Mathematical Programming Series B, vol. 96, no. 2, pp. 293-320, 2003.
9. O. Toker and H. Ozbay, "On the NP-hardness of solving bilinear matrix inequalities and simultaneous stabilization with static output feedback," in Proc. American Control Conf., 1995, pp. 2525-2526.
10. M. Kočvara and M. Stingl, "PENBMI User's Guide (Version 2.0), available from http://www.penopt.com." 2005.
11. S. Boyd and L. Vandenberghe, "Semidefinite programming relaxations of non-convex problems in control and combinatorial optimization," in Communications, Computation, Control and Signal Processing: A Tribute To Thomas Kailath, A. Paulraj, V. Rovchowdhuri, and C. Schaper. Eds. Kluwer. 1997, pp. 279-288.
12. nd ed. Prentice Hall. 1993.
13. S. Boyd. L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory. Philadelphia: SIAM. 1994.
14. R. Tempo, G. Calafiore, and F. Dabbene, Randomized Algorithms for Analysis and Control of Uncertain Systems. Springer, 2005.
15. J. Lofberg, "YALMIP : A toolbox for modeling and optimization in MATLAB," in Proc. CACSD Conf., Taiwan, 2004, pp. 2525-2526.
16. S. Prajna. A. Papachristodoulou, P. Seiler, and P. A. Parrilo, SOS-TOOLS: Sum of squares optimization toolbox for MATLAB, Available from http://www.cds.caltech.edu/sostools and http://www.mit.edu/~parrilo/sostools, 2004.