Analytical validation tools for safety critical systems

AIAA Infotech at Aerospace Conference and Exhibit and AIAA Unmanned...Unlimited Conference

Volumn , Issue , 2009, Pages

  Seiler, Peter ^a   Balas, Gary ^a   Packard, Andrew ^b   Topcu, Ufuk ^c  

^a University of Minnesota   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BINARY CODES; CONTROL THEORY; FLIGHT CONTROL SYSTEMS; FLIGHT SIMULATORS; NONLINEAR EQUATIONS; SAFETY ENGINEERING;

ANALYTICAL VALIDATION; CLOSED LOOP STABILITY; DYNAMIC CHARACTERISTICS; FREELY AVAILABLE SOFTWARE; NONLINEAR SIMULATIONS; PERFORMANCE CHARACTERISTICS; SAFETY CRITICAL SYSTEMS; SUM OF SQUARES OPTIMIZATION;

NONLINEAR ANALYSIS;

EID: 77958501488     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2009-1991     Document Type: Conference Paper

References (35)

1. Parrilo, P., Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization, Ph.D. thesis, California Institute of Technology, 2000.
2. Parrilo, P., "Semidefinite programming relaxations for semialgebraic problems," Mathematical Programming Ser. B, 2003.
3. Lasserre, J., "Global Optimization with Polynomials and the Problem of Moments," SIAM Journal on Optimization, Vol. 11, No. 3, 2001, pp. 796-817.
4. Reznick, B., "Some concrete aspects of Hilberts 17th problem," Contemporary Mathematics, Vol. 253, No. 251-272, 2000.
5. Vandenberghe, L. and Boyd, S., "Semidefinite Programming," SIAM Review, Vol. 38, No. 1, 1996, pp. 49-95.
6. Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory, Vol. 15 of Studies in Applied Mathematics, SIAM, 1994.
7. Sturm, J., "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optimization Methods and Software, 1999, pp. 625-653.
8. Sturm, J., "SeDuMi version 1.05," http://fewcal.kub.nl/sturm/ software/sedumi.html, 2001.
9. Reznick, B., "Extremal PSD forms with few terms," Duke Mathematical Journal, Vol. 45, No. 2, 1978, pp. 363-374.
10. Choi, M., Lam, T., and Reznick, B., "Sums of Squares of Real Polynomials," Proceedings of Symposia in Pure Mathe- matics, Vol. 58, No. 2, 1995, pp. 103-126.
11. Powers, V. and Ẅormann, T., "An Algorithm for sums of squares of real polynomials," Journal of Pure and Applied Algebra, Vol. 127, 1998, pp. 99-104.
12. Prajna, S., Papachristodoulou, A., Seiler, P., and Parrilo, P. A., SOSTOOLS: Sum of squares optimization toolbox for MATLAB, 2004.
13. Lofberg, J., "YALMIP : A Toolbox for Modeling and Optimization in MATLAB," Proceedings of the CACSD Conference, Taipei, Taiwan, 2004.
14. Gatermann, K. and Parrilo, P., "Symmetry groups, semidefinite programs, and sums of squares," Journal of Pure and Applied Algebra, Vol. 192, 2004, pp. 95-128.
15. Topcu, U., Packard, A., Seiler, P., and Wheeler, T., "Stability region analysis using simulations and sum-of-squares programming," Proceedings of the American Control Conference, 2007, pp. 6009-6014.
16. Tan, W., Topcu, U., Seiler, P., Balas, G., and Packard, A., "Simulation-aided Reachability and Local Gain Analysis for Nonlinear Dynamical Systems," Proceedings of the IEEE Conference on Decision and Control, 2008, pp. 4097-4102.
17. Topcu, U., Packard, A., and Seiler, P., "Local stability analysis using simulations and sum-of-squares programming," Automatica, Vol. 44, No. 10, 2008, pp. 2669-2675.
18. Tibken, B., "Estimation of the domain of attraction for polynomial systems via LMIs," Proceedings of the IEEE Conference on Decision and Control, 2000, pp. 3860-3864.
19. Hachicho, O. and Tibken, B., "Estimating domains of attraction of a class of nonlinear dynamical systems with LMI methods based on the theory of moments," Proceedings of the IEEE Conference on Decision and Control, 2002, pp. 3150-3155.
20. Jarvis-Wloszek, Z., Lyapunov Based Analysis and Controller Synthesis for Polynomial Systems using Sum-of-Squares Optimization, Ph.D. thesis, University of California, Berkeley, 2003.
21. Jarvis-Wloszek, Z., Feeley, R., Tan, W., Sun, K., and Packard, A., "Some Controls Applications of Sum of Squares Programming," Proceedings of the 42nd IEEE Conference on Decision and Control, Vol. 5, 2003, pp. 4676-4681.
22. Tan, W. and Packard, A., "Searching for control Lyapunov functions using sums of squares programming," 42nd Annual Allerton Conference on Communications, Control and Computing, 2004, pp. 210-219.
23. Chesi, G., "On the estimation of the domain of attraction for uncertain polynomial systems via LMIs," Proceedings of the IEEE Conference on Decision and Control, 2004, pp. 881-886.
24. Papachristodoulou, A., Scalable analysis of nonlinear systems using convex optimization, Ph.D. thesis, California Institute of Technology, 2005.
25. Jarvis-Wloszek, Z., Feeley, R., Tan, W., Sun, K., and Packard, A., Positive Polynomials in Control, Vol. 312 of Lecture Notes in Control and Information Sciences, chap. Controls Applications of Sum of Squares Programming, Springer-Verlag, 2005, pp. 3-22.
26. Chesi, G., Garulli, A., Tesi, A., and Vicino, A., "LMI-based computation of optimal quadratic Lyapunov functions for odd polynomial systems," International Journal of Robust and Nonlinear Control, Vol. 15, 2005, pp. 35-49.
27. Prajna, S., Optimization-Based Methods for Nonlinear and Hybrid Systems Verification, Ph.D. thesis, California Institute of Technology, 2005.
28. Tan, W., Packard, A., and Wheeler, T., "Local gain analysis of nonlinear systems," Proceedings of the American Control Conference, pp. 92-96.
29. Tan, W., Nonlinear Control Analysis and Synthesis using Sum-of-Squares Programming, Ph.D. thesis, University of California, Berkeley, 2006.
30. Tibken, B. and Fan, Y., "Computing the domain of attraction for polynomial systems via BMI optimization methods," Proceedings of the American Control Conference, 2006, pp. 117-122.
31. Topcu, U., Quantitative Local Analysis of Nonlinear Systems, Ph.D. thesis, University of California, Berkeley, 2008.
32. Topcu, U. and Packard, A., "Linearized analysis versus optimization-based nonlinear analysis for nonlinear systems," submitted to the 2009 American Control Conference, 2009.
33. Vidyasagar, M., Nonlinear Systems Analysis, Prentice Hall, 2nd ed., 1993.
34. Khalil, H., Nonlinear Systems, Prentice Hall, 3rd ed., 2002.
35. J. Tierno, R. Murray, J. D. I. G., "Numerically efficient robustness analysis of trajectory tracking for nonlinear systems," AIAA Journal of Guidance, Control, and Dynamics, Vol. 20, 1997, pp. 640-647.