Nonlinear robust H∞ static output feedback controller design for parameter dependent polynomial systems: An iterative sum of squares approach

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2011, Pages 3502-3507

  Krug, Matthias ^a   Saat, Shakir ^a   Nguang, Sing Kiong ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

[No Author keywords available]

Indexed keywords

FEEDBACK CONTROL; ITERATIVE METHODS; NONLINEAR CONTROL SYSTEMS; NUMERICAL METHODS; POLYNOMIALS;

COMPUTATIONAL RELAXATION; ITERATIVE DESIGN; PARAMETER DEPENDENTS; POLYNOMIAL MATRIX INEQUALITIES; POLYNOMIAL SYSTEMS; SOLVABILITY CONDITIONS; STATIC OUTPUT FEEDBACK CONTROLLERS; SUM OF SQUARES DECOMPOSITIONS;

CONTROLLERS;

EID: 84860672179     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2011.6161455     Document Type: Conference Paper

References (27)

1. ∞ control for nonlinear plants: connections with differential games," in Conference on Decision and Control, 1989, pp. 956-962.
2. T. Başar and G. J. Olsder, Dynamic noncooperative game theory. London; New York: Academic Press, 1995.
3. ∞ control," IEEE Transactions on Automatic Control, vol. 37, no. 6, pp. 770-784, 1992.
4. ∞-control via measurement feedback in nonlinear systems," IEEE Transactions on Automatic Control, vol. 37, no. 9, pp. 1283-1293, 1992.
5. T. Başar, "Optimum performance levels for minimax filters, predictors and smoothers," Systems & Control Letters, vol. 16, no. 5, pp. 309-317, 1991.
6. D. J. Hill and P. J. Moylan, "Dissipative dynamical systems: Basic input-output and state properties," Journal of the Franklin Institute, vol. 309, no. 5, pp. 327-357, 1980.
7. J. C. Willems, "Dissipative dynamical systems part i: General theory," Archive for Rational Mechanics and Analysis, vol. 45, pp. 321-351, 1972.
8. P. A. Parrilo, "Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization," Ph.D. Thesis, California Institute of Technology, May 2000.
9. V. Powers and T. Wörmann, "An algorithm for sums of squares of real polynomials," Journal of Pure and Applied Algebra, vol. 127, no. 1, pp. 99-104, 1998.
10. L. Vandenberghe and S. P. Boyd, "Semidefinite programming," SIAM Review, vol. 38, no. 1, pp. 49-95, 1996.
11. S. P. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear matrix inequalities in system and control theory. Philadelphia: SIAM, 1994.
12. S. Prajna, A. Papachristodoulou, and P. A. Parrilo, "Introducing SOSTOOLS: a general purpose sum of squares programming solver," in Conference on Decision and Control, vol. 1, 2002, pp. 741-746.
13. J. Löfberg, "YALMIP: a toolbox for modeling and optimization in Matlab," in IEEE International Symposium on Computer Aided Control Systems Design, 2004, pp. 284-289.
14. M. Grant and S. Boyd, "Graph implementations for nonsmooth convex programs," in Recent Advances in Learning and Control, ser. Lecture Notes in Control and Information Sciences, V. Blondel, S. Boyd, and H. Kimura, Eds. Springer-Verlag Limited, 2008, pp. 95-110.
15. D. Henrion, J.-B. Lasserre, and J. Löfberg, "GloptiPoly 3: moments, optimization and semidefinite programming," Optimization Methods and Software, vol. 24, no. 4, pp. 761-779, 2009.
16. S. Prajna, A. Papachristodoulou, and F. Wu, "Nonlinear control synthesis by sum of squares optimization: a Lyapunov-based approach," in Asian Control Conference, vol. 1, 2004, pp. 157-165.
17. A. Papachristodoulou and S. Prajna, "On the construction of Lyapunov functions using the sum of squares decomposition," in Conference on Decision and Control, vol. 3, 2002, pp. 3482-3487.
18. H.-J. Ma and G.-H. Yang, "Fault-tolerant control synthesis for a class of nonlinear systems: Sum of squares optimization approach," International Journal of Robust and Nonlinear Control, vol. 19, no. 5, pp. 591-610, 2009.
19. ∞ synthesis for parameter-dependent polynomial nonlinear systems using SOS programming," in American Control Conference, 2009, pp. 796-801.
20. V. Syrmos, C. Abdallah, P. Dorato, and K. Grigoriadis, "Static output feedback - a survey," Automatica, vol. 33, no. 2, pp. 125-137, 1997.
21. Y.-Y. Cao, J. Lam, and Y.-X. Sun, "Static output feedback stabilization: An ILMI approach," Automatica, vol. 34, no. 12, pp. 1641-1645, 1998.
22. D. Huang and S. K. Nguang, "Static output feedback controller design for fuzzy systems: An ILMI approach," Journal of Information Sciences, vol. 177, no. 14, pp. 3005-3015, 2007.
23. ∞ static output feedback control of fuzzy systems: An ILMI approach," IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 36, no. 1, pp. 216-222, 2006.
24. D. Zhao and J.-L. Wang, "Robust static output feedback design for polynomial nonlinear systems," International Journal of Robust and Nonlinear Control, vol. 20, no. 14, pp. 1637-1654, 2010.
25. H. Hindi, "A tutorial on convex optimization," in American Control Conference, vol. 4, 2004, pp. 3252-3265.
26. A. Papachristodoulou and S. Prajna, "A tutorial on sum of squares techniques for systems analysis," in American Control Conference, vol. 4, 2005, pp. 2686-2700.
27. B. Reznick, "Some concrete aspects of Hilbert's 17th problem," Contemporary Mathematics, vol. 253, pp. 251-272, 2000.