Nonlinear control synthesis by sum of squares optimization: A Lyapunov-based approach

2004 5th Asian Control Conference

Volumn 1, Issue , 2004, Pages 157-165

  Prajna, Stephen ^a   Papachristodoulou, Antonis ^a   Wu, Fen ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b North Carolina State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; CONTROL SYSTEM SYNTHESIS; FEEDBACK CONTROL; LYAPUNOV METHODS; MATHEMATICAL PROGRAMMING; MATRIX ALGEBRA; PARAMETER ESTIMATION; POLYNOMIALS; PROBLEM SOLVING;

COMPUTATIONAL RELAXATION; CONTROL LYAPUNOV FUNCTIONS (CLF); LINEAR MATRIX; NONLINEAR CONTROL SYNTHESIS;

NONLINEAR CONTROL SYSTEMS;

EID: 16244409837     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (28)

1. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1994.
2. J. R. Cloutier. State dependent Riccati equation techniques: An overview. In Proc. American Control Conf., 1997.
3. D. F. Coutinho, A. Trofino, and M. Fu. Guaranteed cost control of uncertain nonlinear systems via polynomial Lyapunov function. IEEE Trans. Automatic Control, 47(9):1575-1580, 2002.
4. D. F. Coutinho, A. Trofino, and M. Fu. Nonlinear H-infinity control: An LMI approach. In Proc. IFAC World Congress, 2002.
5. ∞ control problems. IEEE Trans. Automatic Control, 34(8):831-847, 1989.
6. ∞ control. Internat. J. Robust Nonlinear Control, 4(4):421-448, 1994.
7. K. Gatermann and P. A. Parrilo. Symmetry groups, semidefinite programs, and sums of squares. Submitted, 2002.
8. Y. Huang. Nonlinear Optimal Control: An Enhanced Quasi-LPV Approach. PhD thesis, California Institute of Technology, Pasadena, CA, 1999.
9. Y. Huang and A. Jadbabaie. Nonlinear H-infinity control: An enhanced quasi-LPV approach. In Proc. IFAC World Congress, 1999.
10. Y. Huang and W. M. Lu. Nonlinear optimal control: Alternatives to Hamilton-Jacob! equation. In Proc. IEEE Conf. on Decision and Control, 1996.
11. Z. Jarvis-Wloszek, R. Feeley, W. Tan, K. Sun, and A. Packard. Some controls applications of sum of squares programming. In Proc. IEEE Conf. on Decision and Control, 2003.
12. H. K. Khalil. Nonlinear Systems. Prentice-Hall, Inc., Upper Saddle River, NJ, second edition, 1996.
13. ∞ control of nonlinear systems: a convex characterization. IEEE Trans. Automatic Control, 40(9):1668-1675, 1995.
14. A. Papachristodoulou and S. Prajna. On the construction of Lyapunov functions using the sum of squares decomposition. In Proc. IEEE Conf. on Decision and Control, 2002.
15. P. A. Parrilo. Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization. PhD thesis, California Institute of Technology, Pasadena, CA, 2000.
16. P. A. Parrilo and B. Sturmfels. Minimizing polynomial functions. In Workshop on Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science, 2001.
17. S. Prajna, A. Papachristodoulou, and P. A. Parrilo. Introducing SOSTOOLS: A general purpose sum of squares programming solver. In Proc. IEEE Conf. on Decision and Control, 2002. Available at http://www.cd3.caltech.edu/sostools and http://www.aut.ee.ethz.ch/~parrilo/sostools.
18. S. Prajna, P. A. Parrilo, and A. Rantzer. Nonlinear control synthesis by convex optimization. IEEE Trans. Automatic Control, 49(2):310-314, 2004.
19. A. Rantzer. A dual to Lyapunov's stability theorem. Systems & Control Letters, 42(3):161-168, 2001.
20. B. Reznick. Extremal PSD forms with few terms. Duke Mathematical Journal, 45(2):363-374, 1978.
21. C. Scherer, P. Gahinet, and M. Chilali. Multiobjective output-feedback control via LMI optimization. IEEE Trans. Automatic Control, 42(7):896-911, 1997.
22. J. S. Shamma and M. Athans. Gain scheduling: Potential hazards and possible remedies. IEEE Control Systems Magazine, pages 101-107, June 1992.
23. N. Z. Shor. Class of global minimum bounds of polynomial functions. Cybernetics, 23(6):731-734, 1987.
24. E. D. Sontag. A "universal" construction of Artstein's theorem on nonlinear stabilization. Systems & Control Letters, 13(2):117-123, 1989.
25. L. Vandenberghe and S. Boyd. Semidefinite programming. SIAM Review, 38(1):49-95, 1996.
26. J. C. Willems. Dissipative dynamical systems. Part I: General theory, Part II: Linear systems with quadratic supply rates. Arch. Rational Mech. Anal., 45:321-393, 1972.
27. F. Wu and S. Prajna. A new solution approach to polynomial LPV System analysis and synthesis. In Proc. American Control Conf., 2004.
28. 2-norm control for LPV systems with bounded parameter variation rates. Internat. J. Robust Nonlinear Control, 6(9-10):983-998, 1996.