Stability Region Estimates for SDRE Controlled Systems Using Sum of Squares Optimization

Proceedings of the American Control Conference

Volumn 3, Issue , 2003, Pages 1867-1872

  Seiler, Pete ^a,b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b United States of America   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; POLYNOMIALS; RICCATI EQUATIONS; SYSTEM STABILITY; THEOREM PROVING;

STABILITY REGION;

NONLINEAR CONTROL SYSTEMS;

EID: 0142215889     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (17)

1. B.D.O. Anderson and J.B. Moore. Optimal Control: Linear Quadratic Methods. Prentice-Hall, 1990.
2. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. SIAM, 1994.
3. M.D. Choi, T.Y. Lam, and B. Reznick. Sums of squares of real polynomials. Proc. of Symposia in Pure Mathematica, 58(2):103-126, 1995.
4. J.R. Cloutier. State-dependent Riccati equation techniques: An overview. In Proc. of the ACC, pages 932-936, 1997.
5. J.R. Cloutier and D.T. Stansbery. The capabilities and art of state-dependent Riccati equation-based design. In Proc. of the ACC, pages 86-91, 2002.
6. D.F. Delchamps. Analytic stabilization and the algebraic Riccati equation. In Proc. of the 22nd CDC, pages 1396-1401, 1983.
7. E.B. Erdem and A.G. Alleyne. Globally stabilizing second order nonlinear systems by SDRE control. In Proc. of the ACC, pages 2501-2505, 1999.
8. E.B. Erdem and A.G. Alleyne. Estimation of stability regions of SDRE controlled systems using vector norms. In Proc. of the ACC, pages 80-85, 2002.
9. Y. Huang and W.-M. Lu. Nonlinear optimal control: Alternatives to Hamilton-Jacobi equation. In Proc. of the CDC, pages 3942-3947, 1996.
10. R.A. Hull, J.R. Cloutier, C.P. Mracek, and D.T. Stansbery. State-dependent Riccati equation solution of the toy nonlinear optimal control problem. In Proc. of the ACC, pages 1658-1662, 1998.
11. H. Khalil. Nonlinear Systems. Prentice-Hall, 1996.
12. W. Langson and A.G. Alleyne. A stability result with application to nonlinear regulation: Theory and experiments. In Proc. of the ACC, pages 3051-3056, 1999.
13. A. Papachristodoulou and S. Prajna. On the construction of Lyapunov functions using sum of squares decomposition. In Proc. of the CDC, 2002. Submitted.
14. P. Parrilo. Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization. PhD thesis, California Institute of Technology, 2000.
15. P. Parrilo. Semidefinite programming relaxations for semialgebraic problems. Submitted to Mathematical Programming, 2002.
16. S. Prajna, A. Papachristodoulou, and P. A. Parrilo. SOSTOOLS: Sum of squares optimization toolbox for MATLAB, 2002. Available from http://www.cds.caltech.edu/sostools and http://www.aut.ee.ethz.ch/̃parrilo/sostools.
17. K. Zhou, J.C. Doyle, and K. Glover. Robust and Optimal Control. Prentice-Hall, 1996.