A spectral quadratic-SDP method with applications to fixed-order H 2 and H∞ synthesis

2004 5th Asian Control Conference

Volumn 2, Issue , 2004, Pages 1337-1345

  Apkarian, Pierre ^a,b   Noll, Dominikus ^c   Thevenet, Jean Baptiste ^b   Tuan, Hoang Duong ^d  

^a ONERA   (France)

^b UNIVERSITÉ PAUL SABATIER   (France)

^c INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^d UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Augmented lagrangian method (AL); Bilinear matrix inequality (BMI); Fixed order synthesis; Linear matrix inequality (LMI); Rank constraints; Reduced order synthesis; Robust synthesis; Semidefinite programming (SDP)

Indexed keywords

ALGORITHMS; CLOSED LOOP CONTROL SYSTEMS; CONTROL EQUIPMENT; MATRIX ALGEBRA; PROBLEM SOLVING; QUADRATIC PROGRAMMING; SYSTEM STABILITY; VECTORS;

AUGMENTED LAGRANGIAN METHOD (AL); BILINEAR MATRIX INEQUALITY (BMI); FIXED ORDER SYNTHESIS; LINEAR MATRIX INEQUALITY (LMI); RANK CONSTRAINTS; REDUCED-ORDER SYNTHESIS; ROBUST SYNTHESIS; SEMIDEFINITE PROGRAMMING (SDP);

CONTROL THEORY;

EID: 16244367500     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (30)

1. B. ANDERSON AND S. VONGPANITLBRD, Network analysis and synthesis: a modern systems theory approach, Prentice-Hall, 1973.
2. P. APKARIAN AND D. NOLL, Controller design via non-smooth multi-directional search, submitted, (2004). Rapport Interne, MIP, CNRS UMR 5640, Dép. de Math. Université Paul Sabatier.
3. ∞ Synthesis, submitted, (2003). Rapport Interne, MIP, UMR 5640, Maths. Dept. Paul Sabatier University.
4. ∞ control design via an augmented Lagrangian method, Int. J. Robust and Nonlinear Control, 13 (2003), pp. 1137-1148.
5. P. APKARIAN AND H. D. TUAN, Concave Programming in Control Theory, Journal of Global Optimization, 15 (1999), pp. 343-370.
6. P. T. BOGGS AND J. W. TOLLE, Sequential Quadratic Programming, Acta Numerica, (1995), pp. 1-52.
7. J. BONNANS, Local analysis of Newton-type methods for variational inegualitites and nonlinear programming, Appl. Math. Optim., 29 (1994), pp. 161-186.
8. ∞ Control and Its Applications, vol. 235 of Lectures Notes in Control and Information Sciences, Springer Verlag, New York, Heidelberg, Berlin, 1998.
9. A. R. CONN, N. GOULD, AND P. L. TOINT, A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds, SIAM J. Numer. Anal., 28 (1991), pp. 545-572.
10. A. R. CONN, N. I. M. GOULD, A. SARTENAER, AND P. L. TOINT, Local convergence properties of two augmented Lagrangian algorithms for optimization with a combination of general equality and linear constraints, Tech. Report TR/PA/93/27, CERFACS, Toulouse, France, 1993.
11. _, Convergence properties of an augmented Lagrangian algorithm for optimization with a combination of general equality and linear constraints, SIAM J. on Optimization, 6 (1996), pp. 674-703.
12. A. R. CONN, N. I. M. GOULD, AND P. L. TOINT, Trust-Region Methods, MPS/SIAM Series on Optimization, SIAM, Philadelphia, 2000.
13. B. FARES, P. APKARIAN, AND D. NOLL, An Augmented Lagrangian Method for a Class of LMI-Constrained Problems in Robust Control Theory, Int. J. Control, 74 (2001), pp. 348-360.
14. B. FARES, D. NOLL, AND P. APKARIAN, Robust Control via Sequential Semidefinite Programming, SIAM J. on Control and Optimization, 40 (2002), pp. 1791-1820.
15. R. FLETCHER, Practical Methods of Optimization, John Wiley & Sons, 1987.
16. ∞ central controllers near the optimum, Technical Report 13, INRIA, Domaine de Voluceau, Rocquencourt, 78150, Le Chesnay, France, 1992.
17. ∞ Control, Int. J. Robust and Nonlinear Control, 4 (1994), pp. 421-448.
18. P. GAHINET, A. NEMIROVSKI, A. J. LAUB, AND M. CHILALI, LMI Control Toolbox, The MathWorks Inc., 1995.
19. D. GANGSAAS, K. BRUCE, J. BLIGHT, AND U.-L. LY, Application of modern synthesis to aircraft control: Three case studies, IEEE Trans. Aut. Control, AC-31 (1986), pp. 995-1014.
20. J. W. HELTON AND O. MERINO, Coordinate optimization for bi-convex matrix inequalitites, in Proc. IEEE Conf. on Decision and Control, San Diego, CA, 1997, pp. 3609-3613.
21. Y. S. HUNG AND A. G. J. MACFARLANE, Multivariable feedback: A classical approach, Lectures Notes in Control and Information Sciences, Springer Verlag, New York, Heidelberg, Berlin, 1982.
22. L. H. KEEL, S. P. BHATTACHARYYA, AND J. W. HOWZE, Robust control with structured perturbations, IEEE Trans. Aut. Control, 36 (1988), pp. 68-77.
23. F. LEIBFRITZ, Computational design of stabilizing static output feedback controller, Rapports 1 et 2 Mathematik/Informatik, Forschungsbericht 99-02, Universitt Trier, 1998.
24. A. LEWIS, Derivatives of spectral functions, Mathematics of Operations Research, 21 (1996), pp. 576-588.
25. _, Twice differentiate spectral functions, SIAM J. on Matrix Analysis and Applications, 23 (2001), pp. 368-386.
26. M. MESBAHI AND G. P. PAPAVASSILOPOULOS, Solving a Class of Rank Minimization Problems via Semi-Definite Programs, with Applications to the Fixed Order Output Feedback Synthesis, in Proc. American Control Conf., 1997.
27. L. MOSHEYEV AND M. ZIBULEVSKY, Penalty/barrier multiplier algorithm for semidefinite programming, Optimization Methods and Software, 13 (2000), pp. 235-261.
28. D. NOLL, M. TORKI, AND P. APKARIAN, Partially Augmented Lagrangiah Method for Matrix Inequality Constraints, submitted, (2002). Rapport Interne, MIP, UMR 5640, Maths. Dept. - Paul Sabatier University.
29. A. SHAPIRO, On differentiability of symmetric matrix valued functions, School of Industrial and Systems Engineering, Georgia Institute of Technology, (2002). Preprint.
30. J. F. STURM, Using SeDuMi 1.02, A Matlab Toolbox for Optimization over Symmetric Cones, tech. report, Tilburg University, Tilburg, Netherlands, Oct. 2001.