Second-order nonsmooth optimization for H ∞ synthesis

Numerische Mathematik

Volumn 107, Issue 3, 2007, Pages 433-454

  Bompart, Vincent ^a,b   Noll, Dominikus ^a   Apkarian, Pierre ^a,b  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b ONERA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34548067100     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-007-0095-9     Document Type: Article

References (37)

1. Apkarian P. and Noll D. (2006). Controller design via nonsmooth multi-directional search. SIAM J. Control Optim. 44(6): 1923-1949
2. ∞ synthesis. IEEE Trans. Autom. Control 51(1): 71-86
3. ∞ synthesis. Eur. J. Control 12(3): 229-244
4. Apkarian P. and Noll D. (2007). Nonsmooth optimization for multiband frequency domain control design. Automatica 43(4): 724-731
5. ∞ synthesis. Eur. J. Control 10(6): 527-538
6. Apkarian P. and Tuan H.D. (2000). Robust control via concave minimization-local and global algorithms. IEEE Trans. Autom. Control 45(2): 299-305
7. Balakrishnan V., Boyd S. and Balemi S. (1991). Branch and bound algorithm for computing the minimum stability degree of parameter-dependent linear systems. Int. J. Robust Nonlinear Control 1(4): 295-317
8. Bompart, V., Apkarian, P., Noll, D.: Nonsmooth techniques for stabilizing linear systems. In: Proceedings of the American Control Conference, New York (2007)
9. ∞-norm. Syst. Control Lett. 15(1): 1-7
10. Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear matrix inequalities in system and control theory. In: SIAM Studies in Applied Mathematics, vol 15. SIAM, Philadelphia (1994)
11. ∞-norm of a transfer function matrix. Syst. Control Lett. 14(5): 287-293
12. Conn, A., Gould, N., Toint, Ph.: Trust-region methods. In: MPS-SIAM Series on Optimization, Philadelphia (2000)
13. Fares B., Apkarian P. and Noll D. (2001). An augmented Lagrangian method for a class of LMI-constrained problems in robust control. Int. J. Control 74(4): 348-360
14. Fares B., Noll D. and Apkarian P. (2002). Robust control via sequential semidefinite programming. SIAM J. Control Optim. 40(6): 1791-1820
15. Fletcher R. (1985). Semi-definite matrix constraints in optimization. SIAM J. Control Optim. 23(4): 493-513
16. ∞-norm revisited. In: Proceedings of the IEEE Conference on Decision and Control, Tucson, pp 2257-2258 (1992)
17. Golub G. and Van Loan C. (1989). Matrix Computations. Johns Hopkins University Press, Baltimore, London
18. Hettich R. and Kortanek K. (1993). Semi-infinite programming: theory, methods and applications. SIAM Rev. 35(3): 380-429
19. Jarre F. (1993). An interior-point method for minimizing the maximum eigenvalue of a linear combination of matrices. SIAM J. Control Optim. 31(5): 1360-1377
20. Jongen H.Th., Meer K. and Triesch E. (2004). Optimization Theory. Kluwer, Dordrecht
21. Kato T. (1980). Perturbation theory for linear operators. Springer, New York
22. Laub A. (1981) Efficient multivariable frequency response computations. IEEE Trans. Autom. Control 26(2), 407-408
23. e ib: COnstrained Matrix-optimization Problem ph library-a collection of test examples for nonlinear semidefinite programs, control system design and related problems. Technical report, Universität Trier (2003)
24. Leibfritz F. and Mostafa E.M.E. (2002). An interior-point constrained trust region method for a special class of nonlinear semi-definite programming problems. SIAM J. Optim. 12(4): 1048-1074
25. Leibfritz F. and Mostafa E.M.E. (2003). Trust region methods for solving the optimal output feedback design problem. Int. J. Control 76(5): 501-519
26. MacFarlane A.G.J. and Hung Y.S. (1983). Analytic properties of the singular value of a rational matrix. Int. J. Control 37(2): 221-234
27. Mayne D.Q. and Polak E. (1975). Algorithms for the design of control systems subject to singular value inequalities. IEEE Trans. Autom. Control AC-20(4): 546-548
28. Nocedal J. and Wright S. (1999). Numerical Optimization. Springer, New York
29. Noll D. and Apkarian P. (2005). Spectral bundle methods for nonconvex maximum eigenvalue functions: second-order methods. Math. Program. Ser. B 104(2): 729-747
30. Noll D., Torki M. and Apkarian P. (2004). Partially augmented Lagrangian method for matrix inequality constraints. SIAM J. Optim. 15(1): 161-184
31. Overton M.L. (1983). A quadratically convergent method for minimizing a sum of Euclidean norms. Math. Program. 27: 34-63
32. Overton M.L. (1988). On minimizing the maximum eigenvalue of a symmetric matrix. SIAM J. Matrix Anal. Appl. 9(2): 256-268
33. Polak E. and Wardi Y. (1982). A nondifferentiable optimization algorithm for the design of control systems subject to singular value inequalities over a frequency range. Automatica 18(3): 267-283
34. Safonov, M.G., Goh, K.C., Ly, J.H.: Control system synthesis via bilinear matrix inequalities. In: Proceedings of the American Control Conference, pp 45-49 (1994)
35. Shapiro A. (1997). First and second order analysis of nonlinear semidefinite programs. Math. Program. 77(2): 301-320
36. Thevenet J.-B., Noll D. and Apkarian P. (2006). Nonlinear spectral SDP method for BMI-constrained problems: applications to control design. In: Braz, J., Araújo, H., Vieira, A., and Encarnação, B. (eds) Informatics in Control, Automation and Robotics I., pp 61-72. Springer, Heidelberg
37. Tuan H.D., Apkarian P. and Nakashima Y. (2000). A new Lagrangian dual global optimization algorithm for solving bilinear matrix inequalities. Int. J. Robust Nonlinear Control 10(7): 561-578