메뉴 건너뛰기




Volumn 43, Issue 12, 2007, Pages 2022-2033

A probabilistic analytic center cutting plane method for feasibility of uncertain LMIs

Author keywords

Randomized algorithms; Robust control; Uncertain linear matrix inequalities

Indexed keywords

ALGORITHMS; PROBABILISTIC LOGICS; PROBLEM SOLVING; RANDOM PROCESSES; ROBUST CONTROL; UNCERTAIN SYSTEMS;

EID: 36248929488     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2007.04.003     Document Type: Article
Times cited : (50)

References (31)
  • 1
    • 36248941736 scopus 로고    scopus 로고
    • Alamo, T., Tempo, R., Ramirez, D. R., & Camacho, E. F. (2007). A new vertex result for robustness problems with interval matrix uncertainty. In Proceedings of the European control conference.
  • 2
    • 0346348683 scopus 로고
    • A cutting plane algorithm for convex programming that uses analytic centers
    • Atkinson D.S., and Vaidya P.M. A cutting plane algorithm for convex programming that uses analytic centers. Mathematical Programming, Series B 69 (1995) 1-43
    • (1995) Mathematical Programming, Series B , vol.69 , pp. 1-43
    • Atkinson, D.S.1    Vaidya, P.M.2
  • 5
    • 0036353423 scopus 로고    scopus 로고
    • On tractable approximations of uncertain linear matrix inequalities affected by interval uncertainty
    • Ben-Tal A., and Nemirovski A. On tractable approximations of uncertain linear matrix inequalities affected by interval uncertainty. SIAM Journal on Optimization 12 3 (2002) 811-833
    • (2002) SIAM Journal on Optimization , vol.12 , Issue.3 , pp. 811-833
    • Ben-Tal, A.1    Nemirovski, A.2
  • 6
    • 9644290119 scopus 로고    scopus 로고
    • A convex approach to robust stability for linear systems with uncertain scalar parameters
    • Bliman P.-A. A convex approach to robust stability for linear systems with uncertain scalar parameters. SIAM Journal on Control and Optimization 42 6 (2004) 2016-2042
    • (2004) SIAM Journal on Control and Optimization , vol.42 , Issue.6 , pp. 2016-2042
    • Bliman, P.-A.1
  • 8
    • 36249008830 scopus 로고    scopus 로고
    • Boyd, S., & Vandenberghe, L. (2004). Convex optimization. Cambridge.
  • 9
    • 36249025442 scopus 로고    scopus 로고
    • Calafiore, G. (2006). Cutting plane methods for probabilistically-robust feasibility problems. In Proceedings of mathematical theory of networks and systems, Kyoto, Japan.
  • 10
    • 12344268988 scopus 로고    scopus 로고
    • Uncertain convex programs: randomized solutions and confidence levels
    • Calafiore G., and Campi M.C. Uncertain convex programs: randomized solutions and confidence levels. Mathematical Programming 102 1 (2005) 25-46
    • (2005) Mathematical Programming , vol.102 , Issue.1 , pp. 25-46
    • Calafiore, G.1    Campi, M.C.2
  • 12
    • 36248975552 scopus 로고    scopus 로고
    • Calafiore, G., & Dabbene, F. (Eds.) (2006). Probabilistic and randomized methods for design under uncertainty. London: Springer.
  • 13
    • 0035508269 scopus 로고    scopus 로고
    • Stochastic algorithms for exact and approximate feasibility of robust LMIs
    • Calafiore G., and Polyak B.T. Stochastic algorithms for exact and approximate feasibility of robust LMIs. IEEE Transactions on Automatic Control 46 (2001) 1755-1759
    • (2001) IEEE Transactions on Automatic Control , vol.46 , pp. 1755-1759
    • Calafiore, G.1    Polyak, B.T.2
  • 15
    • 0030303856 scopus 로고    scopus 로고
    • Complexity analysis of an interior point cutting plane method for convex feasibility problems
    • Goffin J.-L., Luo Z.Q., and Ye Y. Complexity analysis of an interior point cutting plane method for convex feasibility problems. SIAM Journal on Optimization 6 (1996) 638-652
    • (1996) SIAM Journal on Optimization , vol.6 , pp. 638-652
    • Goffin, J.-L.1    Luo, Z.Q.2    Ye, Y.3
  • 16
    • 0001857004 scopus 로고    scopus 로고
    • Shallow, deep and very deep cuts in the analytic center cutting plane method
    • Goffin J.-L., and Vial J.-P. Shallow, deep and very deep cuts in the analytic center cutting plane method. Mathematical Programming 84 (1999) 89-103
    • (1999) Mathematical Programming , vol.84 , pp. 89-103
    • Goffin, J.-L.1    Vial, J.-P.2
  • 17
    • 0036817928 scopus 로고    scopus 로고
    • Convex non-differentiable optimization: A survey focused on the analytic center cutting plane method
    • Goffin J.-L., and Vial J.-P. Convex non-differentiable optimization: A survey focused on the analytic center cutting plane method. Optimization Methods & Software 17 (2002) 805-867
    • (2002) Optimization Methods & Software , vol.17 , pp. 805-867
    • Goffin, J.-L.1    Vial, J.-P.2
  • 18
    • 0038729656 scopus 로고    scopus 로고
    • An ellipsoid algorithm for probabilistic robust controller design
    • Kanev S., De Schutter B., and Verhaegen M. An ellipsoid algorithm for probabilistic robust controller design. Systems & Control Letters 49 (2003) 365-375
    • (2003) Systems & Control Letters , vol.49 , pp. 365-375
    • Kanev, S.1    De Schutter, B.2    Verhaegen, M.3
  • 20
    • 0000564361 scopus 로고
    • A polynomial time algorithm for linear programming
    • Khachiyan L.G. A polynomial time algorithm for linear programming. Soviet Math. Doklady 20 (1979) 191-194
    • (1979) Soviet Math. Doklady , vol.20 , pp. 191-194
    • Khachiyan, L.G.1
  • 22
    • 0242551555 scopus 로고    scopus 로고
    • Polynomial interior point cutting plane methods
    • Mitchell J.E. Polynomial interior point cutting plane methods. Optimization Methods & Software 18 (2003) 507-534
    • (2003) Optimization Methods & Software , vol.18 , pp. 507-534
    • Mitchell, J.E.1
  • 24
    • 85128535409 scopus 로고    scopus 로고
    • Oishi, Y. (2003). Probabilistic design of a robust state-feedback controller based on parameter-dependent Lyapunov functions. In Proceedings of the IEEE conference on decision and control.
  • 25
    • 33846781128 scopus 로고    scopus 로고
    • Polynomial-time algorithms for probabilistic solutions of parameter-dependent linear matrix inequalities
    • Oishi Y. Polynomial-time algorithms for probabilistic solutions of parameter-dependent linear matrix inequalities. Automatica 43 (2007) 538-545
    • (2007) Automatica , vol.43 , pp. 538-545
    • Oishi, Y.1
  • 26
    • 0242366131 scopus 로고    scopus 로고
    • Computational complexity of randomized algorithms for solving parameter-dependent linear matrix inequalities
    • Oishi Y., and Kimura H. Computational complexity of randomized algorithms for solving parameter-dependent linear matrix inequalities. Automatica 39 (2003) 2149-2156
    • (2003) Automatica , vol.39 , pp. 2149-2156
    • Oishi, Y.1    Kimura, H.2
  • 27
    • 36248953507 scopus 로고    scopus 로고
    • Péton, O. (2002). The homogeneous analytic center cutting plane method. Ph.D. Thesis, Université de Genève.
  • 28
    • 0034916989 scopus 로고    scopus 로고
    • Probabilistic robust design with linear quadratic regulators
    • Polyak B.T., and Tempo R. Probabilistic robust design with linear quadratic regulators. Systems & Control Letters 43 (2001) 343-353
    • (2001) Systems & Control Letters , vol.43 , pp. 343-353
    • Polyak, B.T.1    Tempo, R.2
  • 29
    • 33646254843 scopus 로고    scopus 로고
    • Relaxations for robust linear matrix inequality problems with verifications for exactness
    • Scherer C.W. Relaxations for robust linear matrix inequality problems with verifications for exactness. SIAM Journal on Matrix Analysis and Applications 27 2 (2005) 365-395
    • (2005) SIAM Journal on Matrix Analysis and Applications , vol.27 , Issue.2 , pp. 365-395
    • Scherer, C.W.1
  • 30
    • 36248991064 scopus 로고
    • Utilization of the operation of space dilatation in the minimization of convex functions
    • Shor N.Z. Utilization of the operation of space dilatation in the minimization of convex functions. Cybernetics 13 (1970) 94-96
    • (1970) Cybernetics , vol.13 , pp. 94-96
    • Shor, N.Z.1
  • 31
    • 36248982938 scopus 로고    scopus 로고
    • Tempo, R., Calafiore, G., & Dabbene, F. (2004). Randomized algorithms for analysis and control of uncertain systems. Communications and control engineering series. London: Springer.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.