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Volumn 44, Issue 6, 2006, Pages 1923-1949

Controller design via nonsmooth multidirectional search

Author keywords

subgradients; Fixed order synthesis; Mixed H2 H synthesis; Moving polytope; Nonsmooth analysis; Np hard design problems; Pattern search algorithm; Simultaneous stabilization; Spectral bundle method; Static output feedback

Indexed keywords

ALGORITHMS; BENCHMARKING; FEEDBACK CONTROL; OPTIMIZATION; PROBLEM SOLVING; SYSTEM STABILITY;

EID: 31344446586     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012904441684     Document Type: Article
Times cited : (59)

References (68)
  • 1
    • 21044450838 scopus 로고    scopus 로고
    • Generalized pattern searches with derivative information
    • M. A. ABRAMSON, C. AUDET, AND J. E. DENNIS JR., Generalized pattern searches with derivative information, Math. Program. Ser. B, 100 (2004), pp. 3-25.
    • (2004) Math. Program. Ser. B , vol.100 , pp. 3-25
    • Abramson, M.A.1    Audet, C.2    Dennis Jr., J.E.3
  • 7
    • 33750265086 scopus 로고    scopus 로고
    • Mesh adaptive direct search algorithms for constrained optimization
    • to appear
    • C. AUDET AND J. E. DENNIS JR., Mesh adaptive direct search algorithms for constrained optimization, SIAM J. Optim., to appear.
    • SIAM J. Optim.
    • Audet, C.1    Dennis Jr., J.E.2
  • 8
    • 0027851588 scopus 로고
    • Simultaneous stabilizability question of three linear systems is rationally undecidable
    • V. BLONDEL AND M. GEVERS, Simultaneous stabilizability question of three linear systems is rationally undecidable, Math. Control Signals Syst., 6 (1994), pp. 135-145.
    • (1994) Math. Control Signals Syst. , vol.6 , pp. 135-145
    • Blondel, V.1    Gevers, M.2
  • 11
    • 0002525028 scopus 로고
    • Evolutionary operation: A method for increasing industrial productivity
    • G. E. P. Box, Evolutionary operation: A method for increasing industrial productivity, Appl. Stat., 6 (1957), pp. 81-101.
    • (1957) Appl. Stat. , vol.6 , pp. 81-101
    • Box, G.E.P.1
  • 14
  • 17
    • 84943765256 scopus 로고    scopus 로고
    • Two numerical methods for optimizing matrix stability
    • J. BURKE, A. LEWIS, AND M. OVERTON, Two numerical methods for optimizing matrix stability, Linear Algebra Appl., 351-352 (2002), pp. 147-184.
    • (2002) Linear Algebra Appl. , vol.351-352 , pp. 147-184
    • Burke, J.1    Lewis, A.2    Overton, M.3
  • 18
    • 23844446458 scopus 로고    scopus 로고
    • A robust gradient sampling algorithm for nonsmooth, nonconvex optimization
    • J. BURKE, A. LEWIS, AND M. OVERTON, A robust gradient sampling algorithm for nonsmooth, nonconvex optimization, SIAM J. Optim., 15 (2003), pp. 751-779.
    • (2003) SIAM J. Optim. , vol.15 , pp. 751-779
    • Burke, J.1    Lewis, A.2    Overton, M.3
  • 19
    • 0037828294 scopus 로고    scopus 로고
    • Robust stability and a criss-cross algorithm for pseudospectra
    • J. BURKE, A. LEWIS, AND M. OVERTON, Robust stability and a criss-cross algorithm for pseudospectra, IMA J. Numer. Anal., 23 (2003), pp. 1-17.
    • (2003) IMA J. Numer. Anal. , vol.23 , pp. 1-17
    • Burke, J.1    Lewis, A.2    Overton, M.3
  • 20
    • 0032121549 scopus 로고    scopus 로고
    • Static output feedback simultaneous stabilization: ILMI approach
    • Y. Y. CAO AND Y. X. SUN, Static output feedback simultaneous stabilization: ILMI approach, Int. J. Control, 70 (1998), pp. 803-814.
    • (1998) Int. J. Control , vol.70 , pp. 803-814
    • Cao, Y.Y.1    Sun, Y.X.2
  • 21
    • 0003712185 scopus 로고    scopus 로고
    • ∞, control and its applications
    • Springer-Verlag, New York, Heidelberg, Berlin
    • ∞, Control and Its Applications, Lecture Notes in Control and Inform. Sci. 235, Springer-Verlag, New York, Heidelberg, Berlin, 1998.
    • (1998) Lecture Notes in Control and Inform. Sci. , vol.235
    • Chen, B.M.1
  • 22
    • 0003859933 scopus 로고
    • Optimization and nonsmooth analysis
    • John Wiley & Sons, New York
    • F. H. CLARKE, Optimization and Nonsmooth Analysis, Canadian Math. Soc. Series, John Wiley & Sons, New York, 1983.
    • (1983) Canadian Math. Soc. Series
    • Clarke, F.H.1
  • 23
    • 0016624432 scopus 로고
    • The minimization of certain nondifferentiable sums of eigenvalues of symmetric matrices
    • J. CULLUM, W. DONATH, AND P. WOLFE, The minimization of certain nondifferentiable sums of eigenvalues of symmetric matrices, Math. Program. Stud., 3 (1975), pp. 35-55.
    • (1975) Math. Program. Stud. , vol.3 , pp. 35-55
    • Cullum, J.1    Donath, W.2    Wolfe, P.3
  • 24
    • 0348011468 scopus 로고
    • Benchmark problems for control system design
    • Technical report, Pergamon Press, Oxford
    • E. E. J. DAVISON, Benchmark Problems for Control System Design, Technical report, IFAC Technical Committee Reports, Pergamon Press, Oxford, 1990.
    • (1990) IFAC Technical Committee Reports
    • Davison, E.E.J.1
  • 25
    • 0036930053 scopus 로고    scopus 로고
    • Robust control via sequential semidefinite programming
    • B. FARES, D. NOLL, AND P. APKARIAN, Robust control via sequential semidefinite programming, SIAM J. Control Optim., 40 (2002), pp. 1791-1820.
    • (2002) SIAM J. Control Optim. , vol.40 , pp. 1791-1820
    • Fares, B.1    Noll, D.2    Apkarian, P.3
  • 29
    • 0022808435 scopus 로고
    • Application of modern synthesis to aircraft control: Three case studies
    • D. GANGSAAS, K. BRUCE, J. BLIGHT, AND U.-L. LY, Application of modern synthesis to aircraft control: Three case studies, IEEE Trans. Automat. Control, AC-31 (1986), pp. 995-1014.
    • (1986) IEEE Trans. Automat. Control , vol.AC-31 , pp. 995-1014
    • Gangsaas, D.1    Bruce, K.2    Blight, J.3    Ly, U.-L.4
  • 30
    • 0026119236 scopus 로고
    • On a convex parameter space method for linear control design of uncertain systems
    • J. C. GEROMEL, P. L. D. PERES, AND J. BERNUSSOU, On a convex parameter space method for linear control design of uncertain systems, SIAM J. Control Optim., 29 (1991), pp. 381-402.
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 381-402
    • Geromel, J.C.1    Peres, P.L.D.2    Bernussou, J.3
  • 32
    • 0034415006 scopus 로고    scopus 로고
    • Spectral bundle method for semidefinite programming
    • C. HELMBERG AND F. RENDL, Spectral bundle method for semidefinite programming, SIAM J. Optim., 10 (2000), pp. 673-696.
    • (2000) SIAM J. Optim. , vol.10 , pp. 673-696
    • Helmberg, C.1    Rendl, F.2
  • 34
    • 33751162624 scopus 로고    scopus 로고
    • Rank-one LMI approach to simultaneous stabilization of linear systems
    • D. HENRION, S. TARBOURIECH, AND M. SEBEK, Rank-one LMI approach to simultaneous stabilization of linear systems, Syst. Control Lett., 11 (1998), pp. 167-172.
    • (1998) Syst. Control Lett. , vol.11 , pp. 167-172
    • Henrion, D.1    Tarbouriech, S.2    Sebek, M.3
  • 35
    • 0003316862 scopus 로고
    • Convex analysis and minimization algorithms II: Advanced theory and bundle methods
    • Springer-Verlag, New York
    • J.-B. HIRIART-URRUTY AND C. LEMARÉCHAL, Convex Analysis and Minimization Algorithms II: Advanced Theory and Bundle Methods, Grundlehren Math. Wiss. 306, Springer-Verlag, New York, 1993.
    • (1993) Grundlehren Math. Wiss. , vol.306
    • Hiriart-Urruty, J.-B.1    Lemaréchal, C.2
  • 36
    • 33750422151 scopus 로고    scopus 로고
    • A nonlinear SDP approach to fixed-order controller synthesis and comparison with two other methods applied to an active suspension system
    • C. HOL, C. SCHERER, E. VAN DER MECHÉ, AND O. BOSGRA, A nonlinear SDP approach to fixed-order controller synthesis and comparison with two other methods applied to an active suspension system, Eur. J. Control, 9 (2003), pp. 13-28.
    • (2003) Eur. J. Control , vol.9 , pp. 13-28
    • Hol, C.1    Scherer, C.2    Van Der Meché, E.3    Bosgra, O.4
  • 37
    • 84938447945 scopus 로고
    • "Direct search" solution of numerical and statistical problems
    • R. HOOK AND T. A. JEEVES, "Direct search" solution of numerical and statistical problems, J. Assoc. Comput. Mach., 8 (1961), pp. 212-229.
    • (1961) J. Assoc. Comput. Mach. , vol.8 , pp. 212-229
    • Hook, R.1    Jeeves, T.A.2
  • 38
    • 0016094490 scopus 로고
    • Solution of the optimal constant output feedback problem by conjugate gradients
    • H. P. HORISBERGER AND P. R. BELANGER, Solution of the optimal constant output feedback problem by conjugate gradients, IEEE Trans. Automat. Control, 19 (1974), pp. 434-435.
    • (1974) IEEE Trans. Automat. Control , vol.19 , pp. 434-435
    • Horisberger, H.P.1    Belanger, P.R.2
  • 39
    • 0003561462 scopus 로고
    • Multivariable feedback: A classical approach
    • Springer-Verlag, New York, Heidelberg, Berlin
    • Y. S. HUNG AND A. G. J. MACFARLANE, Multivariable Feedback: A Classical Approach, Lecture Notes in Control and Inform. Sci. 40, Springer-Verlag, New York, Heidelberg, Berlin, 1982.
    • (1982) Lecture Notes in Control and Inform. Sci. , vol.40
    • Hung, Y.S.1    Macfarlane, A.G.J.2
  • 43
    • 0003296464 scopus 로고
    • Methods of descent for nondifferentiable optimization
    • A. Dold and B. Eckmann, eds., Springer-Verlag, Berlin, Heidelberg, New York
    • K. C. KIWIEL, Methods of Descent for Nondifferentiable Optimization, Lecture Notes in Math. 1133, A. Dold and B. Eckmann, eds., Springer-Verlag, Berlin, Heidelberg, New York, 1985.
    • (1985) Lecture Notes in Math. , vol.1133
    • Kiwiel, K.C.1
  • 44
    • 0022757520 scopus 로고
    • A linearization algorithm for optimizing control systems subject to singular value inequalities
    • K. C. KIWIEL, A linearization algorithm for optimizing control systems subject to singular value inequalities, IEEE Trans. Automat. Control, AC-31 (1986), pp. 595-602.
    • (1986) IEEE Trans. Automat. Control , vol.AC-31 , pp. 595-602
    • Kiwiel, K.C.1
  • 45
    • 0041844993 scopus 로고    scopus 로고
    • A code for convex nonlinear and semidefinite programming
    • M. KOCVARA AND M. STINGL, A code for convex nonlinear and semidefinite programming, Optim Methods Software, 18 (2003), pp. 317-333.
    • (2003) Optim Methods Software , vol.18 , pp. 317-333
    • Kocvara, M.1    Stingl, M.2
  • 46
    • 0242667172 scopus 로고    scopus 로고
    • Optimization by direct search: New perspectives on some classical and modern methods
    • T. G. KOLDA, R. M. LEWIS, AND V. TORCZON, Optimization by direct search: New perspectives on some classical and modern methods, SIAM Rev., 45 (2003), pp. 385-482.
    • (2003) SIAM Rev. , vol.45 , pp. 385-482
    • Kolda, T.G.1    Lewis, R.M.2    Torczon, V.3
  • 48
    • 0142230430 scopus 로고    scopus 로고
    • Trust region methods for solving the optimal output feedback design problem
    • F. LEIBFRITZ AND E. M. E. MOSTAFA, Trust region methods for solving the optimal output feedback design problem, Int. J. Control, 76 (2000), pp. 501-519.
    • (2000) Int. J. Control , vol.76 , pp. 501-519
    • Leibfritz, F.1    Mostafa, E.M.E.2
  • 49
    • 0036434767 scopus 로고    scopus 로고
    • An interior point constrained trust region method for a special class of nonlinear semidefinite programming problems
    • F. LEIBFRITZ AND E. M. E. MOSTAFA, An interior point constrained trust region method for a special class of nonlinear semidefinite programming problems, SIAM J. Optim., 12 (2002), pp. 1048-1074.
    • (2002) SIAM J. Optim. , vol.12 , pp. 1048-1074
    • Leibfritz, F.1    Mostafa, E.M.E.2
  • 50
    • 77957820648 scopus 로고
    • Nondifferentiable optimization
    • G. L. Nemhauser and A. H. G. Rinnooy Kan, eds., Elsevier North-Holland, New York
    • C. LEMARECHAL, Nondifferentiable optimization, in Optimization, G. L. Nemhauser and A. H. G. Rinnooy Kan, eds., Elsevier North-Holland, New York, 1989, pp. 529-572.
    • (1989) Optimization , pp. 529-572
    • Lemarechal, C.1
  • 51
    • 0013238081 scopus 로고    scopus 로고
    • Wedge trust region methods for derivative free optimization
    • M. MARAZZI AND J. NOCEDAL, Wedge trust region methods for derivative free optimization, Math. Program. Ser. A, 91 (2002), pp. 289-305.
    • (2002) Math. Program. Ser. A , vol.91 , pp. 289-305
    • Marazzi, M.1    Nocedal, J.2
  • 52
    • 0032252855 scopus 로고    scopus 로고
    • Convergence of the Nelder-Mead simplex method to a nonstationary point
    • K. I. M. MCKINNON, Convergence of the Nelder-Mead simplex method to a nonstationary point, SIAM J. Optim., 9 (1998), pp. 148-158.
    • (1998) SIAM J. Optim. , vol.9 , pp. 148-158
    • Mckinnon, K.I.M.1
  • 53
    • 0027903975 scopus 로고
    • An interactive method for nonsmooth multiobjective with an application to optimal control
    • K. MIETTINEN AND M. M. MÄKELÄ, An interactive method for nonsmooth multiobjective with an application to optimal control, Optim. Methods Software, 2 (1993), pp. 31-44.
    • (1993) Optim. Methods Software , vol.2 , pp. 31-44
    • Miettinen, K.1    Mäkelä, M.M.2
  • 54
    • 0034517243 scopus 로고    scopus 로고
    • Penalty/barrier multiplier algorithm for semidefinite programming
    • L. MOSHEYEV AND M. ZIBULEVSKY, Penalty/barrier multiplier algorithm for semidefinite programming, Optim. Methods Software, 13 (2000), pp. 235-261.
    • (2000) Optim. Methods Software , vol.13 , pp. 235-261
    • Mosheyev, L.1    Zibulevsky, M.2
  • 55
    • 0000238336 scopus 로고
    • A simplex method for function minimization
    • J. A. NELDER AND R. MEAD, A simplex method for function minimization, Comput. J., (1965), pp. 441-461.
    • (1965) Comput. J. , pp. 441-461
    • Nelder, J.A.1    Mead, R.2
  • 56
    • 0027798081 scopus 로고
    • Several NP-hard problems arising in robust stability analysis
    • A. NEMIROVSKII, Several NP-hard problems arising in robust stability analysis, Math. Control Signals Syst., 6 (1993), pp. 99-105.
    • (1993) Math. Control Signals Syst. , vol.6 , pp. 99-105
    • Nemirovskii, A.1
  • 57
    • 33751187882 scopus 로고    scopus 로고
    • Spectral bundle methods for non-convex maximum eigenvalue functions: First-order methods
    • to appear
    • D. NOLL AND P. APKARIAN, Spectral bundle methods for non-convex maximum eigenvalue functions: First-order methods, Math. Program. Ser. B, to appear.
    • Math. Program. Ser. B
    • Noll, D.1    Apkarian, P.2
  • 58
    • 33751187882 scopus 로고    scopus 로고
    • Spectral bundle methods for non-convex maximum eigenvalue functions: Second-order methods
    • to appear
    • D. NOLL AND P. APKARIAN, Spectral bundle methods for non-convex maximum eigenvalue functions: Second-order methods, Math. Program. Ser. B, to appear.
    • Math. Program. Ser. B
    • Noll, D.1    Apkarian, P.2
  • 59
    • 14944347490 scopus 로고    scopus 로고
    • Partially augmented Lagrangian method for matrix inequality constraints
    • D. NOLL, M. TORKI, AND P. APKARIAN, Partially augmented Lagrangian method for matrix inequality constraints, SIAM J. Optim., 15 (2004), pp. 161-184.
    • (2004) SIAM J. Optim. , vol.15 , pp. 161-184
    • Noll, D.1    Torki, M.2    Apkarian, P.3
  • 60
    • 0002928322 scopus 로고    scopus 로고
    • A second-order bundle method to minimize the maximum eigenvalue function
    • F. OUSTRY, A second-order bundle method to minimize the maximum eigenvalue function, Math. Program. Ser. A, 89 (2000), pp. 1-33.
    • (2000) Math. Program. Ser. A , vol.89 , pp. 1-33
    • Oustry, F.1
  • 62
    • 0020128980 scopus 로고
    • A nondifferentiable optimization algorithm for the design of control systems subject to singular value inequalities over a frequency range
    • E. POLAK AND Y. WARDI, A nondifferentiable optimization algorithm for the design of control systems subject to singular value inequalities over a frequency range, Automatica, 18 (1982), pp. 267-283.
    • (1982) Automatica , vol.18 , pp. 267-283
    • Polak, E.1    Wardi, Y.2
  • 63
    • 84946640734 scopus 로고
    • Sequential application of simplex designs in optimisation and evolutionary operation
    • W. SPENDLEY, G. R. HEXT, AND F. R. HIMSWORTH, Sequential application of simplex designs in optimisation and evolutionary operation, Technometrics, 4 (1962), pp. 441-461.
    • (1962) Technometrics , vol.4 , pp. 441-461
    • Spendley, W.1    Hext, G.R.2    Himsworth, F.R.3
  • 64
    • 33751163271 scopus 로고    scopus 로고
    • A bundle-type method for "large scale" output feedback control design
    • Stockholm, Sweden
    • J. THEVENET, P. APKARIAN, AND D. NOLL, A bundle-type method for "large scale" output feedback control design, SIAM Conference on Optimization, Stockholm, Sweden, 2005.
    • (2005) SIAM Conference on Optimization
    • Thevenet, J.1    Apkarian, P.2    Noll, D.3
  • 65
    • 31344454154 scopus 로고    scopus 로고
    • Nonlinear spectral SDP method for BMI-constrained problems: Applications to control design
    • Setúbal, Portugal
    • J. THEVENET, D. NOLL, AND P. APKARIAN, Nonlinear spectral SDP method for BMI-constrained problems: Applications to control design, in ICINCO Proceedings, Setúbal, Portugal, 2004, pp. 237-248.
    • (2004) ICINCO Proceedings , pp. 237-248
    • Thevenet, J.1    Noll, D.2    Apkarian, P.3
  • 66
    • 84964345631 scopus 로고
    • On the convergence of the multidirectional search algorithm
    • V. TORCZON, On the convergence of the multidirectional search algorithm, SIAM J. Optim., 1 (1991), pp. 123-145.
    • (1991) SIAM J. Optim. , vol.1 , pp. 123-145
    • Torczon, V.1
  • 67
    • 0031540855 scopus 로고    scopus 로고
    • On the convergence of pattern search algorithms
    • V. TORCZON, On the convergence of pattern search algorithms, SIAM J. Optim., 7 (1997), pp. 1-25.
    • (1997) SIAM J. Optim. , vol.7 , pp. 1-25
    • Torczon, V.1
  • 68
    • 0031238062 scopus 로고    scopus 로고
    • Pseudospectra of linear operators
    • L. TREFETHEN, Pseudospectra of linear operators, SIAM Rev., 39 (1997), pp. 383-406.
    • (1997) SIAM Rev. , vol.39 , pp. 383-406
    • Trefethen, L.1


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