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Volumn 32, Issue 3 SPEC. ISS., 2003, Pages 555-584

Second order optimality conditions for bang-bang control problems

Author keywords

Bang bang control; Critical cone; Numerical verification of second order conditions; Second order necessary and sufficient conditions; Transformation of quadratic forms; Van der Pol oscillator

Indexed keywords

BOUNDARY CONDITIONS; MATHEMATICAL TRANSFORMATIONS; OPTIMIZATION; ORDINARY DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; SENSITIVITY ANALYSIS;

EID: 1542312234     PISSN: 03248569     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (33)

References (44)
  • 2
    • 0041786633 scopus 로고    scopus 로고
    • Computational sensitivity analysis for state constrained optimal control problems
    • AUGUSTIN, D. and MAURER, H. (2001a) Computational sensitivity analysis for state constrained optimal control problems. Annals of Operations Research, 101, 75-99.
    • (2001) Annals of Operations Research , vol.101 , pp. 75-99
    • Augustin, D.1    Maurer, H.2
  • 3
    • 0021817336 scopus 로고
    • A high order test for optimality of bang-bang controls
    • BRESSAN, A. (1985) A high order test for optimality of bang-bang controls. SIAM J. Control and Optimization, 23, 38-48.
    • (1985) SIAM J. Control and Optimization , vol.23 , pp. 38-48
    • Bressan, A.1
  • 6
    • 0029378576 scopus 로고
    • Second order optimality conditions in sets of L∞ functions with range in a polyhedron
    • DUNN, J.C. (1995) Second order optimality conditions in sets of L∞ functions with range in a polyhedron. SIAM J. Control Optimization, 33, 1603-1635.
    • (1995) SIAM J. Control Optimization , vol.33 , pp. 1603-1635
    • Dunn, J.C.1
  • 7
    • 0030194742 scopus 로고    scopus 로고
    • 2 sufficient conditions and the gradient projection method for optimal control problems
    • 2 sufficient conditions and the gradient projection method for optimal control problems. SIAM J. Control Optimization, 34, 1270-1290.
    • (1996) SIAM J. Control Optimization , vol.34 , pp. 1270-1290
    • Dunn, J.C.1
  • 8
    • 0347590910 scopus 로고    scopus 로고
    • On stability of bang-bang type controls
    • FELGENHAUER, U. (2003) On stability of bang-bang type controls, SIAM J. Control and Optimization, 41, 1843-1867.
    • (2003) SIAM J. Control and Optimization , vol.41 , pp. 1843-1867
    • Felgenhauer, U.1
  • 11
    • 0347747983 scopus 로고    scopus 로고
    • High-speed switch-on of a semiconductor gas discharge image converter using optimal control methods
    • KIM, J.-H. R., MAURER, H., ASTROV, YU.A., BODE, M. and PURWINS, H.G. (2001) High-speed switch-on of a semiconductor gas discharge image converter using optimal control methods. J. Computational Physics, 170, 395-414.
    • (2001) J. Computational Physics , vol.170 , pp. 395-414
    • Kim, J.-H.R.1    Maurer, H.2    Astrov, Yu.A.3    Bode, M.4    Purwins, H.G.5
  • 12
    • 1542621767 scopus 로고    scopus 로고
    • Single mode semiconductor lasers with homogeneous transverse profile
    • Submitted to
    • KIM, J.-H. R., LIPPI, G.L., MAURER, H. (2003) Single mode semiconductor lasers with homogeneous transverse profile. Submitted to Physica-D.
    • (2003) Physica-D
    • Kim, J.-H.R.1    Lippi, G.L.2    Maurer, H.3
  • 13
  • 14
    • 84956208613 scopus 로고
    • Higher order conditions for a local minimum in the problems with constraints
    • LEVITIN, E.S., MILYUTIN, A.A. and OSMOLOVSKII, N.P. (1978) Higher order conditions for a local minimum in the problems with constraints. Russian Math. Surveys, 33, 6, 97-168.
    • (1978) Russian Math. Surveys , vol.33 , Issue.6 , pp. 97-168
    • Levitin, E.S.1    Milyutin, A.A.2    Osmolovskii, N.P.3
  • 15
    • 0026680941 scopus 로고
    • Second order conditions and constraint qualifications in stability and sensitivity analysis of solutions to optimization problems in Hubert spaces
    • MALANOWSKI, K. (1992) Second order conditions and constraint qualifications in stability and sensitivity analysis of solutions to optimization problems in Hubert spaces. Applied Math. Optimization, 25, 51-79.
    • (1992) Applied Math. Optimization , vol.25 , pp. 51-79
    • Malanowski, K.1
  • 16
    • 0000146438 scopus 로고
    • Two-norm approach in stability and sensitivity analysis of optimization and optimal control problems
    • MALANOWSKI, K. (1993) Two-norm approach in stability and sensitivity analysis of optimization and optimal control problems. Advances in Math. Sciences and Applications, 2, 397-443.
    • (1993) Advances in Math. Sciences and Applications , vol.2 , pp. 397-443
    • Malanowski, K.1
  • 17
    • 0001620726 scopus 로고
    • Stability and sensitivity of solutions to nonlinear optimal control problems
    • MALANOWSKI, K. (1994) Stability and sensitivity of solutions to nonlinear optimal control problems. Applied Math. Optimization, 32, 111-141.
    • (1994) Applied Math. Optimization , vol.32 , pp. 111-141
    • Malanowski, K.1
  • 18
    • 84861974811 scopus 로고    scopus 로고
    • Sensitivity analysis for parametric control problems with control-state constraints
    • Polska Akademia Nauk, Instytut Matematyczny, Warszawa
    • MALANOWSKI, K. (2001) Sensitivity analysis for parametric control problems with control-state constraints. Dissertationes Mathematicae CCCXCIV, 1-51, Polska Akademia Nauk, Instytut Matematyczny, Warszawa.
    • (2001) Dissertationes Mathematicae , vol.394 , pp. 1-51
    • Malanowski, K.1
  • 19
    • 0030145422 scopus 로고    scopus 로고
    • Sensitivity analysis for parametric control problems with control-state constraints
    • MALANOWSKI, K. and MAURER, H. (1996) Sensitivity analysis for parametric control problems with control-state constraints. Comput. Optim. and Applications, 5, 253-283.
    • (1996) Comput. Optim. and Applications , vol.5 , pp. 253-283
    • Malanowski, K.1    Maurer, H.2
  • 20
    • 0032360653 scopus 로고    scopus 로고
    • Sensitivity analysis for state constrained optimal control problems
    • MALANOWSKI, K. and MAURER, H. (1998) Sensitivity analysis for state constrained optimal control problems. Discrete and Continuous Dynamical Systems, 4, 241-272.
    • (1998) Discrete and Continuous Dynamical Systems , vol.4 , pp. 241-272
    • Malanowski, K.1    Maurer, H.2
  • 21
    • 0035634179 scopus 로고    scopus 로고
    • Sensitivity analysis for optimal control problems subject to higher order state constraints
    • MALANOWSKI, K. and MAURER, H. (2001) Sensitivity analysis for optimal control problems subject to higher order state constraints. Annals of Operations Research, 101, 43-74.
    • (2001) Annals of Operations Research , vol.101 , pp. 43-74
    • Malanowski, K.1    Maurer, H.2
  • 22
    • 0000570227 scopus 로고
    • First and second order sufficient optimality conditions in mathematical programming and optimal control
    • MAURER, H. (1981) First and second order sufficient optimality conditions in mathematical programming and optimal control. Mathematical Programming Study, 14, 163-177.
    • (1981) Mathematical Programming Study , vol.14 , pp. 163-177
    • Maurer, H.1
  • 23
    • 1542373167 scopus 로고    scopus 로고
    • Sensitivity analysis and real-time control of parametric optimal control problems using boundary value methods
    • M. Grötschel et al., eds, Springer Verlag, Berlin
    • MAURER, H. and AUGUSTIN, D. (2001b) Sensitivity analysis and real-time control of parametric optimal control problems using boundary value methods. M. Grötschel et al., eds. In: On-line Optimization of Large Scale Systems, 17-55, Springer Verlag, Berlin.
    • (2001) On-line Optimization of Large Scale Systems , pp. 17-55
    • Maurer, H.1    Augustin, D.2
  • 24
    • 0037252440 scopus 로고    scopus 로고
    • Second order sufficient conditions for optimal control problems with free final time: The Riccati approach
    • MAURER, H. and OBERLE, H. J. (2002) Second order sufficient conditions for optimal control problems with free final time: the Riccati approach. SIAM J. on Control and Optimization, 41, 380-403.
    • (2002) SIAM J. on Control and Optimization , vol.41 , pp. 380-403
    • Maurer, H.1    Oberle, H.J.2
  • 25
    • 1542727011 scopus 로고    scopus 로고
    • Second order sufficient conditions for time optimal bang-bang control problems
    • Submitted to
    • MAURER, H. and OSMOLOVSKII, N.P. (2001) Second order sufficient conditions for time optimal bang-bang control problems. Submitted to SIAM J. Control and Optimization.
    • (2001) SIAM J. Control and Optimization
    • Maurer, H.1    Osmolovskii, N.P.2
  • 26
    • 21844518109 scopus 로고
    • Second order sufficient conditions for optimal control problems with mixed control-state constraints
    • MAURER, H. and PICKENHAIN, S. (1995) Second order sufficient conditions for optimal control problems with mixed control-state constraints. J. Optim. Theory and Applications, 86, 649-667.
    • (1995) J. Optim. Theory and Applications , vol.86 , pp. 649-667
    • Maurer, H.1    Pickenhain, S.2
  • 29
    • 0003981931 scopus 로고
    • BNDSCO - A program for the numerical solution of optimal control problems
    • Institute for Flight Systems Dynamics, DLR, Oberpfaffenhofen, Germany
    • OBERLE, H.J. and GRIMM, W. (1989) BNDSCO - A program for the numerical solution of optimal control problems. Institute for Flight Systems Dynamics, DLR, Oberpfaffenhofen, Germany, Internal Report No. 515-89/22.
    • (1989) Internal Report No. 515-89/22
    • Oberle, H.J.1    Grimm, W.2
  • 30
    • 1542412412 scopus 로고    scopus 로고
    • private communication
    • OBERLE, H.J. and PESCH, H.J. (2000) private communication.
    • (2000)
    • Oberle, H.J.1    Pesch, H.J.2
  • 31
    • 0012225452 scopus 로고
    • High-order necessary and sufficient conditions for Pontryagin and bounded-strong minima in the optimal control problems
    • OSMOLOVSKII, N.P. (1988a) High-order necessary and sufficient conditions for Pontryagin and bounded-strong minima in the optimal control problems. Dokl. Akad. Nauk SSSR, Ser. Cybernetics and Control Theory 303, 1052-1056, English transl., Sov. Phys. Dokl., 33, No. 12 (1988), 883-885.
    • (1988) Dokl. Akad. Nauk SSSR, Ser. Cybernetics and Control Theory , vol.303 , pp. 1052-1056
    • Osmolovskii, N.P.1
  • 32
    • 0007546253 scopus 로고
    • OSMOLOVSKII, N.P. (1988a) High-order necessary and sufficient conditions for Pontryagin and bounded-strong minima in the optimal control problems. Dokl. Akad. Nauk SSSR, Ser. Cybernetics and Control Theory 303, 1052-105, English transl., Sov. Phys. Dokl., 33, No. 12 (1988), 883-885.
    • (1988) Sov. Phys. Dokl. , vol.33 , Issue.12 , pp. 883-885
  • 34
    • 0001641024 scopus 로고
    • Quadratic conditions for nonsingular extremals in optimal control (A theoretical treatment)
    • OSMOLOVSKII, N.P. (1995) Quadratic conditions for nonsingular extremals in optimal control (A theoretical treatment). Russian J. of Mathematical Physics, 2, 487-516.
    • (1995) Russian J. of Mathematical Physics , vol.2 , pp. 487-516
    • Osmolovskii, N.P.1
  • 35
    • 31544444005 scopus 로고    scopus 로고
    • Quadratic optimality conditions for broken extremals in the general problem of calculus of variations
    • Submitted to
    • OSMOLOVSKII, N.P. (2003) Quadratic optimality conditions for broken extremals in the general problem of calculus of variations. Submitted to Journal of Math. Science.
    • (2003) Journal of Math. Science
    • Osmolovskii, N.P.1
  • 36
    • 0012227039 scopus 로고    scopus 로고
    • Jacobi-type conditions and Riccati equation for broken extremal
    • OSMOLOVSKII, N.P. and LEMPIO, F. (2000) Jacobi-type conditions and Riccati equation for broken extremal. Journal of Math. Science, 100, No.5, 2572-2592.
    • (2000) Journal of Math. Science , vol.100 , Issue.5 , pp. 2572-2592
    • Osmolovskii, N.P.1    Lempio, F.2
  • 39
    • 0030826051 scopus 로고    scopus 로고
    • First and second-order sufficient optimality conditions for bang-bang controls
    • SARYCHEV, A. (1997) First and second-order sufficient optimality conditions for bang-bang controls. SIAM J. Control and Optimization, 35, 315-340.
    • (1997) SIAM J. Control and Optimization , vol.35 , pp. 315-340
    • Sarychev, A.1
  • 41
    • 0018515818 scopus 로고
    • A bang-bang theorem with bounds on the number of switchings
    • SUSSMANN, H. J. (1979) A bang-bang theorem with bounds on the number of switchings. SIAM J. Control and Optimization, 17, 629-651.
    • (1979) SIAM J. Control and Optimization , vol.17 , pp. 629-651
    • Sussmann, H.J.1
  • 42
    • 0023305961 scopus 로고
    • The structure of time-optimal trajectories for single-input systems in the the plane: The C∞ nonsingular case
    • SUSSMANN, H.J. (1987a) The structure of time-optimal trajectories for single-input systems in the the plane: the C∞ nonsingular case. SIAM J. Control and Optimization, 25, 433-465.
    • (1987) SIAM J. Control and Optimization , vol.25 , pp. 433-465
    • Sussmann, H.J.1
  • 43
    • 0023383491 scopus 로고
    • The structure of time-optimal trajectories for single-input systems in the the plane: The general real analytic case
    • SUSSMANN, H.J. (1987b) The structure of time-optimal trajectories for single-input systems in the the plane: the general real analytic case. SIAM J. Control and Optimization, 25, 868-904.
    • (1987) SIAM J. Control and Optimization , vol.25 , pp. 868-904
    • Sussmann, H.J.1
  • 44
    • 0028501238 scopus 로고
    • The Riccati equation for optimal control problems with mixed state-control constraints: Necessity and sufficiency
    • ZEIDAN, V. (1994) The Riccati equation for optimal control problems with mixed state-control constraints: necessity and sufficiency. SIAM J. Control and Optimization, 32, 1297-1321.
    • (1994) SIAM J. Control and Optimization , vol.32 , pp. 1297-1321
    • Zeidan, V.1


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