메뉴 건너뛰기




Volumn 41, Issue 6, 2003, Pages 1843-1867

On stability of bang-bang type controls

Author keywords

Control stability; Ocontrol; Optimality conditions; Solution structure stability; Strong local minimality

Indexed keywords

DATA REDUCTION; HAMILTONIANS; LINEAR SYSTEMS; OPTIMAL CONTROL SYSTEMS; PERTURBATION TECHNIQUES; SWITCHING FUNCTIONS; SYSTEM STABILITY;

EID: 0347590910     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012901399271     Document Type: Article
Times cited : (71)

References (36)
  • 1
    • 0002975781 scopus 로고
    • Symplectic geometry for optimal control
    • H. J. Sussmann, ed., Marcel Dekker, New York
    • A. A. AGRACHEV AND R. V. GAMKRELIDZE, Symplectic geometry for optimal control, in Nonlinear Controllability and Optimal Control, H. J. Sussmann, ed., Marcel Dekker, New York, 1990, pp. 727-785.
    • (1990) Nonlinear Controllability and Optimal Control , pp. 727-785
    • Agrachev, A.A.1    Gamkrelidze, R.V.2
  • 5
    • 0002154878 scopus 로고
    • Sufficiency and the Jacobi condition in the calculus of variation
    • F. H. CLARKE AND V. ZEIDAN, Sufficiency and the Jacobi condition in the calculus of variation, Canad. J. Math., 38 (1986), pp. 1199-1209.
    • (1986) Canad. J. Math. , vol.38 , pp. 1199-1209
    • Clarke, F.H.1    Zeidan, V.2
  • 6
    • 0035605971 scopus 로고    scopus 로고
    • The Euler approximation in state constrained optimal control
    • A. L. DONTCHEV AND W. W. HAGER, The Euler approximation in state constrained optimal control, Math. Comp., 70 (2001), pp. 173-203.
    • (2001) Math. Comp. , vol.70 , pp. 173-203
    • Dontchev, A.L.1    Hager, W.W.2
  • 7
    • 0007902573 scopus 로고    scopus 로고
    • A characterization of Lipschitzian stability in optimal control
    • Haifa, Chapman and Hall/CRC Press, Boca Raton, FL
    • A. L. DONTCHEV AND K. MALANOWSKI, A characterization of Lipschitzian stability in optimal control, in Calculus of Variations and Optimal Control, Haifa, 1998, Chapman and Hall/CRC Press, Boca Raton, FL, 2001, pp. 62-76.
    • (1998) Calculus of Variations and Optimal Control , pp. 62-76
    • Dontchev, A.L.1    Malanowski, K.2
  • 9
    • 0035613917 scopus 로고    scopus 로고
    • On smoothness properties and approximability of optimal control functions
    • D. Ward, D. Klatte, and J. Rückmann, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands
    • U. FELGENHAUER, On smoothness properties and approximability of optimal control functions, in Optimization with Data Perturbation II, Ann. Oper. Res. 101, D. Ward, D. Klatte, and J. Rückmann, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001, pp. 23-42.
    • (2001) Optimization with Data Perturbation II, Ann. Oper. Res. , vol.101 , pp. 23-42
    • Felgenhauer, U.1
  • 10
    • 0347242311 scopus 로고    scopus 로고
    • Stability and local growth near bounded-strong local optimal controls
    • Trier, Kluwer Academic Publishers, Dordrecht, The Netherlands, to appear
    • U. FELGENHAUER, Stability and local growth near bounded-strong local optimal controls, in System Modelling and Optimization XX, Proceedings of the 20th IFIP TC7 Conference, Trier 2001, Kluwer Academic Publishers, Dordrecht, The Netherlands, to appear.
    • (2001) System Modelling and Optimization XX, Proceedings of the 20th IFIP TC7 Conference
    • Felgenhauer, U.1
  • 11
    • 0035425120 scopus 로고    scopus 로고
    • Structural properties and approximation of optimal controls
    • U. FELGENHAUER, Structural properties and approximation of optimal controls, Nonlinear Anal., 47 (2001), pp. 1869-1880.
    • (2001) Nonlinear Anal. , vol.47 , pp. 1869-1880
    • Felgenhauer, U.1
  • 12
    • 0035536767 scopus 로고    scopus 로고
    • Weak and strong optimality conditions for constrained control problems with discontinuous control
    • U. FELGENHAUER, Weak and strong optimality conditions for constrained control problems with discontinuous control, J. Optim. Theory Appl., 110 (2001), pp. 361-387.
    • (2001) J. Optim. Theory Appl. , vol.110 , pp. 361-387
    • Felgenhauer, U.1
  • 13
    • 0007297218 scopus 로고
    • On a general conception of duality in optimal control
    • Springer-Verlag, New York
    • R. KLÖTZLER, On a general conception of duality in optimal control, in Lecture Notes in Math. 703, Springer-Verlag, New York, 1979, pp. 189-196.
    • (1979) Lecture Notes in Math. , vol.703 , pp. 189-196
    • Klötzler, R.1
  • 14
    • 0002883583 scopus 로고
    • Pontryagin's maximum principle for multidimensional control problems
    • Birkhauser, Basel
    • R. KLÖTZLER AND S. PICKENHAIN, Pontryagin's maximum principle for multidimensional control problems, in Internat. Ser. Numer. Math. 111, Birkhauser, Basel, 1993, pp. 21-30.
    • (1993) Internat. Ser. Numer. Math. , vol.111 , pp. 21-30
    • Klötzler, R.1    Pickenhain, S.2
  • 16
    • 0000146438 scopus 로고
    • Two-norm approach in stability and sensitivity analysis of optimization and optimal control problems
    • K. MALANOWSKI, Two-norm approach in stability and sensitivity analysis of optimization and optimal control problems, Adv. Math. Sci. Appl., 2 (1993), pp. 397-443.
    • (1993) Adv. Math. Sci. Appl. , vol.2 , pp. 397-443
    • Malanowski, K.1
  • 18
    • 0001620726 scopus 로고
    • Stability and sensitivity analysis of solutions to nonlinear optimal control problems
    • K. MALANOWSKI, Stability and sensitivity analysis of solutions to nonlinear optimal control problems, Appl. Math. Optim., 32 (1995), pp. 111-141.
    • (1995) Appl. Math. Optim. , vol.32 , pp. 111-141
    • Malanowski, K.1
  • 21
    • 0030145422 scopus 로고    scopus 로고
    • Sensitivity analysis for parametric optimal control problems with control-state constraints
    • K. MALANOWSKI AND H. MAURER, Sensitivity analysis for parametric optimal control problems with control-state constraints, Comput. Optim. Appl., 5 (1996), pp. 253-283.
    • (1996) Comput. Optim. Appl. , vol.5 , pp. 253-283
    • Malanowski, K.1    Maurer, H.2
  • 22
    • 0035634179 scopus 로고    scopus 로고
    • Sensitivity analysis for optimal control problems subject to higher order state constraints
    • D. Ward, D. Klatte, and J. Rückmann, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands
    • K. MALANOWSKI AND H. MAURER, Sensitivity analysis for optimal control problems subject to higher order state constraints, in Optimization with Data Perturbation II, Ann. Oper. Res 101, D. Ward, D. Klatte, and J. Rückmann, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001, pp. 43-73.
    • (2001) Optimization with Data Perturbation II, Ann. Oper. Res , vol.101 , pp. 43-73
    • Malanowski, K.1    Maurer, H.2
  • 23
    • 0032360653 scopus 로고    scopus 로고
    • Sensitivity analysis for state constrained optimal control problems
    • K. MALANOWSKI AND H. MAURER, Sensitivity analysis for state constrained optimal control problems, Discrete Contin. Dynam. Systems, 4 (1998), pp. 241-272.
    • (1998) Discrete Contin. Dynam. Systems , vol.4 , pp. 241-272
    • Malanowski, K.1    Maurer, H.2
  • 24
    • 0012775730 scopus 로고
    • Second order sufficient conditions for control problems with free final time
    • A. Isidori et al., eds.
    • H. MAURER, Second order sufficient conditions for control problems with free final time, in Proceedings of the 3rd European Control Conference, Rome, 1995, A. Isidori et al., eds., 1995, pp. 3602-3606.
    • (1995) Proceedings of the 3rd European Control Conference, Rome, 1995 , pp. 3602-3606
    • Maurer, H.1
  • 25
    • 0037252440 scopus 로고    scopus 로고
    • Second order sufficient conditions for optimal control problems with free final time: The Riccati approach
    • H. MAURER AND H. J. OBERLE, Second order sufficient conditions for optimal control problems with free final time: The Riccati approach, SIAM J. Control Optim., 41 (2002), pp. 380-403.
    • (2002) SIAM J. Control Optim. , vol.41 , pp. 380-403
    • Maurer, H.1    Oberle, H.J.2
  • 26
    • 21844518109 scopus 로고
    • Second order sufficient conditions for optimal control problems with mixed control-state constraints
    • H. MAURER AND S. PICKENHAIN, Second order sufficient conditions for optimal control problems with mixed control-state constraints, J. Optim. Theory Appl., 86 (1995), pp. 649-667.
    • (1995) J. Optim. Theory Appl. , vol.86 , pp. 649-667
    • Maurer, H.1    Pickenhain, S.2
  • 27
    • 0003558940 scopus 로고    scopus 로고
    • Calculus of Variations and Optimal Control
    • Providence, Ri
    • A. A. MILYUTIN AND N. P. OSMOLOVSKII, Calculus of Variations and Optimal Control, Amer. Math. Soc., Providence, RI, 1998.
    • (1998) Amer. Math. Soc.
    • Milyutin, A.A.1    Osmolovskii, N.P.2
  • 28
    • 0036575268 scopus 로고    scopus 로고
    • Sufficient conditions for relative minima of broken extremals in optimal control theory
    • J. NOBLE AND H. SCHAETTLER, Sufficient conditions for relative minima of broken extremals in optimal control theory, J. Math. Anal. Appl., 269 (2002), pp. 98-128.
    • (2002) J. Math. Anal. Appl. , vol.269 , pp. 98-128
    • Noble, J.1    Schaettler, H.2
  • 29
    • 0001641024 scopus 로고
    • Quadratic conditions for nonsingular extremals in optimal control (a theoretical treatment)
    • N. P. OSMOLOVSKII, Quadratic conditions for nonsingular extremals in optimal control (a theoretical treatment), Russian J. Math. Phys., 2 (1995), pp. 487-512.
    • (1995) Russian J. Math. Phys. , vol.2 , pp. 487-512
    • Osmolovskii, N.P.1
  • 30
    • 0031327651 scopus 로고    scopus 로고
    • Quadratic conditions for nonsingular extremals in optimal control (examples)
    • N. P. OSMOLOVSKII, Quadratic conditions for nonsingular extremals in optimal control (examples), Russian J. Math. Phys., 5 (1998), pp. 373-388.
    • (1998) Russian J. Math. Phys. , vol.5 , pp. 373-388
    • Osmolovskii, N.P.1
  • 31
    • 0002356718 scopus 로고    scopus 로고
    • Second-order conditions for broken extremals
    • Chapman and Hall/crc Press, Boca Raton, Fl
    • N. P. OSMOLOVSKII, Second-order conditions for broken extremals, in Calculus of Variations and Optimal Control, Haifa, 1998, Chapman and Hall/CRC Press, Boca Raton, FL, 2001, pp. 198-216.
    • (1998) Calculus of Variations and Optimal Control, Haifa, 1998 , pp. 198-216
    • Osmolovskii, N.P.1
  • 32
    • 0000925716 scopus 로고
    • Sufficiency conditions for weak local minima in multidimensional optimal control problems with mixed control-state restrictions
    • S. PICKENHAIN, Sufficiency conditions for weak local minima in multidimensional optimal control problems with mixed control-state restrictions, Z. Anal. Anwendungen, 11 (1992), pp. 559-568.
    • (1992) Z. Anal. Anwendungen , vol.11 , pp. 559-568
    • Pickenhain, S.1
  • 33
    • 0347242284 scopus 로고    scopus 로고
    • Duality in optimal control with first order differential equations
    • C. A. Floudas and P. M. Pardalos, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands
    • S. PICKENHAIN, Duality in optimal control with first order differential equations, in Encyclopedia of Optimization, Vol. I, C. A. Floudas and P. M. Pardalos, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001, pp. 472-477.
    • (2001) Encyclopedia of Optimization , vol.1 , pp. 472-477
    • Pickenhain, S.1
  • 34
    • 0000847161 scopus 로고
    • Sufficient conditions for local optimality in multidimensional control problems with state restrictions
    • S. PICKENHAIN AND K. TAMMER, Sufficient conditions for local optimality in multidimensional control problems with state restrictions, Z. Anal. Anwendungen, 10 (1991), pp. 397-405.
    • (1991) Z. Anal. Anwendungen , vol.10 , pp. 397-405
    • Pickenhain, S.1    Tammer, K.2
  • 35
    • 0030826051 scopus 로고    scopus 로고
    • First- and second-order sufficient optimlaity conditions for bang-bang controls
    • A. V. SARYCHEV, First- and second-order sufficient optimlaity conditions for bang-bang controls, SIAM J. Control Optim., 35 (1997), pp. 315-340.
    • (1997) SIAM J. Control Optim. , vol.35 , pp. 315-340
    • Sarychev, A.V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.