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Volumn 46, Issue 4, 2007, Pages 1398-1430

Well-posedness of the shooting algorithm for state constrained optimal control problems with a single constraint and control

Author keywords

Directional derivatives; Junction conditions; No gap second order optimality conditions; Optimal control; Pontryagin's principle; Sensitivity analysis; Shooting algorithm; State constraints; Strong regularity

Indexed keywords

BOOLEAN FUNCTIONS; INTERSECTIONS; THEOREM PROVING;

EID: 48249135751     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/06065756X     Document Type: Article
Times cited : (28)

References (29)
  • 1
    • 0040226652 scopus 로고
    • Comportement lipschitzien des solutions de problèmes de minimisation convexes
    • J. P. AUBIN, Comportement lipschitzien des solutions de problèmes de minimisation convexes, C. R. Acad. Sci. Paris Sér. I Math., 295 (1982), pp. 235-238.
    • (1982) C. R. Acad. Sci. Paris Sér. I Math , vol.295 , pp. 235-238
    • AUBIN, J.P.1
  • 2
    • 0041786633 scopus 로고    scopus 로고
    • Computational sensitivity analysis for state constrained optimal control problems
    • D. AUGUSTIN AND H. MAURER, Computational sensitivity analysis for state constrained optimal control problems, Ann. Oper. Res., 101 (2001), pp. 75-99.
    • (2001) Ann. Oper. Res , vol.101 , pp. 75-99
    • AUGUSTIN, D.1    MAURER, H.2
  • 3
    • 21844506576 scopus 로고
    • Abort landing in windshear: Optimal control problem with third-order state constraint and varied switching structure
    • P. BERKMANN AND H. J. PESCH, Abort landing in windshear: Optimal control problem with third-order state constraint and varied switching structure, J. Optim. Theory Appl., 85 (1995), pp. 21-57.
    • (1995) J. Optim. Theory Appl , vol.85 , pp. 21-57
    • BERKMANN, P.1    PESCH, H.J.2
  • 4
    • 48249111245 scopus 로고    scopus 로고
    • Second-Order Analysis for Optimal Control Problems with Pure and Mixed State Constraints
    • 6199, INRIA, Le Chesnay, France
    • J. F. BONNANS AND A. HERMANT, Second-Order Analysis for Optimal Control Problems with Pure and Mixed State Constraints, Research Report 6199, INRIA, Le Chesnay, France, 2007.
    • (2007) Research Report
    • BONNANS, J.F.1    HERMANT, A.2
  • 5
    • 48249152894 scopus 로고    scopus 로고
    • No-gap second-order optimality conditions for optimal control problems with a single state constraint and control
    • to appear
    • J. F. BONNANS AND A. HERMANT, No-gap second-order optimality conditions for optimal control problems with a single state constraint and control, Math. Program, Ser. B, to appear.
    • Math. Program, Ser. B
    • BONNANS, J.F.1    HERMANT, A.2
  • 6
    • 33750039952 scopus 로고    scopus 로고
    • Conditions d'optimalité du second-ordre nécessaires ou suffisantes pour les problèmes de commande optimale avec une contrainte sur l'état et une commande scalaires
    • Sér. I
    • J. F. BONNANS AND A. HERMANT, Conditions d'optimalité du second-ordre nécessaires ou suffisantes pour les problèmes de commande optimale avec une contrainte sur l'état et une commande scalaires, C. R. Math. Acad. Sci. Paris Sér. I, 343 (2006), pp. 473-478.
    • (2006) C. R. Math. Acad. Sci. Paris , vol.343 , pp. 473-478
    • BONNANS, J.F.1    HERMANT, A.2
  • 8
    • 85003393986 scopus 로고
    • Optimal programming problems with inequality constraints I: Necessary conditions for extremal solutions
    • A. E. BRYSON, W. F. DENHAM, AND S. E. DREYFUS, Optimal programming problems with inequality constraints I: Necessary conditions for extremal solutions, AIAA J., 1 (1963), pp. 2544-2550.
    • (1963) AIAA J , vol.1 , pp. 2544-2550
    • BRYSON, A.E.1    DENHAM, W.F.2    DREYFUS, S.E.3
  • 10
    • 0026185765 scopus 로고
    • Abort landing in the presence of windshear as a minimax optimal control problem. I. Necessary conditions
    • R. BULIRSCH, F. MONTRONE, AND H. J. PESCH, Abort landing in the presence of windshear as a minimax optimal control problem. I. Necessary conditions, J. Optim. Theory Appl., 70 (1991), pp. 1-23.
    • (1991) J. Optim. Theory Appl , vol.70 , pp. 1-23
    • BULIRSCH, R.1    MONTRONE, F.2    PESCH, H.J.3
  • 12
    • 0032026016 scopus 로고    scopus 로고
    • Lipschitzian stability for state constrained nonlinear optimal control
    • A. L. DONTCHEV AND W. W. HAGER, Lipschitzian stability for state constrained nonlinear optimal control, SIAM J. Control Optim., 36 (1998), pp. 698-718.
    • (1998) SIAM J. Control Optim , vol.36 , pp. 698-718
    • DONTCHEV, A.L.1    HAGER, W.W.2
  • 13
    • 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
  • 14
    • 0024082641 scopus 로고
    • A maximum principle for differential inclusion problems with state constraints
    • H. FRANKOWSKA AND B. KAS̀KOSZ, A maximum principle for differential inclusion problems with state constraints, Systems Control Lett., 11 (1988), pp. 189-194.
    • (1988) Systems Control Lett , vol.11 , pp. 189-194
    • FRANKOWSKA, H.1    KAS̀KOSZ, B.2
  • 15
    • 84972502575 scopus 로고
    • How to differentiate the projection on a convex set in Hubert space. Some applications to variational inequalities
    • A. HARAUX, How to differentiate the projection on a convex set in Hubert space. Some applications to variational inequalities, J. Math. Soc. Japan, 29 (1977), pp. 615-631.
    • (1977) J. Math. Soc. Japan , vol.29 , pp. 615-631
    • HARAUX, A.1
  • 16
    • 0029324375 scopus 로고
    • A survey of the maximum principles for optimal control problems with state constraints
    • R. F. HARTL, S. P. SETHI, AND R. G. VICKSON, A survey of the maximum principles for optimal control problems with state constraints, SIAM Rev., 37 (1995), pp. 181-218.
    • (1995) SIAM Rev , vol.37 , pp. 181-218
    • HARTL, R.F.1    SETHI, S.P.2    VICKSON, R.G.3
  • 17
    • 0004237334 scopus 로고
    • North-Holland Publishing Company, Amsterdam, Russian edition, Nauka, Moscow
    • A. D. IOFFE AND V. M. TIHOMIROV, Theory of Extrernal Problems, North-Holland Publishing Company, Amsterdam, 1979; Russian edition, Nauka, Moscow, 1974.
    • (1974) Theory of Extrernal Problems
    • IOFFE, A.D.1    TIHOMIROV, V.M.2
  • 18
    • 0000794342 scopus 로고
    • New necessary conditions of optimality for control problems with state-variable inequality constraints
    • D. H. JACOBSON. M. M. LELE, AND J. L. SPEYER, New necessary conditions of optimality for control problems with state-variable inequality constraints, J. Math. Anal. Appl., 35 (1971), pp. 255-284.
    • (1971) J. Math. Anal. Appl , vol.35 , pp. 255-284
    • JACOBSON, D.H.1    LELE, M.M.2    SPEYER, J.L.3
  • 19
    • 0024011499 scopus 로고
    • An envelope-like effect of infinitely many inequality constraints on second order necessary conditions for minimization problems
    • H. KAWASAKI, An envelope-like effect of infinitely many inequality constraints on second order necessary conditions for minimization problems, Math. Programming, 41 (1988), pp. 73-96.
    • (1988) Math. Programming , vol.41 , pp. 73-96
    • KAWASAKI, H.1
  • 20
    • 19644377940 scopus 로고
    • Second order necessary optimality conditions for minimizing a sup-type function
    • H. KAWASAKI, Second order necessary optimality conditions for minimizing a sup-type function, Math. Programming, 49 (1990/91), pp. 213-229.
    • (1990) Math. Programming , vol.49 , pp. 213-229
    • KAWASAKI, H.1
  • 21
    • 0001620726 scopus 로고
    • Stability and sensitivity of solutions to nonlinear optimal control problems
    • K. MALANOWSKI, Stability and sensitivity of solutions to nonlinear optimal control problems, J. Appl. Math. Optim., 32 (1995), pp. 111-141.
    • (1995) J. Appl. Math. Optim , vol.32 , pp. 111-141
    • MALANOWSKI, K.1
  • 22
    • 0030736426 scopus 로고    scopus 로고
    • Sufficient optimality conditions for optimal control subject to state constraints
    • K. MALANOWSKI, Sufficient optimality conditions for optimal control subject to state constraints, SIAM J. Control Optim., 35 (1997), pp. 205-227.
    • (1997) SIAM J. Control Optim , vol.35 , pp. 205-227
    • MALANOWSKI, K.1
  • 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
    • 0035634179 scopus 로고    scopus 로고
    • Sensitivity analysis for optimal control problems subject to higher order state constraints. Optimization with data perturbations
    • K. MALANOWSKI AND H. MAURER, Sensitivity analysis for optimal control problems subject to higher order state constraints. Optimization with data perturbations, II, Ann. Oper. Res., 101 (2001), pp. 43-73.
    • (2001) II, Ann. Oper. Res , vol.101 , pp. 43-73
    • MALANOWSKI, K.1    MAURER, H.2
  • 25
    • 48249093717 scopus 로고    scopus 로고
    • H. MAURER, On the Minimum Principle for Optimal Control Problems with State Constraints, Tech. report, Schriftenreihe des Rechenzentrum 41, Universität Münster, Münster, Germany, 1979.
    • H. MAURER, On the Minimum Principle for Optimal Control Problems with State Constraints, Tech. report, Schriftenreihe des Rechenzentrum 41, Universität Münster, Münster, Germany, 1979.
  • 26
    • 0003227259 scopus 로고
    • A practical guide to the solution of real-life optimal control problems
    • H. J. PESCH, A practical guide to the solution of real-life optimal control problems, Control Cybernet., 23 (1994), pp. 7-60.
    • (1994) Control Cybernet , vol.23 , pp. 7-60
    • PESCH, H.J.1
  • 27
    • 0019018216 scopus 로고
    • Junction phenomena for optimal control with state-variable inequality constraints of third order
    • H. M. ROBBINS, Junction phenomena for optimal control with state-variable inequality constraints of third order, J. Optim. Theory Appl., 31 (1980), pp. 85-99.
    • (1980) J. Optim. Theory Appl , vol.31 , pp. 85-99
    • ROBBINS, H.M.1
  • 28
    • 0018977011 scopus 로고
    • Strongly regular generalized equations
    • S. M. ROBINSON, Strongly regular generalized equations, Math. Oper. Res., 5 (1980), pp. 43-62.
    • (1980) Math. Oper. Res , vol.5 , pp. 43-62
    • ROBINSON, S.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.