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Volumn 101, Issue 1-4, 2001, Pages 43-73

Sensitivity Analysis for Optimal Control Problems Subject to Higher Order State Constraints

Author keywords

Differentiability of solutions; Higher order state constraints; Implicit function theorem; Parametric optimal control

Indexed keywords


EID: 0035634179     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1023/A:1010956104457     Document Type: Article
Times cited : (58)

References (36)
  • 1
    • 26444477534 scopus 로고    scopus 로고
    • Computational sensitivity analysis for state constrained optimal control problems
    • this volume
    • D. Augustin and H. Maurer, Computational sensitivity analysis for state constrained optimal control problems, Annals of Operations Research (2000), this volume.
    • (2000) Annals of Operations Research
    • Augustin, D.1    Maurer, H.2
  • 2
    • 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. of Optimization Theory and Applications 85 (1995) 21-57.
    • (1995) J. of Optimization Theory and Applications , vol.85 , pp. 21-57
    • Berkmann, P.1    Pesch, H.J.2
  • 3
    • 0043115384 scopus 로고
    • Zur numerischen Behandlung zustandsbeschränkter Steuerungsprobleme mit Mehrzielmethode und Homotopieverfahren
    • H.G. Bock, Zur numerischen Behandlung zustandsbeschränkter Steuerungsprobleme mit Mehrzielmethode und Homotopieverfahren, Zeitschrift Angewandte Mathematik Mechanik 57 (1977) T 266-T268.
    • (1977) Zeitschrift Angewandte Mathematik Mechanik , vol.57
    • Bock, H.G.1
  • 5
    • 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 Journal 1 (1963) 2544-2550.
    • (1963) AIAA Journal , vol.1 , pp. 2544-2550
    • Bryson, A.E.1    Denham, W.F.2    Dreyfus, S.E.3
  • 7
    • 0026185765 scopus 로고
    • Abort landing in the presence of a windshear as a minimax optimal control problem, Part 1: Necessary conditions
    • R. Bulirsch, F. Montrone and H.J. Pesch, Abort landing in the presence of a windshear as a minimax optimal control problem, Part 1: Necessary conditions, J. of Optimization Theory and Applications 70 (1991) 1-23.
    • (1991) J. of Optimization Theory and Applications , vol.70 , pp. 1-23
    • Bulirsch, R.1    Montrone, F.2    Pesch, H.J.3
  • 8
    • 0026204534 scopus 로고
    • Abort landing in the presence of a windshear as a minimax optimal control problem, Part 2: Multiple shooting and homotopy
    • R. Bulirsch, F. Montrone and H.J. Pesch, Abort landing in the presence of a windshear as a minimax optimal control problem, Part 2: Multiple shooting and homotopy, J. of Optimization Theory and Applications 70 (1991) 223-254.
    • (1991) J. of Optimization Theory and Applications , vol.70 , pp. 223-254
    • Bulirsch, R.1    Montrone, F.2    Pesch, H.J.3
  • 9
  • 12
    • 0030147955 scopus 로고    scopus 로고
    • Best interpolation in a strip II: Reduction to unconstrained convex optimization
    • A.L. Dontchev and I. Kolmanovsky, Best interpolation in a strip II: Reduction to unconstrained convex optimization, Computational Optimization and Applications 5 (1996) 233-251.
    • (1996) Computational Optimization and Applications , vol.5 , pp. 233-251
    • Dontchev, A.L.1    Kolmanovsky, I.2
  • 13
    • 0018468242 scopus 로고
    • Lipschitz continuity for constrained processes
    • W.W. Hager, Lipschitz continuity for constrained processes, SIAM J. Control and Optimization 17 (1979) 321-338.
    • (1979) SIAM J. Control and Optimization , vol.17 , pp. 321-338
    • Hager, W.W.1
  • 14
    • 0029324375 scopus 로고
    • A survey of the maximum principle for optimal control problems with state constraints
    • R.F. Hartl, S.P. Sethi and R.G. Vickson, A survey of the maximum principle for optimal control problems with state constraints, SIAM Review 37 (1995) 181-218.
    • (1995) SIAM Review , vol.37 , pp. 181-218
    • Hartl, R.F.1    Sethi, S.P.2    Vickson, R.G.3
  • 15
    • 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. of Mathematical Analysis and Applications 35 (1971) 255-284.
    • (1971) J. of Mathematical Analysis and Applications , vol.35 , pp. 255-284
    • Jacobson, D.H.1    Lele, M.M.2    Speyer, J.L.3
  • 16
    • 25444506507 scopus 로고
    • Ein Mehrzielverfahren zur numerischen Berechnung optimaler Feedback-steuerungen bei beschränkten nichtlinearen Steuerungsproblemen
    • Bonn, Germany
    • P. Krämer-Eis, Ein Mehrzielverfahren zur numerischen Berechnung optimaler Feedback-Steuerungen bei beschränkten nichtlinearen Steuerungsproblemen, Bonner Mathematische Schriften 164 (Bonn, Germany, 1985).
    • (1985) Bonner Mathematische Schriften , pp. 164
    • Krämer-Eis, P.1
  • 17
    • 17744409891 scopus 로고    scopus 로고
    • Application of the classical implicit function theorem in sensitivity analysis of parametric optimal control
    • K. Malanowski, Application of the classical implicit function theorem in sensitivity analysis of parametric optimal control, Control and Cybernetics 27 (1998) 335-352.
    • (1998) Control and Cybernetics , vol.27 , pp. 335-352
    • Malanowski, K.1
  • 18
    • 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, Computational Optimization and Applications 5 (1996) 253-283.
    • (1996) Computational Optimization and Applications , vol.5 , pp. 253-283
    • Malanowski, K.1    Maurer, H.2
  • 19
    • 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 and Continuous Dynamical Systems 4 (1998) 241-272.
    • (1998) Discrete and Continuous Dynamical Systems , vol.4 , pp. 241-272
    • Malanowski, K.1    Maurer, H.2
  • 20
    • 0001706435 scopus 로고
    • On optimal control problems with bounded state variables and control appearing linearly
    • H. Maurer, On optimal control problems with bounded state variables and control appearing linearly, SIAM J. Control and Optimization 15 (1977) 345-362.
    • (1977) SIAM J. Control and Optimization , vol.15 , pp. 345-362
    • Maurer, H.1
  • 22
    • 0000570227 scopus 로고
    • First- and second-order sufficient optimality conditions in mathematical programming and optimal control
    • H. Maurer, First- and second-order sufficient optimality conditions in mathematical programming and optimal control, Math. Programming Study 14 (1981) 43-62.
    • (1981) Math. Programming Study , vol.14 , pp. 43-62
    • Maurer, H.1
  • 23
    • 0016598968 scopus 로고
    • Application of multiple shooting to the numerical solution of optimal control problems with bounded state variables
    • H. Maurer and W. Gillessen, Application of multiple shooting to the numerical solution of optimal control problems with bounded state variables, Computing 15 (1975) 105-126.
    • (1975) Computing , vol.15 , pp. 105-126
    • Maurer, H.1    Gillessen, W.2
  • 24
    • 84873007444 scopus 로고
    • Optimale Steuerprozesse mit Zustandsbeschränkungen
    • Optimization and Optimal Control, Springer, Berlin
    • H. Maurer and U. Heidemann, Optimale Steuerprozesse mit Zustandsbeschränkungen, in: Optimization and Optimal Control, Proceedings Conf. Oberwolfach, Lecture Notes in Mathematics, Vol. 477 (Springer, Berlin, 1975) pp. 244-260.
    • (1975) Proceedings Conf. Oberwolfach, Lecture Notes in Mathematics , vol.477 , pp. 244-260
    • Maurer, H.1    Heidemann, U.2
  • 25
    • 0025755022 scopus 로고
    • The nonlinear beam via optimal control with bounded state variables
    • H. Maurer and H. D. Mittelmann, The nonlinear beam via optimal control with bounded state variables, Optimal Control Applications & Methods 12 (1991) 19-31.
    • (1991) Optimal Control Applications & Methods , vol.12 , pp. 19-31
    • Maurer, H.1    Mittelmann, H.D.2
  • 26
    • 0022766307 scopus 로고
    • Numerical solution of minimax optimal control problems by multiple shooting technique
    • H.J. Oberle, Numerical solution of minimax optimal control problems by multiple shooting technique, J. of Optimization Theory and Applications 50 (1986) 331-357.
    • (1986) J. of Optimization Theory and Applications , vol.50 , pp. 331-357
    • Oberle, H.J.1
  • 27
    • 0023834093 scopus 로고
    • Numerical treatment of minimax optimal control problems with application to the reentry flight path problem
    • H.J. Oberle, Numerical treatment of minimax optimal control problems with application to the reentry flight path problem, J. of the Astron. Sciences 36 (1988) 159-178.
    • (1988) J. of the Astron. Sciences , vol.36 , pp. 159-178
    • Oberle, H.J.1
  • 29
    • 0032335632 scopus 로고    scopus 로고
    • Non-negative splines, in particular of degree five
    • H.J. Oberle and G. Opfer, Non-negative splines, in particular of degree five, Numerische Mathematik 79 (1998) 427-450.
    • (1998) Numerische Mathematik , vol.79 , pp. 427-450
    • Oberle, H.J.1    Opfer, G.2
  • 30
    • 0003200501 scopus 로고
    • The derivation of cubic splines with obstacles by methods of optimization and optimal control
    • G. Opfer and H.J. Oberle, The derivation of cubic splines with obstacles by methods of optimization and optimal control, Numerische Mathematik 52 (1988) 17-31.
    • (1988) Numerische Mathematik , vol.52 , pp. 17-31
    • Opfer, G.1    Oberle, H.J.2
  • 32
    • 0024646179 scopus 로고
    • Real-time computation of feedback controls for constrained optimal control problems, Part 1: Neighbouring extremals
    • H.J. Pesch, Real-time computation of feedback controls for constrained optimal control problems, Part 1: Neighbouring extremals, Optimal Control Applications & Methods 10 (1989) 129-145.
    • (1989) Optimal Control Applications & Methods , vol.10 , pp. 129-145
    • Pesch, H.J.1
  • 33
    • 0024648170 scopus 로고
    • Real-time computation of feedback controls for constrained optimal control problems, Part 2: A correction method based on multiple shooting
    • H.J. Pesch, Real-time computation of feedback controls for constrained optimal control problems, Part 2: A correction method based on multiple shooting, Optimal Control Applications & Methods 10 (1989) 147-171.
    • (1989) Optimal Control Applications & Methods , vol.10 , pp. 147-171
    • Pesch, H.J.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, Zeitschrift für Analysis and ihre Anwendungen 10 (1991) 397-405.
    • (1991) Zeitschrift für Analysis and Ihre Anwendungen , vol.10 , pp. 397-405
    • Pickenhain, S.1    Tammer, K.2
  • 35
    • 0019018216 scopus 로고
    • Junction phenomena for optimal control with state-variable inequality constraints of third order
    • H. Robbins, Junction phenomena for optimal control with state-variable inequality constraints of third order, J. of Optimization Theory and Applications 31 (1980) 85-99.
    • (1980) J. of Optimization Theory and Applications , vol.31 , pp. 85-99
    • Robbins, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.