메뉴 건너뛰기




Volumn 59, Issue 11, 2010, Pages 720-733

Asymptotic approach on conjugate points for minimal time bangbang controls

Author keywords

Bangbang control; Conjugate time; Minimal time problem; Optimal control

Indexed keywords

ARBITRARY VECTORS; BANG-BANG; BANG-BANG CONTROL; CONJUGATE POINTS; CONJUGATE TIME; CONTROL-AFFINE SYSTEMS; CONVERGENCE PROPERTIES; EFFICIENT IMPLEMENTATION; EXTREMAL; INITIAL PROBLEM; LOCAL OPTIMALITY; MINIMAL TIME PROBLEM; OPTIMAL CONTROL PROBLEM; OPTIMAL CONTROLS; PRACTICAL ISSUES; SCALAR CONTROL; STANDARD THEORIES; TIME CONDITION; TIME CONTROL;

EID: 78650180202     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2010.08.008     Document Type: Article
Times cited : (7)

References (45)
  • 1
    • 0003287433 scopus 로고
    • Optimization Theory and Applications. Problems with Ordinary Differential Equations
    • Springer-Verlag New York
    • L. Cesari Optimization Theory and Applications. Problems with Ordinary Differential Equations Applications of Mathematics vol. 17 1983 Springer-Verlag New York
    • (1983) Applications of Mathematics , vol.17
    • Cesari, L.1
  • 3
    • 0021817336 scopus 로고
    • A high order test for optimality of bangbang controls
    • A. Bressan A high order test for optimality of bangbang controls SIAM J. Control Optim. 23 1985 38 48
    • (1985) SIAM J. Control Optim. , vol.23 , pp. 38-48
    • Bressan, A.1
  • 5
    • 3943090734 scopus 로고
    • The index of second variation of a control system
    • A.V. Sarychev The index of second variation of a control system Mat. Sb. 113 1980 464 486 English transl. in Math. USSR Sbornik 41 (1982) 383401
    • (1980) Mat. Sb. , vol.113 , pp. 464-486
    • Sarychev, A.V.1
  • 6
    • 0005335685 scopus 로고
    • Envelopes, conjugate points and optimal bangbang extremals
    • H.J. Sussmann Envelopes, conjugate points and optimal bangbang extremals M. Fliess, M. Hazewinkel, Proc. 1985 Paris Conf. on Nonlinear Systems 1987 Reidel Publishers Dordrecht, the Netherlands
    • (1987) Proc. 1985 Paris Conf. on Nonlinear Systems
    • Sussmann, H.J.1
  • 7
    • 0024478824 scopus 로고
    • The structure of small-time reachable sets in low dimensions
    • A.J. Krener, and H. Schttler The structure of small-time reachable sets in low dimensions SIAM J. Control Optim. 27 1 1989 120 147
    • (1989) SIAM J. Control Optim. , vol.27 , Issue.1 , pp. 120-147
    • Krener, A.J.1    Schttler, H.2
  • 8
    • 0000401789 scopus 로고
    • Sufficient conditions for optimality and the justification of the dynamic programming method
    • V.G. Boltyanskii Sufficient conditions for optimality and the justification of the dynamic programming method SIAM J. Control 4 1966 326 361
    • (1966) SIAM J. Control , vol.4 , pp. 326-361
    • Boltyanskii, V.G.1
  • 9
    • 0029378576 scopus 로고
    • Second-order optimality conditions in sets of L∞ functions with range in a polyhedron
    • J.C. Dunn Second-order optimality conditions in sets of L∞ functions with range in a polyhedron SIAM J. Control Optim. 33 1995 1603 1635
    • (1995) SIAM J. Control Optim. , vol.33 , pp. 1603-1635
    • Dunn, J.C.1
  • 10
    • 0030145422 scopus 로고    scopus 로고
    • Sensitivity analysis for parametric control problems with control-state constraints
    • K. Malanowski, and H. Maurer Sensitivity analysis for parametric control problems with control-state constraints Comput. Optim. Appl. 5 1996 253 283
    • (1996) Comput. Optim. Appl. , vol.5 , pp. 253-283
    • Malanowski, K.1    Maurer, H.2
  • 11
    • 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. Program. Study 14 1981 163 177
    • (1981) Math. Program. Study , vol.14 , pp. 163-177
    • Maurer, H.1
  • 12
    • 1542373167 scopus 로고    scopus 로고
    • Sensitivity analysis and real-time control of parametric optimal control problems using boundary value methods
    • H. Maurer, and D. Augustin Sensitivity analysis and real-time control of parametric optimal control problems using boundary value methods M. Grtschel, On-line Optimization of Large Scale Systems 2001 Springer-Verlag Berlin 17 55
    • (2001) On-line Optimization of Large Scale Systems , pp. 17-55
    • Maurer, H.1    Augustin, D.2
  • 13
    • 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 380 403
    • (2002) SIAM J. Control Optim. , vol.41 , pp. 380-403
    • Maurer, H.1    Oberle, H.J.2
  • 14
    • 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 649 667
    • (1995) J. Optim. Theory Appl. , vol.86 , pp. 649-667
    • Maurer, H.1    Pickenhain, S.2
  • 15
    • 0040105952 scopus 로고    scopus 로고
    • Calculus of Variations and Optimal Control
    • AMS Providence, RI
    • A.A. Milyutin, and N.P. Osmolovskii Calculus of Variations and Optimal Control Transl. Math. Monogr. vol. 180 1998 AMS Providence, RI
    • (1998) Transl. Math. Monogr. , vol.180
    • Milyutin, A.A.1    Osmolovskii, N.P.2
  • 16
    • 0028501238 scopus 로고
    • The Riccati equation for optimal control problems with mixed state-control constraints: Necessity and sufficiency
    • V. Zeidan The Riccati equation for optimal control problems with mixed state-control constraints: Necessity and sufficiency SIAM J. Control Optim. 32 1994 1297 1321
    • (1994) SIAM J. Control Optim. , vol.32 , pp. 1297-1321
    • Zeidan, V.1
  • 17
    • 0041786633 scopus 로고    scopus 로고
    • Computational Sensitivity Analysis for State Constrained Optimal Control Problems
    • DOI 10.1023/A:1010960221295
    • D. Augustin, and H. Maurer Computational sensitivity analysis for state constrained optimal control problems Ann. Oper. Res. 101 2001 75 99 (Pubitemid 33634363)
    • (2001) Annals of Operations Research , vol.101 , Issue.1-4 , pp. 75-99
    • Augustin, D.1    Maurer, H.2
  • 18
    • 0035634179 scopus 로고    scopus 로고
    • Sensitivity Analysis for Optimal Control Problems Subject to Higher Order State Constraints
    • DOI 10.1023/A:1010956104457
    • 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 43 73 (Pubitemid 33634362)
    • (2001) Annals of Operations Research , vol.101 , Issue.1-4 , pp. 43-73
    • Malanowski, K.1    Maurer, H.2
  • 19
    • 0141568839 scopus 로고    scopus 로고
    • Transformation of quadratic forms to perfect squares for broken extremal
    • N.P. Osmolovskii, and F. Lempio Transformation of quadratic forms to perfect squares for broken extremal Set-Valued Anal. 10 2002 209 232
    • (2002) Set-Valued Anal. , vol.10 , pp. 209-232
    • Osmolovskii, N.P.1    Lempio, F.2
  • 20
    • 0030826051 scopus 로고    scopus 로고
    • First- and second-order sufficient optimality conditions for bangbang controls
    • A.V. Sarychev First- and second-order sufficient optimality conditions for bangbang controls SIAM J. Control Optim. 35 1997 315 440
    • (1997) SIAM J. Control Optim. , vol.35 , pp. 315-440
    • Sarychev, A.V.1
  • 21
    • 4644331767 scopus 로고    scopus 로고
    • Second order sufficient conditions for time-optimal bangbang control problems
    • H. Maurer, and N.P. Osmolovskii Second order sufficient conditions for time-optimal bangbang control problems SIAM J. Control Optim. 42 2004 2239 2263
    • (2004) SIAM J. Control Optim. , vol.42 , pp. 2239-2263
    • Maurer, H.1    Osmolovskii, N.P.2
  • 22
    • 21244449627 scopus 로고    scopus 로고
    • Optimization methods for the verification of second order sufficient conditions for bangbang controls
    • H. Maurer, C. Bskens, J.-H.R. Kim, and C.Y. Kaya Optimization methods for the verification of second order sufficient conditions for bangbang controls Optim. Control Appl. Meth. 26 2005 129 156
    • (2005) Optim. Control Appl. Meth. , vol.26 , pp. 129-156
    • Maurer, H.1    Bskens, C.2    Kim, J.-H.R.3    Kaya, C.Y.4
  • 23
    • 0041926724 scopus 로고    scopus 로고
    • Strong optimality for a bangbang trajectory
    • A. Agrachev, G. Stefani, and P. Zezza Strong optimality for a bangbang trajectory SIAM J. Control Optim. 41 4 2002 991 1014
    • (2002) SIAM J. Control Optim. , vol.41 , Issue.4 , pp. 991-1014
    • Agrachev, A.1    Stefani, G.2    Zezza, P.3
  • 24
    • 21244437982 scopus 로고    scopus 로고
    • Equivalence of second order optimality conditions for bangbang control problems. Part 1: Main results
    • N.P. Osmolovskii, and H. Maurer Equivalence of second order optimality conditions for bangbang control problems. Part 1: main results Control Cybernet. 34 3 2005 927 949
    • (2005) Control Cybernet. , vol.34 , Issue.3 , pp. 927-949
    • Osmolovskii, N.P.1    Maurer, H.2
  • 25
    • 33846092985 scopus 로고    scopus 로고
    • Equivalence of second order optimality conditions for bang-bang control problems. Part 2: Proofs, variational derivatives and representations
    • N.P. Osmolovskii, H. Maurer, Equivalence of second order optimality conditions for bangbang control problems. Part 2: Proofs, variational derivatives and representations, Control Cybernet., 36 555584.
    • Control Cybernet. , vol.36 , pp. 555-584
    • Osmolovskii, N.P.1    Maurer, H.2
  • 26
    • 4644330525 scopus 로고    scopus 로고
    • State-local optimality of a bangbang trajectory: A Hamiltonian apprach
    • L. Poggiolini, and G. Stefani State-local optimality of a bangbang trajectory: a Hamiltonian apprach Syst. Control Lett. 53 2004 269 279
    • (2004) Syst. Control Lett. , vol.53 , pp. 269-279
    • Poggiolini, L.1    Stefani, G.2
  • 27
    • 1942509708 scopus 로고    scopus 로고
    • On the local structure of optimal trajectories in R3
    • A. Agrachev, and M. Sigalotti On the local structure of optimal trajectories in R 3 SIAM J. Control Optim. 42 2003 513 531
    • (2003) SIAM J. Control Optim. , vol.42 , pp. 513-531
    • Agrachev, A.1    Sigalotti, M.2
  • 28
    • 0036575268 scopus 로고    scopus 로고
    • Sufficient conditions for relative minima of broken extremals in optimal control theory
    • J. Noble, and H. Schttler Sufficient conditions for relative minima of broken extremals in optimal control theory J. Math. Anal. Appl. 269 2002 98 128
    • (2002) J. Math. Anal. Appl. , vol.269 , pp. 98-128
    • Noble, J.1    Schttler, H.2
  • 29
    • 1542517195 scopus 로고    scopus 로고
    • Optimal bangbang controls for a two-compartment model in cancer chemotherapy
    • U. Ledzewicz, and H. Schttler Optimal bangbang controls for a two-compartment model in cancer chemotherapy J. Optim. Theory Appl. 114 2002 609 637
    • (2002) J. Optim. Theory Appl. , vol.114 , pp. 609-637
    • Ledzewicz, U.1    Schttler, H.2
  • 30
    • 0034453280 scopus 로고    scopus 로고
    • Regular synthesis and sufficient conditions for optimality
    • H.J. Sussmann, and B. Piccoli Regular synthesis and sufficient conditions for optimality SIAM J. Control Optim. 39 2 2000 359 410
    • (2000) SIAM J. Control Optim. , vol.39 , Issue.2 , pp. 359-410
    • Sussmann, H.J.1    Piccoli, B.2
  • 32
    • 0003040740 scopus 로고    scopus 로고
    • A Hamitonian approach to strong minima in optimal control
    • American Mathematical Society
    • A. Agrachev, G. Stefani, and P. Zezza A Hamitonian approach to strong minima in optimal control Proceedings of Symposia in Pure Mathematics vol. 64 1998 American Mathematical Society 11 22
    • (1998) Proceedings of Symposia in Pure Mathematics , vol.64 , pp. 11-22
    • Agrachev, A.1    Stefani, G.2    Zezza, P.3
  • 33
    • 84972487915 scopus 로고
    • Application of the theory of quadratic forms in Hilbert spaces to the calculus of variations
    • M.R. Hestenes Application of the theory of quadratic forms in Hilbert spaces to the calculus of variations Pacific J. Math. 1 1951 525 582
    • (1951) Pacific J. Math. , vol.1 , pp. 525-582
    • Hestenes, M.R.1
  • 34
    • 1542312234 scopus 로고    scopus 로고
    • Second order optimality conditions for bangbang control problems
    • H. Maurer, and N.P. Osmolovskii Second order optimality conditions for bangbang control problems Control Cybernet. 32 3 2003 555 584
    • (2003) Control Cybernet. , vol.32 , Issue.3 , pp. 555-584
    • Maurer, H.1    Osmolovskii, N.P.2
  • 35
    • 34547510460 scopus 로고    scopus 로고
    • Second order optimality conditions in the smooth case and applications in optimal control
    • B. Bonnard, J.-B. Caillau, and E. Trlat Second order optimality conditions in the smooth case and applications in optimal control ESAIM Control Optim. Calc. Var. 13 2 2007 207 236
    • (2007) ESAIM Control Optim. Calc. Var. , vol.13 , Issue.2 , pp. 207-236
    • Bonnard, B.1    Caillau, J.-B.2    Trlat, E.3
  • 38
    • 19244367902 scopus 로고
    • The relationship between the maximum principle and dynamic programming
    • F.H. Clarke, and R. Vinter The relationship between the maximum principle and dynamic programming SIAM J. Control Optim. 25 5 1987 1291 1311
    • (1987) SIAM J. Control Optim. , vol.25 , Issue.5 , pp. 1291-1311
    • Clarke, F.H.1    Vinter, R.2
  • 40
    • 17444430784 scopus 로고    scopus 로고
    • Morse-Sard type results in sub-Riemannian geometry
    • L. Rifford, and E. Trlat Morse-Sard type results in sub-Riemannian geometry Math. Ann. 332 1 2005 145 159
    • (2005) Math. Ann. , vol.332 , Issue.1 , pp. 145-159
    • Rifford, L.1    Trlat, E.2
  • 41
    • 74249110334 scopus 로고    scopus 로고
    • On the stabilization problem for nonholonomic distributions
    • L. Rifford, and E. Trlat On the stabilization problem for nonholonomic distributions J. Eur. Math. Soc. 11 2 2009 223 255
    • (2009) J. Eur. Math. Soc. , vol.11 , Issue.2 , pp. 223-255
    • Rifford, L.1    Trlat, E.2
  • 42
    • 78149239813 scopus 로고
    • Regularity properties of the minimum-time map
    • Birkhuser Boston Boston, MA Nonlinear synthesis (Sopron, 1989)
    • G. Stefani Regularity properties of the minimum-time map Nonlinear synthesis (Sopron, 1989) Progr. Systems Control Theory vol. 9 1991 Birkhuser Boston Boston, MA 270 282
    • (1991) Progr. Systems Control Theory , vol.9 , pp. 270-282
    • Stefani, G.1
  • 43
    • 28444476416 scopus 로고    scopus 로고
    • Control theory from the geometric viewpoint
    • Springer-Verlag Berlin Control Theory and Optimization, II
    • A. Agrachev, and Y. Sachkov Control theory from the geometric viewpoint Control Theory and Optimization, II Encyclopaedia of Mathematical Sciences vol. 87 2004 Springer-Verlag Berlin
    • (2004) Encyclopaedia of Mathematical Sciences , vol.87
    • Agrachev, A.1    Sachkov, Y.2
  • 44
    • 0343090918 scopus 로고    scopus 로고
    • Parametrized families of extremals and singularities in solutions to the HamiltonJacobiBellman equation
    • M.D. Kiefer, and H. Schttler Parametrized families of extremals and singularities in solutions to the HamiltonJacobiBellman equation SIAM J. Control Optim. 37 1999 1346 1371
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 1346-1371
    • Kiefer, M.D.1    Schttler, H.2
  • 45
    • 0012780415 scopus 로고    scopus 로고
    • Second order sufficient conditions and sensitivity analysis for the controlled Rayleigh problem
    • H. Maurer, and D. Augustin Second order sufficient conditions and sensitivity analysis for the controlled Rayleigh problem J. Guddat, Parametric Optimization and Related Topics, IV 1997 Lang Frankfurt 245 259
    • (1997) Parametric Optimization and Related Topics, IV , pp. 245-259
    • Maurer, H.1    Augustin, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.