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Volumn 16, Issue 2-3, 2003, Pages 158-174

Lipschitzian regularity of the minimizing trajectories for nonlinear optimal control problems

Author keywords

Boundedness of minimizers; Lipschitzian regularity; Nonlinear dynamics; Optimal control; Pontryagin maximum principle

Indexed keywords

BOUNDARY CONDITIONS; INTEGRAL EQUATIONS; MAXIMUM PRINCIPLE; NONLINEAR CONTROL SYSTEMS; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION;

EID: 0142216445     PISSN: 09324194     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00498-003-0132-x     Document Type: Article
Times cited : (19)

References (35)
  • 2
    • 0000467856 scopus 로고
    • Lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands
    • Ambrosio L, Ascenzi O, Buttazzo G (1989) Lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands. J. Math. Anal. Appl., 142(2):301-316
    • (1989) J. Math. Anal. Appl. , vol.142 , Issue.2 , pp. 301-316
    • Ambrosio, L.1    Ascenzi, O.2    Buttazzo, G.3
  • 3
    • 0001135181 scopus 로고
    • One-dimensional variational problems whose minimizers do not satisfy the Euler Lagrange equation
    • Ball JM, Mizel VJ (1985) One-dimensional variational problems whose minimizers do not satisfy the Euler Lagrange equation. Arch. Rational Mech. Anal., 90(4):325-388
    • (1985) Arch. Rational Mech. Anal. , vol.90 , Issue.4 , pp. 325-388
    • Ball, J.M.1    Mizel, V.J.2
  • 6
    • 0030283903 scopus 로고    scopus 로고
    • On the Lavrentiev phenomenon for optimal control problems with second-order dynamics
    • Cheng C-W, Mizel VJ (1996) On the Lavrentiev phenomenon for optimal control problems with second-order dynamics. SIAM J. Control Optim., 34(6):2172-2179
    • (1996) SIAM J. Control Optim. , vol.34 , Issue.6 , pp. 2172-2179
    • Cheng, C.-W.1    Mizel, V.J.2
  • 7
    • 0017016966 scopus 로고
    • The maximum principle under minimal hypotheses
    • Clarke FH (1976) The maximum principle under minimal hypotheses. SIAM J. Control Optim., 14(6):1078-1091
    • (1976) SIAM J. Control Optim. , vol.14 , Issue.6 , pp. 1078-1091
    • Clarke, F.H.1
  • 10
    • 0006484428 scopus 로고
    • An indirect method in the calculus of variations
    • Clarke FH (1993) An indirect method in the calculus of variations. Trans. Amer. Math. Soc., 336(2):655-673
    • (1993) Trans. Amer. Math. Soc. , vol.336 , Issue.2 , pp. 655-673
    • Clarke, F.H.1
  • 11
    • 0042420100 scopus 로고    scopus 로고
    • The calculus of variations, nonsmooth analysis and optimal control
    • Birkhäuser, Basel
    • Clarke FH (2000) The calculus of variations, nonsmooth analysis and optimal control. In Development of Mathematics 1950-2000, Birkhäuser, Basel, pp. 313-328
    • (2000) Development of Mathematics 1950-2000 , pp. 313-328
    • Clarke, F.H.1
  • 12
    • 0021504076 scopus 로고
    • On the conditions under which the Euler equation or the maximum principle hold
    • Clarke FH, Vinter RB (1984) On the conditions under which the Euler equation or the maximum principle hold. Appl. Math. Optim., 12(1):73-79
    • (1984) Appl. Math. Optim. , vol.12 , Issue.1 , pp. 73-79
    • Clarke, F.H.1    Vinter, R.B.2
  • 13
    • 84966256938 scopus 로고
    • Regularity properties of solutions to the basic problem in the calculus of variations
    • FH Clarke, Vinter RB (1985) Regularity properties of solutions to the basic problem in the calculus of variations. Trans. Amer. Math. Soc., 289(1):73-98
    • (1985) Trans. Amer. Math. Soc. , vol.289 , Issue.1 , pp. 73-98
    • Clarke, F.H.1    Vinter, R.B.2
  • 14
    • 0025460640 scopus 로고
    • Regularity properties of optimal controls
    • Clarke FH, Vinter RB (1990) Regularity properties of optimal controls. SIAM J. Control Optim., 28(4):980-997
    • (1990) SIAM J. Control Optim. , vol.28 , Issue.4 , pp. 980-997
    • Clarke, F.H.1    Vinter, R.B.2
  • 15
    • 84966237528 scopus 로고
    • A regularity theory for variational problems with higher order derivatives
    • Clarke FH, Vinter RB (1990) A regularity theory for variational problems with higher order derivatives. Trans. Amer. Math. Soc., 320(1):227-251
    • (1990) Trans. Amer. Math. Soc. , vol.320 , Issue.1 , pp. 227-251
    • Clarke, F.H.1    Vinter, R.B.2
  • 16
    • 0000408658 scopus 로고
    • The extremum problem in the presence of constraints
    • Dubovitskii AY, Milyutin AA (1963) The extremum problem in the presence of constraints. Dokl. Akad. Nauk SSSR, 149(4):759-762
    • (1963) Dokl. Akad. Nauk SSSR , vol.149 , Issue.4 , pp. 759-762
    • Dubovitskii, A.Y.1    Milyutin, A.A.2
  • 18
    • 0002764036 scopus 로고
    • On certain questions in the theory of optimal control
    • Filippov AF (1962) On certain questions in the theory of optimal control. J. SIAM Control Ser. A, 1:76-84
    • (1962) J. SIAM Control Ser. A , vol.1 , pp. 76-84
    • Filippov, A.F.1
  • 22
    • 0041745050 scopus 로고
    • Sur quelques problèmes du calcul des variations
    • Lavrentiev M (1927) Sur quelques problèmes du calcul des variations. Ann. Mat. Pura Appl., 4:7-28
    • (1927) Ann. Mat. Pura Appl. , vol.4 , pp. 7-28
    • Lavrentiev, M.1
  • 23
    • 0037683304 scopus 로고
    • Sopra un esempio di lavrentieff
    • Manià B (1934) Sopra un esempio di lavrentieff. Boll. Un. Mat. Ital., 13:147-153
    • (1934) Boll. Un. Mat. Ital. , vol.13 , pp. 147-153
    • Manià, B.1
  • 25
    • 0142137907 scopus 로고    scopus 로고
    • New developments concerning the Lavrentiev phenomenon
    • Chapman & Hall/CRC Press, Boca Raton, FL
    • Mizel VJ (2000) New developments concerning the Lavrentiev phenomenon. In Calculus of Variations and Differential Equations (Haifa, 1998), Chapman & Hall/CRC Press, Boca Raton, FL, pages 185-191
    • (2000) Calculus of Variations and Differential Equations (Haifa, 1998) , pp. 185-191
    • Mizel, V.J.1
  • 26
    • 0012593244 scopus 로고    scopus 로고
    • Existence theorems in nonconvex optimal control
    • Chapman & Hall/CRC Press, Boca Raton, FL
    • Mordukhovich BS (2000) Existence theorems in nonconvex optimal control. In Calculus of Variations and Optimal Control (Haifa, 1998), Chapman & Hall/CRC Press, Boca Raton, FL, pp. 173-197
    • (2000) Calculus of Variations and Optimal Control (Haifa, 1998) , pp. 173-197
    • Mordukhovich, B.S.1
  • 28
    • 0034149003 scopus 로고    scopus 로고
    • Lipschitzian regularity of minimizers for optimal control problems with control-affine dynamics
    • Sarychev AV, Torres DFM (2000) Lipschitzian regularity of minimizers for optimal control problems with control-affine dynamics. Appl. Math. Optim., 41(2):237-254
    • (2000) Appl. Math. Optim. , vol.41 , Issue.2 , pp. 237-254
    • Sarychev, A.V.1    Torres, D.F.M.2
  • 30
    • 0001605149 scopus 로고    scopus 로고
    • New theories of set-valued differentials and new versions of the maximum principle of optimal control theory
    • Springer-Verlag, London
    • Sussmann HJ (2001) New theories of set-valued differentials and new versions of the maximum principle of optimal control theory. In Nonlinear Control in the Year 2000 (Paris), Vol. 2, Springer-Verlag, London, pp. 487-526
    • (2001) Nonlinear Control in the Year 2000 (Paris) , vol.2 , pp. 487-526
    • Sussmann, H.J.1
  • 31
    • 54249096254 scopus 로고
    • Sur une méthode directe du calcul des variations
    • Tonelli L (1915) Sur une méthode directe du calcul des variations. Rend. Circ. Mat. Palermo, 39:233-264
    • (1915) Rend. Circ. Mat. Palermo , vol.39 , pp. 233-264
    • Tonelli, L.1
  • 32
    • 0038340532 scopus 로고    scopus 로고
    • On the Noether theorem for optimal control
    • Torres DFM (2002) On the Noether theorem for optimal control. European J. Control, 8(1):56-63
    • (2002) European J. Control , vol.8 , Issue.1 , pp. 56-63
    • Torres, D.F.M.1
  • 33
    • 25344468585 scopus 로고    scopus 로고
    • Regularity of minimizers in the calculus of variations and optimal control
    • Ph.D. thesis, Department of Mathematics, University of Aveiro, November
    • Torres DFM (2002) Regularity of Minimizers in the Calculus of Variations and Optimal Control. Ph.D. thesis, Department of Mathematics, University of Aveiro, November
    • (2002)
    • Torres, D.F.M.1
  • 35
    • 0004284115 scopus 로고    scopus 로고
    • Birkhäuser Boston, Boston, MA
    • Vinter R (2000) Optimal Control. Birkhäuser Boston, Boston, MA
    • (2000) Optimal Control
    • Vinter, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.