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Volumn 5, Issue 4, 2005, Pages 387-409

Automatic Computation of Conservation Laws in the Calculus of Variations and Optimal Control

Author keywords

calculus of variations; computer algebra; conservation laws; Noether's theorem; optimal control; symmetries

Indexed keywords


EID: 84967657635     PISSN: 16094840     EISSN: 16099389     Source Type: Journal    
DOI: 10.2478/cmam-2005-0018     Document Type: Article
Times cited : (17)

References (27)
  • 1
    • 27844587226 scopus 로고    scopus 로고
    • Experimental Mathematics: Examples, Methods and Implications
    • D. H. Bailey and J. M. Borwein, Experimental Mathematics: Examples, Methods and Implications, Notices of the American Math. Society, 52 (2005), no. 5, pp. 502-514.
    • (2005) Notices of the American Math. Society , vol.52 , Issue.5 , pp. 502-514
    • Bailey, D.H.1    Borwein, J.M.2
  • 2
    • 1542366075 scopus 로고    scopus 로고
    • The Calculus of Variations
    • Springer-Verlag New York
    • B. van Brunt, The Calculus of Variations, Springer-Verlag New York, 2004.
    • (2004)
    • van Brunt, B.1
  • 3
    • 0043254844 scopus 로고
    • Noether's theorem for optimum control systems
    • D. S. Djukic, Noether's theorem for optimum control systems, Internat. J. Control, 1 (1973), no. 18, pp. 667-672.
    • (1973) Internat. J. Control , vol.1 , Issue.18 , pp. 667-672
    • Djukic, D.S.1
  • 6
    • 85025302100 scopus 로고    scopus 로고
    • Computagao Algébrica no Cïculo das Variagoes: Determinagao de Simetrïas e Leis de Conservagao
    • (in Portuguese), Dep. Mathematics Univ. of Aveiro, September
    • P. D. F. Gouveia and D. F. M. Torres, Computagao Algébrica no Cïculo das Variagoes: Determinagao de Simetrïas e Leis de Conservagao (in Portuguese), Research report CM04/I-23, Dep. Mathematics, Univ. of Aveiro, September 2004.
    • (2004) Research report CM04/I-23
    • Gouveia, P.D.F.1    Torres, D.F.M.2
  • 7
    • 0022028321 scopus 로고
    • The structure of nonlinear control systems possessing symmetries
    • J. W. Grizzle and S. I. Marcus, The structure of nonlinear control systems possessing symmetries, IEEE Trans. Automat. Control, 30 (1985), no. 3, pp. 248-258.
    • (1985) IEEE Trans. Automat. Control , vol.30 , Issue.3 , pp. 248-258
    • Grizzle, J.W.1    Marcus, S.I.2
  • 9
    • 0003992240 scopus 로고
    • Invariant Variational Principles
    • Academic Press [Harcourt Brace Jovanovićh Publishers]
    • J. D. Logan, Invariant Variational Principles, Academic Press [Harcourt Brace Jovanovićh Publishers], 1977.
    • (1977)
    • Logan, J.D.1
  • 10
    • 0003591813 scopus 로고
    • Applied Mathematics - A Contemporary Approach
    • John Wiley & Sons, New York
    • J. D. Logan, Applied Mathematics - A Contemporary Approach, John Wiley & Sons, New York, 1987.
    • (1987)
    • Logan, J.D.1
  • 12
    • 12144290974 scopus 로고    scopus 로고
    • Reduction in optimal control theory
    • E. Martinez, Reduction in optimal control theory, Rep. Math. Phys. 53 (2004), no. 1, pp. 79-90.
    • (2004) Rep. Math. Phys. , vol.53 , Issue.1 , pp. 79-90
    • Martinez, E.1
  • 13
    • 0001504634 scopus 로고
    • Invariante Variationsprobleme
    • E. Noether, Invariante Variationsprobleme, Gott. Nachr. (1918), pp. 235-257.
    • (1918) Gott. Nachr. , pp. 235-257
    • Noether, E.1
  • 14
    • 0003686926 scopus 로고
    • Applications of Lie Groups to Differential Equations
    • Springer-Verlag
    • P. J. Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag, 1986.
    • (1986)
    • Olver, P.J.1
  • 15
    • 17844407184 scopus 로고    scopus 로고
    • Control System Professional Suite, Product Review
    • B. Paiancz, Z. Benyo, and L. Kovacs, Control System Professional Suite, Product Review, IEEE Control Systems Magazine 25 (2005), no. 4, pp. 67-75.
    • (2005) IEEE Control Systems Magazine , vol.25 , Issue.4 , pp. 67-75
    • Paiancz, B.1    Benyo, Z.2    Kovacs, L.3
  • 16
    • 0003716450 scopus 로고
    • The mathematical theory of optimal processes
    • Interscience Publishers John Wiley & Sons, Inc. New York-London
    • L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The mathematical theory of optimal processes, Interscience Publishers John Wiley & Sons, Inc. New York-London, 1962.
    • (1962)
    • Pontryagin, L.S.1    Boltyanskii, V.G.2    Gamkrelidze, R.V.3    Mishchenko, E.F.4
  • 17
    • 0042223601 scopus 로고    scopus 로고
    • Advanced Mathematical Methods with Maple
    • Cambridge University Press
    • D. Richards, Advanced Mathematical Methods with Maple, Cambridge University Press, 2002.
    • (2002)
    • Richards, D.1
  • 18
    • 0742271504 scopus 로고    scopus 로고
    • Symmetries of flat rank two distributions and sub-Riemannian structures
    • Yu. L. Sachkov, Symmetries of flat rank two distributions and sub-Riemannian structures, Trans. Amer. Math. Soc. 356 (2004), no. 2, pp. 457-494.
    • (2004) Trans. Amer. Math. Soc. , vol.356 , Issue.2 , pp. 457-494
    • Yu., L.1    Sachkov2
  • 19
    • 0001003724 scopus 로고
    • Generalizations of Noether 's theorem in classical mechanics
    • W. Sarlet and F. Cantrijn, Generalizations of Noether 's theorem in classical mechanics, SIAM Rev., 23 (1981), no. 4, pp. 467-494.
    • (1981) SIAM Rev. , vol.23 , Issue.4 , pp. 467-494
    • Sarlet, W.1    Cantrijn, F.2
  • 20
    • 79960089196 scopus 로고    scopus 로고
    • Counterexamples in optimal control theory
    • Inverse and Ill-posed Problems Series, VSP, Utrecht
    • S. Ya. Serovaiskii, Counterexamples in optimal control theory, Inverse and Ill-posed Problems Series, VSP, Utrecht, 2004.
    • (2004)
    • Ya, S.1    Serovaiskii2
  • 21
    • 0030673669 scopus 로고    scopus 로고
    • Integrable geodesic flows of nonholonomic metrics
    • I. A. Taimanov, Integrable geodesic flows of nonholonomic metrics, J. Dynam. Control Systems, 3 (1997), no. 1, pp. 129-147.
    • (1997) J. Dynam. Control Systems , vol.3 , Issue.1 , pp. 129-147
    • Taimanov, I.A.1
  • 22
    • 0038340532 scopus 로고    scopus 로고
    • On the Noether Theorem for Optimal Control
    • D. F. M. Torres, On the Noether Theorem for Optimal Control, European Journal of Control, 8 (2002), no. 1, pp. 56-63.
    • (2002) European Journal of Control , vol.8 , Issue.1 , pp. 56-63
    • Torres, D.F.M.1
  • 23
    • 3042594853 scopus 로고    scopus 로고
    • A Remarkable Properly of the Dynamic Optimization Extremals
    • D. F. M. Torres, A Remarkable Properly of the Dynamic Optimization Extremals, Investigacao Opera-cional, 22 (2002), no. 2, pp. 253-263.
    • (2002) Investigacao Opera-cional , vol.22 , Issue.2 , pp. 253-263
    • Torres, D.F.M.1
  • 24
    • 23044528665 scopus 로고    scopus 로고
    • Conservation Laws in Optimal Control
    • F. Colonius, L. Grüne, eds., Lecture Notes in Control and Information Sciences Springer-Verlag, Berlin, Heidelberg
    • D. F. M. Torres, Conservation Laws in Optimal Control, Dynamics, Bifurcations and Control, F. Colonius, L. Grüne, eds., Lecture Notes in Control and Information Sciences 273 (2002), Springer-Verlag, Berlin, Heidelberg, pp. 287-296.
    • (2002) Dynamics, Bifurcations and Control , vol.273 , pp. 287-296
    • Torres, D.F.M.1
  • 25
    • 24944485940 scopus 로고    scopus 로고
    • Proper Extensions of Noether's Symmetry Theorem for Nonsmooth Extremals of the Calculus of Variations
    • D. F. M. Torres, Proper Extensions of Noether's Symmetry Theorem for Nonsmooth Extremals of the Calculus of Variations, Communications on Pure and Applied Analysis, 3 (2004), no. 3, pp. 491-500.
    • (2004) Communications on Pure and Applied Analysis , vol.3 , Issue.3 , pp. 491-500
    • Torres, D.F.M.1
  • 26
    • 33746721022 scopus 로고    scopus 로고
    • Quasi-Invariant Optimal Control Problems
    • D. F. M. Torres, Quasi-Invariant Optimal Control Problems, Portugals Mathematica (N. S.), 61 (2004), no. 1, pp. 97-114.
    • (2004) Portugals Mathematica (N. S.) , vol.61 , Issue.1 , pp. 97-114
    • Torres, D.F.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.