Absolute extrema of invariant optimal control problems

Communications in Applied Analysis

Volumn 10, Issue 4, 2006, Pages 503-516

  Silva, Cristiana Joao ^a   Torres, Delfim F M ^a  

^a UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33847238725     PISSN: 10832564     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. C. Carathéodory, Calculus of Variations and Partial Differential Equations, Chelsea Publishing Company, New York, 1982.
2. D.A. Carlson, An observation on two methods of obtaining solutions to variational problems, J. Optim. Theory Appl., 114 (2002), no. 2, 345-361.
3. D.A. Carlson and G. Leitmann, Coordinate transformation method for the extremization of multiple integrals, J. Optim. Theory Appl., 127 (2005), no. 3, 523-533.
4. P.D.F. Gouveia and D.F.M. Torres, Computação algébrica no cálculo das variações: determinação de simetrias e leis de conservação, TEMA Tend. Mat. Apl. Comput., 6 (2005), no. 1, 81-90.
5. P.D.F. Gouveia and D.F.M. Torres, Automatic computation of conservation laws in the calculus of variations and optimal control, Computational Methods in Applied Mathematics, 5 (2005), no. 4, 387-409.
6. P.D.F. Gouveia, D.F.M. Torres, and E.A.M. Rocha, Symbolic computation of variational symmetries in optimal control, Control and Cybernetics, To Appear.
7. G. Leitmann, A note on absolute extrema of certain integrals, International Journal of Nonlinear Mechanics, 2 (1967), 55-59.
8. G. Leitmann, The Calculus of Variations and Optimal Control - An Introduction, Plenum Press, New York, 1981.
9. G. Leitmann, On a class of direct optimization problems, J. Optim. Theory Appl., 108 (2001), no. 3, 467-481.
10. G. Leitmann, Some extensions to a direct optimization method, J. Optim. Theory Appl., 111 (2001), no. 1, 1-6.
11. J. W. Macki and A. Strauss, Introduction to Optimal Control Theory, Springer, New York, 1982.
12. E. Noether, Invariante variationsprobleme, Gött. Nachr. (1918), 235-257.
13. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, and ER Mishchenko, The Mathematical Theory of Optimal Processes, Interscience Publishers John Wiley and Sons, Inc,, New York-London, 1962.
14. D.F.M. Torres, On the Noether Theorem for optimal control, European Journal of Control, 8 (2002), no. 1, 56-63.
15. D.F.M. Torres, Carathéodory equivalence, Noether Theorems and Tonelli full-regularity in the calculus of variations and optimal control, Journal of Mathematical Sciences, 120 (2004), no. 1, 1032-1050.
16. D.F.M. Torres, Quasi-invariant optimal control problems, Port. Math., 61 (2004), no. 1, 97-114.