Fractional conservation laws in optimal control theory |
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Authors: | Gastão S F Frederico Delfim F M Torres |
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Institution: | (1) Department of Science and Technology, University of Cape Verde, Praia, Santiago, Cape Verde;(2) Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal |
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Abstract: | Using the recent formulation of Noether’s theorem for the problems of the calculus of variations with fractional derivatives,
the Lagrange multiplier technique, and the fractional Euler–Lagrange equations, we prove a Noether-like theorem to the more
general context of the fractional optimal control. As a corollary, it follows that in the fractional case the autonomous Hamiltonian
does not define anymore a conservation law. Instead, it is proved that the fractional conservation law adds to the Hamiltonian
a new term which depends on the fractional-order of differentiation, the generalized momentum and the fractional derivative
of the state variable.
Partially presented at FDA ’06—2nd IFAC Workshop on Fractional Differentiation and its Applications, 19–21 July 2006, Porto, Portugal. |
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Keywords: | Fractional derivatives Optimal control Noether’ s theorem Conservation laws Symmetry |
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