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Zbl 1170.49017
Frederico, Gastão S.F.; Torres, Delfim F.M.
Fractional conservation laws in optimal control theory. (English)
[J] Nonlinear Dyn. 53, No. 3, 215-222 (2008). ISSN 0924-090X; ISSN 1573-269X/e

Summary: 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.

MSC 2000:: *49K10 Free problems in several independent variables (nec./ suff.)
26A33 Fractional derivatives and integrals (real functions)

Keywords: fractional derivatives; optimal control; Noether's theorem; conservation laws; symmetry

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