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arXiv · 0711.0609

Fractional conservation laws in optimal control theory

Gastao S. F. Frederico·Delfim F. M. Torres
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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.

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Gastao S. F. Frederico, Delfim F. M. Torres. 2007-11-05. Fractional conservation laws in optimal control theory. https://doi.org/10.1007/s11071-007-9309-z

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