Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem

Abstract

The study of fractional variational problems with derivatives in the sense of Caputo is a recent subject, the main results being Agrawal's necessary optimality conditions of Euler-Lagrange and respective transversality conditions. Using Agrawal's Euler-Lagrange equation and the Lagrange multiplier technique, we obtain here a Noether-like theorem for fractional optimal control problems in the sense of Caputo.

16 pages

References in corpus (2)

• A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations
• Necessary Optimality Conditions for Fractional Action-Like Integrals of Variational Calculus with Riemann-Liouville Derivatives of Order $(\alpha ,\beta )$

Cited by in corpus (7)

• Fractional Noether's theorem in the Riesz-Caputo sense
• A formulation of the fractional Noether-type theorem for multidimensional Lagrangians
• Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics
• Fractional Noether's Theorem with Classical and Riemann-Liouville Derivatives
• Optimal control of diffusion equation with fractional time derivative with nonlocal and nonsingular Mittag-Leffler kernel
• A class of fractional optimal control problems and fractional Pontryagin's systems. Existence of a fractional Noether's theorem
• Variational integrator for fractional Pontryagin's systems. Existence of a discrete fractional Noether's theorem