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.

arXiv comment16 pages

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• Fractional Order Optimal Control Problems with Free Terminal Time
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• Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems
• Generalized fractional calculus with applications to the calculus of variations
• A formulation of the fractional Noether-type theorem for multidimensional Lagrangians
• Fractional variational problems depending on indefinite integrals
• Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics
• A Simple Accurate Method for Solving Fractional Variational and Optimal Control Problems
• Generalized Hamilton's Principle with Fractional Derivatives
• Fractional isoperimetric Noether's theorem in the Riemann-Liouville sense
• Generalized Transversality Conditions in Fractional Calculus of Variations
• Time-Fractional Optimal Control of Initial Value Problems on Time Scales
• A Generalized Fractional Calculus of Variations
• 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
• Fractional variational problems depending on indefinite integrals and with delay