Automatic Computation of Conservation Laws in the Calculus of Variations and Optimal Control

Abstract

We present analytic computational tools that permit us to identify, in an automatic way, conservation laws in optimal control. The central result we use is the famous Noether's theorem, a classical theory developed by Emmy Noether in 1918, in the context of the calculus of variations and mathematical physics, and which was extended recently to the more general context of optimal control. We show how a Computer Algebra System can be very helpful in finding the symmetries and corresponding conservation laws in optimal control theory, thus making useful in practice the theoretical results recently obtained in the literature. A Maple implementation is provided and several illustrative examples given.

Partially presented at the 10th International Conference "Mathematical Modelling and Analysis", and "2nd International Conference "Computational Methods in Applied Mathematics", June 1 - 5, 2005, Trakai, Lithuania. A Maple worksheet is available at http://www.mat.ua.pt/delfim/maple.htm

Cited by in corpus (11)

• A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations
• Fractional conservation laws in optimal control theory
• Fractional Noether's theorem in the Riesz-Caputo sense
• The Hahn Quantum Variational Calculus
• The Second Euler-Lagrange Equation of Variational Calculus on Time Scales
• Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay
• Leitmann's direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales
• Contrasting Two Transformation-Based Methods for Obtaining Absolute Extrema
• Conservation laws for invariant functionals containing compositions
• Computing ODE Symmetries as Abnormal Variational Symmetries
• A Non-Newtonian Noether's Symmetry Theorem