Paulo D. F. Gouveia, Delfim F. M. Torres
Published 2005-09-07Version 1
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.
Comments: 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
Journal: Comput. Methods Appl. Math. Vol. 5 (2005), No. 4, 387-409
Optimal Control Theory on almost-Lie Algebroids
Markov-Dubins Path via Optimal Control Theory
Fractional conservation laws in optimal control theory
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