Advances in Nonlinear Control and Calculus of Variations

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Publications

Symbolic computation of variational symmetries in optimal control

Publication . Gouveia, Paulo D.F.; Torres, Delfim F.M.; Rocha, Eugénio A.M.

We use a computer algebra system to compute, in an efficient way, optimal control variational symmetries up to a gauge term. The symmetries are then used to obtain families of Noether’s first integrals, possibly in the presence of nonconservative external forces. As an application, we obtain eight independent first integrals for the sub-Riemannian nilpotent problem (2, 3, 5, 8).

2006Journal article

Open access

Automatic computation of conservation laws in the calculus of variations and optimal control

Publication . Gouveia, Paulo D.F.; Torres, Delfim F.M.

We present analytical 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, which was extended recently to the more general context of optimal control. We show how a Computer Algebra System can be very helpful in ¯nding 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 are given.

2005Journal article

Open access

Scientific computation of conservation laws in the calculus of variations and optimal control

Publication . Gouveia, Paulo D.F.; Torres, Delfim F.M.

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.

2005Report

Open access