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The aim of this work is to study, from an intrinsic and geometric point ofview, second-order constrained variational problems on Lie algebroids, that is,optimization problems defined by a cost functional which depends onhigher-order derivatives of admissible curves on a Lie algebroid. Extending theclassical Skinner and Rusk formalism for the mechanics in the context of Liealgebroids, for second-order constrained mechanical systems, we derive thecorresponding dynamical equations. We find a symplectic Lie subalgebroid where,under some mild regularity conditions, the second-order constrained variationalproblem, seen as a presymplectic Hamiltonian system, has a unique solution. Westudy the relationship of this formalism with the second-order constrainedEuler-Poincar\'e and Lagrange-Poincar\'e equations, among others. Our study isapplied to the optimal control of mechanical systems.

Second-order constrained variational problems on Lie algebroids: applications to optimal control