Title: A variational-geometric approach for the optimal control of nonholonomic systems,
Abstract: Necessary conditions for existence of normal extremals in optimal control of
systems subject to nonholonomic constraints are derived as solutions of a
constrained second order variational problems. In this work, a geometric
interpretation of the derivation is studied from the theory of Lie algebroids.
We employ such a framework to describe the problem into a unifying formalism
for normal extremals in optimal control of nonholonomic systems and including
situations that have not been considered before in the literature from this
perspective. We show that necessary conditions for existence of extremals in
the optimal control problem can be also determined by a Hamiltonian system on
the cotangent bundle of a skew-symmetric algebroid.