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Higher-order variational problems on lie groups and optimal control applications

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  • In this paper, we describe a geometric setting for higher-order La- grangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we deduce an intrinsic framework for this type of dynamical systems. Interesting applications as, for instance, a geometric derivation of the higher-order Euler-Poincaré equations, optimal control of underactuated control systems whose configuration space is a Lie group are shown, among others, along the paper.
    Mathematics Subject Classification: Primary: 70H50, 70H45, 79J15; Secondary: 70G65, 70Hxx.


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