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Optimal control of underactuated mechanical systems with symmetries

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  • The aim of this paper is to study optimal control problems for underactuated mechanical systems with symmetries using higher-order Lagrangian mechanics. We variationally derive the corresponding Lagrange -Poincaré equations for second-order Lagrangians with constraints defined on trivial principal bundles and apply them to study an optimal control problem for an underactuated vehicle.
    Mathematics Subject Classification: Primary: 70Q05, 70G75, 70G65; Secondary: 70H50, 70H03.


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