Optimal trajectories in Abelian-symmetric control problems converge exponentially to trim primitives away from boundary layers via reduction to a hyperbolic static Hamiltonian system.
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A homogeneous Hamiltonian system on a Lie-Poisson manifold has a nontrivial conformal relative equilibrium if and only if its Lie algebra contains a hyperbolic element, with existence in so(2,1)* dynamics but obstruction for the free rigid body on so(3)*.
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Non static exponential turnpike property for optimal control problems with symmetries and boundary conditions
Optimal trajectories in Abelian-symmetric control problems converge exponentially to trim primitives away from boundary layers via reduction to a hyperbolic static Hamiltonian system.
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Scaling Symmetries and Conformal Relative Equilibria on Poisson Manifolds, with Applications to Lie--Poisson Systems
A homogeneous Hamiltonian system on a Lie-Poisson manifold has a nontrivial conformal relative equilibrium if and only if its Lie algebra contains a hyperbolic element, with existence in so(2,1)* dynamics but obstruction for the free rigid body on so(3)*.