Optimal trajectories in Abelian-symmetric control problems converge exponentially to trim primitives away from boundary layers via reduction to a hyperbolic static Hamiltonian system.
Symmetry Reduction of Optimal Control Systems and Princi- pal Connections
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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.