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We address the problem of symmetry reduction of optimal control problemsunder the action of a finite group from a measure relaxation viewpoint. Wepropose a method based on the moment-SOS aka Lasserre hierarchy which allowsone to significantly reduce the computation time and memory requirementscompared to the case without symmetry reduction. We show that the recovery ofoptimal trajectories boils down to solving a symmetric parametric polynomialsystem. Then we illustrate our method on the symmetric integrator and thetime-optimal inversion of qubits.

Symmetry reduction and recovery of trajectories of optimal control problems via measure relaxations