Optimal control and implicit Hamiltonian systems

Optimal control problems naturally lead, via the Maximum Principle, to implicit Hamiltonian systems. It is shown that symmetries of an optimal control problem lead to symmetries of the corresponding implicit Hamiltonian system. Using the reduction theory described in [3,2] one can reduce the system to a lower dimensional implicit Hamiltonian system. It is shown that for symmetries coming from the optimal control problem, doing reduction and applying the Maximum Principle commutes.

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