Title Optimal control problems on the co-adjoint Lie groupoids Type of Research Article Keywords Optimal control problem, Invariant control system, Hamiltonian system, Co-adjoint Lie groupoid. Abstract In this work we study the invariant optimal control problem on Lie groupoids. We show that any invariant optimal control problem on a Lie groupoid reduces to its co-adjoint Lie algebroid. In the final section of the paper, we present an illustrative example. Researchers Ghorbanali Haghighatdoost Bonab (First Researcher)