On removing barriers between mechanics and optimal control: completely integrable systems

Contemporary optimal control finds itself on common grounds with differential geometry and mechanics and faces an elaborate mathematical theory generated by these classical subjects that it needs to absorb and interpret for its further development. This theory consists of a deep understanding of Hamiltonian systems rooted in the symplectic and Poisson geometric foundations. The present paper explains the relevance of this body of mathematics for problems of optimal control, and conversely also explains the new ideas that optimal control brings to the classical theory