Solutions of any optimal control problem are described by trajectories of a Hamiltonian system. The system is intrinsically associated to the problem by a procedure that is a geometric elaboration of the Lagrange multipliers rule. The intimate relation of the optimal control and Hamiltonian dynamics is fruitful for both domains; among other things, it leads to a clarification and a far going generalization of important classical results about Riemannian geodesic flows.
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Agrachev, A. (2008). Hamiltonian systems and optimal control. In: Craig, W. (eds) Hamiltonian Dynamical Systems and Applications. NATO Science for Peace and Security Series. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6964-2_8
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DOI: https://doi.org/10.1007/978-1-4020-6964-2_8
Publisher Name: Springer, Dordrecht
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Online ISBN: 978-1-4020-6964-2
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