Abstract

Abstract We develop a geometric interpretation for solutions to the Bolza problem in optimal control for systems subject to hybrid dynamics. In particular, the idea of a hybrid Lagrangian submanifold is introduced. These submanifolds are invariant under the hybrid Hamiltonian flow arising from the extended maximum principle for hybrid systems. Solutions to the hybrid optimal control problem are characterized from backward propagating these submanifolds under the hybrid Hamiltonian flow. This approach side-steps issues of multi-valuedness and singularities. This paper ends with a brief example of the controlled bouncing ball to illustrate the theory.

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