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We establish a geometric Pontryagin maximum principle for discrete timeoptimal control problems on finite dimensional smooth manifolds under thefollowing three types of constraints: a) constraints on the states pointwise intime, b) constraints on the control actions pointwise in time, c) constraintson the frequency spectrum of the optimal control trajectories. Our prooffollows, in spirit, the path to establish geometric versions of the Pontryaginmaximum principle on smooth manifolds indicated in [Cha11] in the context ofcontinuous-time optimal control.

A simple proof of the discrete time geometric Pontryagin maximum principle on smooth manifolds