A simple proof of the discrete time geometric Pontryagin maximum principle on smooth manifolds
Provides a theoretical foundation for discrete-time optimal control on manifolds, relevant to control theory and robotics, but is an incremental extension of existing continuous-time work.
The paper proves a geometric Pontryagin maximum principle for discrete-time optimal control on smooth manifolds with state, control, and frequency constraints, extending continuous-time results to discrete time.
We establish a geometric Pontryagin maximum principle for discrete time optimal control problems on finite dimensional smooth manifolds under the following three types of constraints: a) constraints on the states pointwise in time, b) constraints on the control actions pointwise in time, c) constraints on the frequency spectrum of the optimal control trajectories. Our proof follows, in spirit, the path to establish geometric versions of the Pontryagin maximum principle on smooth manifolds indicated in [Cha11] in the context of continuous-time optimal control.