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

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) constrai...

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Bibliographic Details
Published in:	Automatica (Oxford) Vol. 114; p. 108791
Main Authors:	P.K., Mishal Assif, Chatterjee, Debasish, Banavar, Ravi
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01-04-2020
Subjects:	Optimal control Pontryagin maximum principle Smooth manifolds Pontryagin maximum principle Smooth manifolds Optimal control
Online Access:	Get full text
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Summary:	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 Chang (2011) in the context of continuous-time optimal control.
ISSN:	0005-1098 1873-2836
DOI:	10.1016/j.automatica.2019.108791