A simple proof of the discrete time geometric Pontryagin maximum principle on smooth manifolds. (April 2020)

• Record Type: Journal Article
• Authors: P.K., Mishal Assif; Chatterjee, Debasish; Banavar, Ravi
• Is Part Of: Automatica. Volume 114(2020)
• Publication Date: 2020-04
• Subjects: Optimal control -- Pontryagin maximum principle -- Smooth manifolds; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2019.108791
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: 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.