A Type II Hamiltonian Variational Principle and Adjoint Systems for Lie Groups

Journal Article · 14 February 2025 · Journal of Dynamical and Control Systems

DOI: https://doi.org/10.1007/s10883-025-09730-7 · OSTI ID:2520138

Tran, Brian K.  ^[1]; Leok, Melvin ^[2]

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1. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
2. Univ. of California, San Diego, CA (United States)

We present a novel Type II variational principle on the cotangent bundle of a Lie group which enforces Type II boundary conditions, i.e., fixed initial position and final momentum. In general, such Type II variational principles are only globally defined on vector spaces or locally defined on general manifolds; however, by left translation, we are able to define this variational principle globally on cotangent bundles of Lie groups. Type II boundary conditions are particularly important for adjoint sensitivity analysis, which is our motivating application. As such, we additionally discuss adjoint systems on Lie groups, their properties, and how they can be used to solve optimization problems subject to dynamics on Lie groups.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: National Science Foundation (NSF); US Air Force Office of Scientific Research (AFOSR); USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 2520138
• Report Number(s): LA-UR--23-32526
• Journal Information: Journal of Dynamical and Control Systems, Journal Name: Journal of Dynamical and Control Systems Journal Issue: 1 Vol. 31; ISSN 1079-2724
• Publisher: Springer NatureCopyright Statement
• Country of Publication: United States
• Language: English