---
abstract: 'In this article we present a geometric discrete-time Pontryagin maximum principle (PMP) on matrix Lie groups that incorporates frequency constraints on the controls in addition to pointwise constraints on the states and control actions directly at the stage of the problem formulation. This PMP gives first order necessary conditions for optimality, and leads to two-point boundary value problems that may be solved by shooting techniques to arrive at optimal trajectories. We validate our theoretical results with a numerical experiment on the attitude control of a spacecraft on the Lie group $\SO(3)$.'
author:
- 'Shruti Kotpalliwar, Pradyumna Paruchuri, Karmvir Singh Phogat, Debasish Chatterjee, Ravi Banavar [^1]'
bibliography:
- 'references.bib'
title: '**A frequency-constrained geometric Pontryagin maximum principle on matrix Lie groups[^2]**'
---

Introduction {#sec:the intro}
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Problem setup {#sec:the prob}
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Main result {#sec:main result}
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Proof of the main result {#sec:proof}
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Numerical experiments {#sec:numerical simulations}
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[^1]: Emails: `{shruti, pradyumn, karmvir.p, chatterjee, banavar} @sc.iitb.ac.in`

[^2]: The authors are with Systems & Control Engineering, IIT Bombay, Powai, Mumbai 400076, India, and acknowledge the support of the grant 17ISROC001 from the Indian Space Research Organization.
