A frequency-constrained geometric Pontryagin maximum principle on matrix\n Lie groups

2018/03/08 by Shruti Kotpalliwar, Pradyumna Paruchuri, Kotpalliwar, Shruti +7
Engineering · #Adaptive Control of Nonlinear Systems #Control and Dynamics of Mobile Robots #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1803.03052

openalex publication_date 2018/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we present a geometric discrete-time Pontryagin maximum\nprinciple (PMP) on matrix Lie groups that incorporates frequency constraints on\nthe controls in addition to pointwise constraints on the states and control\nactions directly at the stage of the problem formulation. This PMP gives first\norder necessary conditions for optimality, and leads to two-point boundary\nvalue problems that may be solved by shooting techniques to arrive at optimal\ntrajectories. We validate our theoretical results with a numerical experiment\non the attitude control of a spacecraft on the Lie group SO(3).\n

Related

• A discrete-time Pontryagin maximum principle on matrix Lie groups
• Robust Discrete-Time Pontryagin Maximum Principle on Matrix Lie Groups
• The Discrete-Time Geometric Maximum Principle
• A simple proof of the discrete time geometric Pontryagin maximum principle on smooth manifolds
• On optimal multiplexing of an ensemble of discrete-time constrained\n control systems on matrix Lie groups