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A frequency‐constrained geometric Pontryagin maximum principle on matrix Lie groups
Author(s) -
Paruchuri Pradyumna,
Kotpalliwar Shruti,
Phogat Karmvir Singh,
Chatterjee Debasish,
Banavar Ravi
Publication year - 2020
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5085
Subject(s) - pointwise , mathematics , maximum principle , optimal control , pontryagin's minimum principle , lie group , control theory (sociology) , trajectory , mathematical optimization , control (management) , mathematical analysis , computer science , pure mathematics , physics , astronomy , artificial intelligence
We present a geometric discrete‐time Pontryagin maximum principle (PMP) on matrix Lie groups that incorporates frequency constraints on the control trajectories 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 numerical techniques to arrive at optimal trajectories. We demonstrate our theoretical results with numerical simulations on the optimal trajectory generation of a wheeled inverted pendulum and an attitude control problem of a spacecraft on the Lie group SO (3).