Optimal Control using Composite Bernstein Approximants

Gage MacLin; Venanzio Cichella; Andrew Patterson; Michael Acheson; Irene Gregory

doi:10.48550/arxiv.2407.18081

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Optimal Control using Composite Bernstein Approximants

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Optimal Control using Composite Bernstein Approximants

Gage MacLin, Venanzio Cichella, Andrew Patterson, Michael Acheson and Irene Gregory

arXiv.org

Cornell University

07/25/2024

DOI: 10.48550/arxiv.2407.18081

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

In this work, we present composite Bernstein polynomials as a direct collocation method for approximating optimal control problems. An analysis of the convergence properties of composite Bernstein polynomials is provided, and beneficial properties of composite Bernstein polynomials for the solution of optimal control problems are discussed. The efficacy of the proposed approximation method is demonstrated through a bang-bang example. Lastly, we apply this method to a motion planning problem, offering a practical solution that emphasizes the ability of this method to solve complex optimal control problems.

Computer Science - Numerical Analysis

Computer Science - Systems and Control

Mathematics - Numerical Analysis

Mathematics - Optimization and Control

Details

Title: Subtitle: Optimal Control using Composite Bernstein Approximants
Creators: Gage MacLin - University of Iowa
Venanzio Cichella - University of Iowa
Andrew Patterson - Langley Research Center
Michael Acheson - Langley Research Center
Irene Gregory - Langley Research Center
Resource Type: Preprint
Publication Details: arXiv.org
DOI: 10.48550/arxiv.2407.18081
eISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 07/25/2024
Academic Unit: Mechanical Engineering
Record Identifier: 9984691556302771

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