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Comparison of Deep Learning and Deterministic Algorithms for Control Modeling
Controlling nonlinear dynamics arises in various engineering fields. We present efforts to model the forced van der Pol system control using physics-informed neural networks (PINN) compared to benchmark methods, including idealized nonlinear feedforward (FF) control, linearized feedback control (FB)...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9459824/ https://www.ncbi.nlm.nih.gov/pubmed/36080819 http://dx.doi.org/10.3390/s22176362 |
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author | Zhai, Hanfeng Sands, Timothy |
author_facet | Zhai, Hanfeng Sands, Timothy |
author_sort | Zhai, Hanfeng |
collection | PubMed |
description | Controlling nonlinear dynamics arises in various engineering fields. We present efforts to model the forced van der Pol system control using physics-informed neural networks (PINN) compared to benchmark methods, including idealized nonlinear feedforward (FF) control, linearized feedback control (FB), and feedforward-plus-feedback combined (C). The aim is to implement circular trajectories in the state space of the van der Pol system. A designed benchmark problem is used for testing the behavioral differences of the disparate controllers and then investigating controlled schemes and systems of various extents of nonlinearities. All methods exhibit a short initialization accompanying arbitrary initialization points. The feedforward control successfully converges to the desired trajectory, and PINN executes good controls with higher stochasticity observed for higher-order terms based on the phase portraits. In contrast, linearized feedback control and combined feed-forward plus feedback failed. Varying trajectory amplitudes revealed that feed-forward, linearized feedback control, and combined feed-forward plus feedback control all fail for unity nonlinear damping gain. Traditional control methods display a robust fluctuation for higher-order terms. For some various nonlinearities, PINN failed to implement the desired trajectory instead of becoming “trapped” in the phase of small radius, yet idealized nonlinear feedforward successfully implemented controls. PINN generally exhibits lower relative errors for varying targeted trajectories. However, PINN also shows evidently higher computational burden compared with traditional control theory methods, with at least more than 30 times longer control time compared with benchmark idealized nonlinear feed-forward control. This manuscript proposes a comprehensive comparative study for future controller employment considering deterministic and machine learning approaches. |
format | Online Article Text |
id | pubmed-9459824 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-94598242022-09-10 Comparison of Deep Learning and Deterministic Algorithms for Control Modeling Zhai, Hanfeng Sands, Timothy Sensors (Basel) Article Controlling nonlinear dynamics arises in various engineering fields. We present efforts to model the forced van der Pol system control using physics-informed neural networks (PINN) compared to benchmark methods, including idealized nonlinear feedforward (FF) control, linearized feedback control (FB), and feedforward-plus-feedback combined (C). The aim is to implement circular trajectories in the state space of the van der Pol system. A designed benchmark problem is used for testing the behavioral differences of the disparate controllers and then investigating controlled schemes and systems of various extents of nonlinearities. All methods exhibit a short initialization accompanying arbitrary initialization points. The feedforward control successfully converges to the desired trajectory, and PINN executes good controls with higher stochasticity observed for higher-order terms based on the phase portraits. In contrast, linearized feedback control and combined feed-forward plus feedback failed. Varying trajectory amplitudes revealed that feed-forward, linearized feedback control, and combined feed-forward plus feedback control all fail for unity nonlinear damping gain. Traditional control methods display a robust fluctuation for higher-order terms. For some various nonlinearities, PINN failed to implement the desired trajectory instead of becoming “trapped” in the phase of small radius, yet idealized nonlinear feedforward successfully implemented controls. PINN generally exhibits lower relative errors for varying targeted trajectories. However, PINN also shows evidently higher computational burden compared with traditional control theory methods, with at least more than 30 times longer control time compared with benchmark idealized nonlinear feed-forward control. This manuscript proposes a comprehensive comparative study for future controller employment considering deterministic and machine learning approaches. MDPI 2022-08-24 /pmc/articles/PMC9459824/ /pubmed/36080819 http://dx.doi.org/10.3390/s22176362 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Zhai, Hanfeng Sands, Timothy Comparison of Deep Learning and Deterministic Algorithms for Control Modeling |
title | Comparison of Deep Learning and Deterministic Algorithms for Control Modeling |
title_full | Comparison of Deep Learning and Deterministic Algorithms for Control Modeling |
title_fullStr | Comparison of Deep Learning and Deterministic Algorithms for Control Modeling |
title_full_unstemmed | Comparison of Deep Learning and Deterministic Algorithms for Control Modeling |
title_short | Comparison of Deep Learning and Deterministic Algorithms for Control Modeling |
title_sort | comparison of deep learning and deterministic algorithms for control modeling |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9459824/ https://www.ncbi.nlm.nih.gov/pubmed/36080819 http://dx.doi.org/10.3390/s22176362 |
work_keys_str_mv | AT zhaihanfeng comparisonofdeeplearninganddeterministicalgorithmsforcontrolmodeling AT sandstimothy comparisonofdeeplearninganddeterministicalgorithmsforcontrolmodeling |