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)...

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Vydáno v:Sensors (Basel, Switzerland) Ročník 22; číslo 17; s. 6362
Hlavní autoři: Zhai, Hanfeng, Sands, Timothy
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 24.08.2022
MDPI
Témata:
Algorithms
Analysis
Blended learning
Complex systems
Control theory
Controllers
Deep learning
deterministic control
Machine learning
Neural networks
nonlinear control
Physics
physics-informed neural networks
Systems stability
van der Pol dynamics
United States
ISSN:1424-8220, 1424-8220
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Shrnutí: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.
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ISSN:1424-8220
1424-8220
DOI:10.3390/s22176362