Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Chaotic Van Der Pol Oscillator Control Algorithm Comparison

Version 1 : Received: 26 January 2023 / Approved: 2 February 2023 / Online: 2 February 2023 (06:17:48 CET)

A peer-reviewed article of this Preprint also exists.

Ribordy, L.; Sands, T. Chaotic van der Pol Oscillator Control Algorithm Comparison. Dynamics 2023, 3, 202-213. Ribordy, L.; Sands, T. Chaotic van der Pol Oscillator Control Algorithm Comparison. Dynamics 2023, 3, 202-213.

DOI: https://doi.org/10.3390/dynamics3010012

Abstract

The Van der Pol oscillator is a chaotic non-linear system. Small perturbations in initial conditions may result in wildly different trajectories. Because of its chaotic nature, controlling, or forcing, the behavior of a Van der Pol oscillator is difficult to achieve through traditional adaptive control methods. Connecting two Van der Pol oscillators together where the output of one oscillator, the driver, drives the behavior of its partner, the responder, is a proven technique for controlling the Van der Pol oscillator. Deterministic AI (DAI) is an adaptive feedback control method that leverages the known physics of the Van der Pol system to learn optimal system parameters for the forcing function. We assessed the performance of DAI employing three different online parameter estimation algorithms. Our evaluation criteria include mean absolute error (MAE) between the target trajectory and the response oscillator trajectory over time. RLS with exponential forgetting (RLS-EF) had the lowest MAE overall, with a 2.46% reduction in error. However, another method was notable. Least Mean Squares with normalized gradient adaptation (LMS-NG) had worse initial error in the first 10% of the simulation, but after that point had consistently better performance. We found that over the last 90% of the simulation, DAI with LMS-NG had a 48.7% reduction in MAE compared to feedforward alone.

Keywords

chaotic systems; Van der Pol oscillator; drive-response; synchronization of chaotic systems; global chaos synchronization; deterministic artificial intelligence; feedforward; feedback; non-linear adaptive control; online estimation; recursive least squares (RLS); exponential forgetting; Kalman filter; least mean squares (LMS).

Subject

PHYSICAL SCIENCES, Applied Physics

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