Abstract
The damped van der Pol oscillator is a chaotic non-linear system. Small perturbations in initial conditions may result in wildly different trajectories. 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 artificial intelligence is a feedforward and 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 deterministic artificial intelligence employing three different online parameter estimation algorithms. Our evaluation criteria include mean absolute error between the target trajectory and the response oscillator trajectory over time. Two algorithms performed better than the benchmark with necessary discussion of the conditions under which they perform best. Recursive least squares with exponential forgetting had the lowest mean absolute error overall, with a 2.46% reduction in error compared to the baseline, feedforward without deterministic artificial intelligence. While least mean squares with normalized gradient adaptation had worse initial error in the first 10% of the simulation, after that point it exhibited consistently lower error. Over the last 90% of the simulation, deterministic artificial intelligence with least mean squares with normalized gradient adaptation achieved a 48.7% reduction in mean absolute error compared to baseline.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.