Chaotic van der Pol Oscillator Control Algorithm Comparison
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Dynamics |
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| Online Access: | https://www.mdpi.com/2673-8716/3/1/12 |
| _version_ | 1797612344791007232 |
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| author | Lauren Ribordy Timothy Sands |
| author_facet | Lauren Ribordy Timothy Sands |
| author_sort | Lauren Ribordy |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T06:39:57Z |
| format | Article |
| id | doaj.art-83f05702bf9c44dda8bf44411e5dfa4d |
| institution | Directory Open Access Journal |
| issn | 2673-8716 |
| language | English |
| last_indexed | 2024-03-11T06:39:57Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Dynamics |
| spelling | doaj.art-83f05702bf9c44dda8bf44411e5dfa4d2023-11-17T10:40:15ZengMDPI AGDynamics2673-87162023-03-013120221310.3390/dynamics3010012Chaotic van der Pol Oscillator Control Algorithm ComparisonLauren Ribordy0Timothy Sands1Department of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USADepartment of Mechanical Engineering (SCPD), Stanford University, Stanford, CA 94305, USAThe 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.https://www.mdpi.com/2673-8716/3/1/12chaotic systemsvan der Pol oscillatordrive-responsesynchronization of chaotic systemsdeterministic artificial intelligencenon-linear adaptive control |
| spellingShingle | Lauren Ribordy Timothy Sands Chaotic van der Pol Oscillator Control Algorithm Comparison Dynamics chaotic systems van der Pol oscillator drive-response synchronization of chaotic systems deterministic artificial intelligence non-linear adaptive control |
| title | Chaotic van der Pol Oscillator Control Algorithm Comparison |
| title_full | Chaotic van der Pol Oscillator Control Algorithm Comparison |
| title_fullStr | Chaotic van der Pol Oscillator Control Algorithm Comparison |
| title_full_unstemmed | Chaotic van der Pol Oscillator Control Algorithm Comparison |
| title_short | Chaotic van der Pol Oscillator Control Algorithm Comparison |
| title_sort | chaotic van der pol oscillator control algorithm comparison |
| topic | chaotic systems van der Pol oscillator drive-response synchronization of chaotic systems deterministic artificial intelligence non-linear adaptive control |
| url | https://www.mdpi.com/2673-8716/3/1/12 |
| work_keys_str_mv | AT laurenribordy chaoticvanderpoloscillatorcontrolalgorithmcomparison AT timothysands chaoticvanderpoloscillatorcontrolalgorithmcomparison |