Abstract
The approximate Prediction-Based Control method (aPBC) is the continuous-time version of the well-known Prediction-Based Chaos Control method applied to stabilize periodic orbits of nonlinear dynamical systems. The method is based on estimating future states of the free system response of continuous-time systems using the solution from the Runge-Kutta implicit method in real time. Some aspects of aPBC are evaluated in the present work, particularly its robustness to low future states estimation precision is exemplified.
Highlights
Oscillatory systems are typical in many problems of engineering, biological sciences, physics, economy, and other areas [1,2,3,4,5,6,7]
In [28], we proposed the approximate Prediction-Based Control with a methodology based on the implicit Runge-Kutta method and state estimation applied to predict future states for the free system in real time based on system model
We use the forced van der Pol oscillator as case study to show an unstable periodic orbits (UPOs) that cannot be stabilized by the Delayed Feedback Control (DFC) method due to the odd-number limitation and is stabilized using the approximated Prediction-Based Control (aPBC)
Summary
Oscillatory systems are typical in many problems of engineering, biological sciences, physics, economy, and other areas [1,2,3,4,5,6,7]. The authors claim that aPBC is the continuous-time applicable version of PBC because it uses prediction and stabilizes free system UPOs, ideally, vanishing steady state control effort. This work presents an UPO of the forced van der Pol oscillator with one of the Floquet multipliers larger than +1 that is stabilized by the aPBC and could not be stabilized by the DFC with constant control gain following the procedures proposed in [18,19,20].
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