Guiding Experiments using Continuation

Abstract: The recently developed method of control based continuation allows the continuation of periodic solutions directly in physical experiments. The key ideas of this approach are (1) to introduce a control scheme that locally stabilizes periodic solutions without perturbing them, and (2) to use continuation to guide the experiment around folds and through bifurcation points. The experiment runs asynchronously from the actual continuation method, which communicates with the experiment by setting a control target and by taking measurements. In this talk we will present results obtained in a lab experiment of an impact oscillator that exhibits a large hysteresis loop. We will indicate current challenges with this method and how we intend to tackle them.