Effects of Controller-Induced Dynamics on Experimental Bifurcation Analysis

Control-based continuation (CBC) is an experimental method that uses feedback control to probe the dynamics of a physical system. CBC relies on finding control targets that render the control system noninvasive, recovering the naturally occurring system behaviours without modifying their geometry or location. Here, we highlight a case where a CBC experiment fails due to the controller-inducing spurious, invasive dynamics in the system. A limit cycle in a slow–fast system is controlled successfully; however, the controller causes it to collapse through a canard explosion in the prediction step of a continuation. We propose strategies to overcome this issue and use it as a case study to highlight how control strategies can impact the results of an experimental bifurcation analysis.