  Experimental continuation encompasses a set of methods that combine control
and continuation to obtain the full bifurcation diagram of a nonlinear system
experimentally, including responses that would be unstable in the system
without feedback control. Such control-based methods thus allow the
experimenter to directly and exhaustively explore the dynamics of the system
without the need for a good mathematical model. The objective of this paper is
twofold, namely (i) to review and present the state-of-the-art methods in a
unified manner and (ii) to introduce a novel experimental derivative-free
arclength continuation procedure, termed arclength control-based continuation.
These methods are also demonstrated and compared on an electronic Duffing
oscillator and a clamped thin plate featuring geometrical nonlinearity.
Finally, the current state of the art is reflected upon, and the challenges
lying ahead for this growing field are discussed.
