  This paper presents a framework to perform bifurcation analysis in laboratory
experiments or simulations. We employ control-based continuation to study the
dynamics of a macroscopic variable of a microscopically defined model,
exploring the potential viability of the underlying feedback control techniques
in an experiment. In contrast to previous experimental studies that used
iterative root-finding methods on the feedback control targets, we propose a
feedback control law that is inherently non-invasive. That is, the control
discovers the location of equilibria and stabilizes them simultaneously. We
call the proposed control zero-in-equilibrium feedback control and we prove
that it is able to stabilize branches of equilibria, except at singularities of
codimension n+1, where n is the number of state space dimensions the feedback
can depend on.
  We apply the method to a simulated evacuation scenario were pedestrians have
to reach an exit after maneuvering left or right around an obstacle. The
scenario shows a hysteresis phenomenon with bistability and tipping between two
possible steady pedestrian flows in microscopic simulations.
  We demonstrate for the evacuation scenario that the proposed control law is
able to uniformly discover and stabilize steady flows along the entire branch,
including points where other non-invasive approaches to feedback control become
singular.
