  We present an Equation/Variable free machine learning (EVFML) framework for
the control of the collective dynamics of complex/multiscale systems modelled
via microscopic/agent-based simulators. The approach obviates the need for
construction of surrogate, reduced-order models.~The proposed implementation
consists of three steps: (A) from high-dimensional agent-based simulations,
machine learning (in particular, non-linear manifold learning (Diffusion Maps
(DMs)) helps identify a set of coarse-grained variables that parametrize the
low-dimensional manifold on which the emergent/collective dynamics evolve. The
out-of-sample extension and pre-image problems, i.e. the construction of
non-linear mappings from the high-dimensional input space to the
low-dimensional manifold and back, are solved by coupling DMs with the Nystrom
extension and Geometric Harmonics, respectively; (B) having identified the
manifold and its coordinates, we exploit the Equation-free approach to perform
numerical bifurcation analysis of the emergent dynamics; then (C) based on the
previous steps, we design data-driven embedded wash-out controllers that drive
the agent-based simulators to their intrinsic, imprecisely known, emergent
open-loop unstable steady-states, thus demonstrating that the scheme is robust
against numerical approximation errors and modelling uncertainty.~The
efficiency of the framework is illustrated by controlling emergent unstable (i)
traveling waves of a deterministic agent-based model of traffic dynamics, and
(ii) equilibria of a stochastic financial market agent model with mimesis.
