  We apply the framework of optimal nonlinear control to steer the dynamics of
a whole-brain network of FitzHugh-Nagumo oscillators. Its nodes correspond to
the cortical areas of an atlas-based segmentation of the human cerebral cortex,
and the inter-node coupling strengths are derived from Diffusion Tensor Imaging
data of the connectome of the human brain. Nodes are coupled using an additive
scheme without delays and are driven by background inputs with fixed mean and
additive Gaussian noise. Optimal control inputs to nodes are determined by
minimizing a cost functional that penalizes the deviations from a desired
network dynamic, the control energy, and spatially non-sparse control inputs.
Using the strength of the background input and the overall coupling strength as
order parameters, the network's state-space decomposes into regions of low and
high activity fixed points separated by a high amplitude limit cycle all of
which qualitatively correspond to the states of an isolated network node. Along
the borders, however, additional limit cycles, asynchronous states and
multistability can be observed. Optimal control is applied to several
state-switching and network synchronization tasks, and the results are compared
to controllability measures from linear control theory for the same connectome.
We find that intuitions from the latter about the roles of nodes in steering
the network dynamics, which are solely based on connectome features, do not
generally carry over to nonlinear systems, as had been previously implied.
Instead, the role of nodes under optimal nonlinear control critically depends
on the specified task and the system's location in state space. Our results
shed new light on the controllability of brain network states and may serve as
an inspiration for the design of new paradigms for non-invasive brain
stimulation.
