  Closed-loop neurotechnology requires the capability to predict the state
evolution and its regulation under (possibly) partial measurements. There is
evidence that neurophysiological dynamics can be modeled by fractional-order
dynamical systems. Therefore, we propose to establish a separation principle
for discrete-time fractional-order dynamical systems, which are inherently
nonlinear and are able to capture spatiotemporal relations that exhibit
non-Markovian properties. The separation principle states that the problems of
controller and state estimator design can be done independently of each other
while ensuring proper estimation and control in closed-loop setups. Lastly, we
illustrate, as proof-of-concept, the application of the separation principle
when designing controllers and estimators for these classes of systems in the
context of neurophysiological data. In particular, we rely on real data to
derive the models used to assess and regulate the evolution of closed-loop
neurotechnologies based on electroencephalographic data.
