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Closed-loop neurotechnology requires the capability to predict the stateevolution and its regulation under (possibly) partial measurements. There isevidence that neurophysiological dynamics can be modeled by fractional-orderdynamical systems. Therefore, we propose to establish a separation principlefor discrete-time fractional-order dynamical systems, which are inherentlynonlinear and are able to capture spatiotemporal relations that exhibitnon-Markovian properties. The separation principle states that the problems ofcontroller and state estimator design can be done independently of each otherwhile ensuring proper estimation and control in closed-loop setups. Lastly, weillustrate, as proof-of-concept, the application of the separation principlewhen designing controllers and estimators for these classes of systems in thecontext of neurophysiological data. In particular, we rely on real data toderive the models used to assess and regulate the evolution of closed-loopneurotechnologies based on electroencephalographic data.

A Separation Principle for Discrete-Time Fractional-Order Dynamical Systems and its Implications to Closed-loop Neurotechnology