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

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 (FODS). Therefore, we propose to establish a separation principle for discrete-time FODS, 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.