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

## TL;DR

This paper establishes a separation principle for discrete-time fractional-order dynamical systems, enabling independent design of controllers and estimators, with applications demonstrated on neurophysiological data for closed-loop neurotechnology.

## Contribution

It introduces a novel separation principle for nonlinear fractional-order systems, facilitating independent controller and estimator design in neurotechnology applications.

## Key findings

- Separation principle holds for fractional-order systems.
- Application to EEG data demonstrates practical viability.
- Improved control and estimation in neurotechnology systems.

## Abstract

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.