Discrete-Time Fractional-Order Dynamical Networks Minimum-Energy State Estimation

Fractional-order dynamical networks are increasingly being used to model and describe processes demonstrating long-term memory or complex interlaced dependencies amongst the spatial and temporal components of a wide variety of dynamical networks. Notable examples include networked control systems or neurophysiological networks which are created using electroencephalographic (EEG) or blood-oxygen-level-dependent (BOLD) data. As a result, the estimation of the states of fractional-order dynamical networks poses an important problem. To this effect, this paper addresses the problem of minimum-energy state estimation for discrete-time fractional-order dynamical networks (DT-FODN), where the state and output equations are affected by an additive noise that is considered to be deterministic, bounded, and unknown. Specifically, we derive the corresponding estimator and show that the resulting estimation error is exponentially input-to-state stable with respect to the disturbances and to a signal that is decreasing with the increase of the accuracy of the adopted approximation model. An illustrative example shows the effectiveness of the proposed method on real-world neurophysiological networks.