Robust synchronization of coupled neural oscillators using the derivative-free nonlinear Kalman Filter

Abstract

A synchronizing control scheme for coupled neural oscillators of the FitzHugh-Nagumo type is proposed. Using differential flatness theory the dynamical model of two coupled neural oscillators is transformed into an equivalent model in the linear canonical (Brunovsky) form. A similar linearized description is succeeded using differential geometry methods and the computation of Lie derivatives. For such a model it becomes possible to design a state feedback controller that assures the synchronization of the membrane's voltage variations for the two neurons. To compensate for disturbances that affect the neurons' model as well as for parametric uncertainties and variations a disturbance observer is designed based on Kalman Filtering. This consists of implementation of the standard Kalman Filter recursion on the linearized equivalent model of the coupled neurons and computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. After estimating the disturbance terms in the neurons' model their compensation becomes possible. The performance of the synchronization control loop is tested through simulation experiments.

Lag synchronization of coupled time-delayed FitzHugh–Nagumo neural networks via feedback control

“…In the literature, the subject of neuronal synchronization, using the FHN model, has been intensively examined as a potential application in cognitive engineering 1,20,28,47,57 . Researchers have developed adaptive 20,41 , nonlinear 28 , robust control 23 , neuralnetwork-, fuzzy 74 , and observer-based control schemes 63 to study the synchronization phenomenon in FHN www.nature.com/scientificreports/ neurons under external electrical stimulations. However, these conventional methodologies were developed for two or three coupled neurons and cannot guarantee synchronization of distant neurons if used for synchronizing the activity of networks of neurons because the mathematical models ignore the time delays arising from the separation between coupled neurons, and hence cannot synchronize distant FHN neurons.…”

“…Therefore, synchronization can be considered as the basis for signal transmission and processing in both healthy and abnormal brains 20 . For instance, previous studies found synchronization in the brain regions including hippocampal and olfactory 22 , and it has been reported that brain disorders and disorder in body functionalities such as heart rhythm and gait could be caused by the absence of synchronization between neurons 23 . Furthermore, past research showed that certain brain diseases, such as Alzheimer's disease, epilepsy, Parkinson's, autism, and schizophrenia could be caused due to abnormal/ absence neural synchronization 20,22,[24][25][26] .…”

Complex Synchronization of a Ring-Structured Network of FitzHugh-Nagumo Neurons With Single-and Dual-State Gap Junctions Under Ionic Gates and External Electrical Disturbance

“…In a neuronal system, synchronization might be the basis of several complex mechanisms of both normal and abnormal brain functions [27]. For instance, synchronization occurs in the olfactory and hippocampal regions of the brain [7], [29], [30], and it has been reported previously that the absence of synchronization between neurons can cause brain disorders, affecting body functionality, such as gait or heart rhythm [31]. Furthermore, brain diseases like epilepsy, Parkinson's disease, schizophrenia, and autism, are disorders caused by a lack of neuronal synchronization [7], [27], [32], [33].…”

“…Therefore, the synchronization phenomenon plays a critical role in processing the brain's signals, to ensure efficient communications between neurons [46], [47]. Furthermore, coupling between neurons can greatly affect the dynamic properties of a neuronal network [31].…”

Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control

“…Since the pioneering work of Pecora and Carrol (1990), much attention have been attracted to synchronization due to its wide applications in engineering such as secure communication, biological systems, information processing (Yan and Wang 2014;Yang et al 2011bYang et al , 2014Liao and Huang 1999;Cao et al 2013;Li et al 2013;Rigatos 2014;Xu 2014. In Pecora and Carroll (1990), complete synchronization (synchronization for brief) was proposed, the mechanism of which is this: a chaotic system, called the driver (or master), generates a signal sent over a channel to a responder (or slave) which is identical with the driver, then the responder uses this signal to control itself so that it oscillates in a synchronized manner with the driver.…”