Adaptive backstepping sliding mode control for chaos synchronization of two coupled neurons in the external electrical stimulation

Robust Adaptive Control for a Class of Nonlinear Systems Using the Backstepping Method

“…New adaptive feedforward cancellations (AFC) control providing periodic tracking and/or periodic disturbance rejection is proposed in [10]. In [11], a robust control system combining backstepping and sliding mode control techniques is used to realize the synchronization of two gap junction coupled chaotic FitzHugh-Nagumo (FHN) neurons in the external electrical stimulation. The paper [12] introduces an optimal H  adaptive PID (OHAPID) control scheme for a class of nonlinear chaotic system with uncertainties and external disturbances.…”

“…In recent decades, a large number of papers have studied the problem of robust adaptive control of nonlinear systems (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and references therein). In [1], a new adaptive law based on an optimal control formulation for the minimization of the 2 L norm of the tracking bounded error is considered.…”

Lyapunov-based synchronization of two coupled chaotic Hindmarsh-Rose neurons

“…The backstepping control technique was utilized to achieve the synchronization in coupled FitzHugh-Nagomo neuron system [21] and in coupled Hindmarsh-Rose neuron system [22]. Various sliding mode control laws were also proposed to synchronize the coupled neuron system [23][24][25][26]. In order to synchronize coupled chaotic neuron system with unknown or uncertain parameters, many adaptive and robust control laws were also proposed [27][28][29][30][31].…”

“…In neuroscience, most investigations have focused on the synchronization of two coupled neurons, whose resolution aids in the understanding of the synchronization processes in neural networks [12-31, and reference therein]. The synchronization between interacting neurons can be classified into two types: the first pertains to natural coupling, in which the effects of the synapse types and internal noises on synchronization (self-synchronization) are issues [12][13][14][15][16][17][18]; the second pertains to artificial coupling, in which an explicit control signal is applied in order to archive synchronization [18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Following the first approach, many studies have confirmed that when the intensity of an internal noise exceeds a critical value, the self-synchronization can be achieved [12][13][14].…”

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

“…In Aqil et al (2012) matrix inequalities on the basis of Lyapunov stability theory are used to design a robust synchronizing controller for the model of the coupled FitzHugh-Nagumo neurons. In Yu et al (2012) robust control system combining backstepping and sliding mode control techniques is used to realize the synchronization of two gap junction coupled chaotic FitzHugh-Nagumo neurons under external electrical stimulation. In Wei et al (2010) a Lyapunov function-based control law is introduced, which transforms the FitzHugh-Nagumo neurons into an equivalent passive system.…”