Controlling chaos in space-clamped FitzHugh–Nagumo neuron by adaptive passive method

De-min, Wei; Luo, Xiao; Zhang, Chao; Qin, Ying

doi:10.1016/j.nonrwa.2009.03.029

Cited by 38 publications

(26 citation statements)

References 19 publications

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“…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. It is proved that the equivalent system can be asymptotically stabilized at any desired fixed state, which means that, synchronization can be succeeded.…”

Section: Introductionmentioning

confidence: 99%

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

Rigatos

2014

Cogn Neurodyn

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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.

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Section: Introductionmentioning

confidence: 99%

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

Rigatos

2014

Cogn Neurodyn

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“…For this reason, designing simple and available control input is extremely relevant for experimental chaos control. Besides the OGY method, many other control algorithms have been proposed in recent years to control chaotic systems, such as PC method [9][10][11], feedback approach [12,13], adaptive control [14][15][16], linear state space feedback [17], backstepping method [18], nonlinear feedback control [19], sliding mode control [20,21], neural network control [22], fuzzy logic control [23], robust control [24][25][26][27][28][29][30], passivity theory control [31], adaptive passive control [32], time-delay feedback approach [33,34], multiple delay feedback control [35], double delayed feedback control [36], hybrid control [37], etc. These control algorithms can be used to stabilize a desired unstable periodic orbit (UPO) embedded within a chaotic attractor.…”

Section: Introductionmentioning

confidence: 99%

Single state feedback stabilization of unified chaotic systems and circuit implementation

Jing

Fan

et al. 2014

Open Physics

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This paper focuses on the single state feedback stabilization problem of uni ed chaotic system and circuit implementation. Some stabilization conditions will be derived via the single state feedback control scheme. The robust performance of controlled uni ed chaotic systems with uncertain parameter will be investigated based on maximum and minimum analysis of uncertain parameter, the robust controller which only requires information of a state of the system is proposed and the controller is linear. Both the uni ed chaotic system and the designed controller are synthesized and implemented by an analog electronic circuit which is simpler because only three variable resistors are required to be adjusted. The numerical simulation and control in MATLAB/Simulink is then provided to show the e ectiveness and feasibility of the proposed method which is robust against some uncertainties. The results presented in this paper improve and generalize the corresponding results of recent works.

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“…The tracking problem is usually divided into two sub-problems: state tracking and output tracking, which deal with the stabilization of the system outputs or states to any reference output or desired state (especially at an equilibrium point) [1][2][3][4]. The stabilization problem has been extensively studied for both linear and nonlinear systems due to its relative simplicity.…”

Section: Introductionmentioning

confidence: 99%

Optimal time-varying P-controller for a class of uncertain nonlinear systems

Miah

Gueaieb

2014

Int. J. Control Autom. Syst.

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In this manuscript, an optimal time-varying P-controller is presented for a class of continuous-time underactuated nonlinear systems in the presence of process noise associated with systems' inputs. This is a state feedback control strategy where the optimization is performed on a time-varying feedback operator (herein called the feedback control gain). The main goal of the current manuscript is to provide a framework for multi-input multi-output nonlinear systems which yields a satisfactory tracking performance based on the optimal time-varying feedback control gain. Unlike other feedback control techniques that perform dynamic linearization of system models, the proposed time-varying P-controller provides the full-state feedback control to the original nonlinear system model. Hence, this P-controller guarantees global asymptotic statetracking. Furthermore, the bounded system's process noise is taken into consideration to measure the controller's robustness. The proposed P-controller is tested for its nonlinear trajectory tracking and fixed-point stabilization capabilities with two nonholonomic systems in the presence of actuators' noise.

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Controlling chaos in space-clamped FitzHugh–Nagumo neuron by adaptive passive method

Cited by 38 publications

References 19 publications

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

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

Single state feedback stabilization of unified chaotic systems and circuit implementation

Optimal time-varying P-controller for a class of uncertain nonlinear systems

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