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Robust control of chaos in modified Fitzhugh-Nagumo neuron model under external electrical stimulation based on internal model principle. (English) Zbl 1227.93033

Summary: This paper treats the question of robust control of chaos in modified FitzHugh-Nagumo neuron model under external electrical stimulation based on internal model principle. We first present the solution of the global robust output regulation problem for output feedback system with nonlinear exosystem. Then, we show that the robust control problem for the modified FitzHugh-Nagumo neuron model can be formulated as the global robust output regulation problem and the solvability conditions for the output regulation problem for the modified FitzHugh-Nagumo neuron model are all satisfied. We apply the obtained output regulation results to the control problem for modified FitzHugh-Nagumo neuron model. Finally, an output feedback control law is designed for the modified FitzHugh-Nagumo neuron model to achieve global stability of the closed-loop system in the presence of uncertain parameters and external stimulus. An example is shown that the proposed algorithm can completely reject the external electrical stimulation generated from a Van der Pol circuit.

MSC:

93B35 Sensitivity (robustness)
93C15 Control/observation systems governed by ordinary differential equations
93B52 Feedback control
93D15 Stabilization of systems by feedback
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