Robust observer-based tracking control of hodgkin-huxley neuron systems under environmental disturbances

A nervous system consists of a large number of highly interconnected nerve cells. Nerve cells communicate by generation and transmission of short electrical pulses (action potential). In addition, membrane voltage is the only measurable state in nervous systems. A robust observer-based model reference tracking control is proposed for Hodgkin-Huxley (HH) neuron systems to generate a desired reference response in spite of environmental noises, uncertain initial values, and diffusion currents from other interconnected nerve cells. In order to simplify the robust tracking control design of nonlinear stochastic HH neuron systems, a fuzzy interpolation method is employed to interpolate several linear stochastic systems to approximate a nonlinear stochastic HH neuron system so that the nonlinear robust tracking control problem can be solved by the linear matrix inequality (LMI) technique with the help of Robust Control Toolbox in Matlab. The proposed robust observer-based tracking control scheme can provide new methods for desired action potential generation, suppression of oscillations, and blockage of action potential transmission under environmental noise and diffusion currents. These new methods are useful for patients with different neuron system dysfunctions. Finally, three simulation examples of tracking control of nervous systems are given to illustrate the design procedure and confirm the tracking performance of the proposed method.