Affine TS Fuzzy Model-Based Estimation and Control of Hindmarsh–Rose Neuronal Model

In this paper, an affine Takagi-Sugeno (TS) fuzzy modeling-based observer and controller are proposed for the estimation and control of a chaotic Hindmarsh-Rose (HR) neuronal model. The main contributions are given as follows. 1) First, an affine TS fuzzy model of the HR chaotic neuronal model is constructed using sector nonlinearity-based approach. 2) Based on the constructed TS fuzzy model, a TS fuzzy observer is designed for simultaneous state and parameter estimation of HR neuronal model for unmeasurable state and parameters. 3) In the same way, a novel affine TS fuzzy model-based output feedback control law is designed with observed state and parameters where the exponential stability of the designs are guaranteed by Lyapunov approach. 4) Finally, numerical simulations are conducted to illustrate the observation and stimulation with regular and fast spiking trains and annihilation of the membrane potential.