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2 Archives of Control Sciences

2 2021

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Synchronization of FitzHugh-Nagumo reaction-diffusion systems via one-dimensional linear control law

Ouannas Adel, Mesdoui Fatiha, Momani Shaher, Batiha Iqbal, Grassi Giuseppe

Archives of Control Sciences

2021

Vol. 31, No. 2

333--345

The Fitzhugh-Nagumo model (FN model), which is successfully employed in modeling the function of the so-called membrane potential, exhibits various formations in neuronal networks and rich complex dynamics. This work deals with the problem of control and synchronization of the FN reaction-diffusion model. The proposed control law in this study is designed to be uni-dimensional and linear law for the purpose of reducing the cost of implementation. In order to analytically prove this assertion, Lyapunov’s second method is utilized and illustrated numerically in one- and/or two-spatial dimensions.

Different linear control laws for fractional chaotic maps using Lyapunov functional

Almatroud A. Othman, Ouannas Adel, Grassi Giuseppe, Batiha Iqbal M., Gasri Ahlem, Al-sawalha M. Mossa

Archives of Control Sciences

2021

Vol. 31, No. 4

765--780

Dynamics and control of discrete chaotic systems of fractional-order have received considerable attention over the last few years. So far, nonlinear control laws have been mainly used for stabilizing at zero the chaotic dynamics of fractional maps. This article provides a further contribution to such research field by presenting simple linear control laws for stabilizing three fractional chaotic maps in regard to their dynamics. Specifically, a one-dimensional linear control law and a scalar control law are proposed for stabilizing at the origin the chaotic dynamics of the Zeraoulia-Sprott rational map and the Ikeda map, respectively. Additionally, a two-dimensional linear control law is developed to stabilize the chaotic fractional flow map. All the results have been achieved by exploiting new theorems based on the Lyapunov method as well as on the properties of the Caputo h-difference operator. The relevant simulation findings are implemented to confirm the validity of the established linear control scheme.