Fractional-order chaos modelization and sliding mode control in a biological enzyme system

Abstract

This paper proposes two main contributions to fractional-order modeling and control of biological systems that may exhibit chaotic behavior. First, a fractional-order chaotic model is designed to represent a biological enzyme using bifurcation diagrams and fractional orders tuning inspired by the available integer order model. This new approach improves the biological model by introducing physical properties specific to fractional order systems such as the memory effect, fractal properties, tissue heterogeneity and non-local behavior. Furthermore, this makes the use of a more effective, robust and powerful fractional-order control easier and more natural. The second main contribution is to propose a fractional-order sliding mode surface in order to derive a sliding mode control (SMC) controller that is able to stabilize this fractional-order biological system asymptotically. We successfully performed the stability analysis using the Lyapunov theory. Numerical simulations using MATLAB are given to demonstrate the efficiency of the proposed fractional-order controller with a drastic improvement in convergence time comparatively to the integer-order counterpart.