Analysis and chaos control of a four-dimensional magnetohydrodynamic model with hyperchaotic solutions

In this paper, the dynamical behavior of a four-dimensional magnetohydrodynamic model, consisting of a generalized Lorenz model, is investigated. A nonlinear dynamical analysis is performed using Lyapunov exponents and bifurcation diagrams, focusing on the chaotic and hyperchaotic behaviors associated with the bifurcation parameter k1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( k_{1} \right) $$\end{document} that couples the equations of fluid displacement to the induced magnetic field. The State-dependent Riccati Equation (SDRE) and the Optimal Linear Feedback Control (OLFC) techniques are considered to design the state feedback control system that stabilizes the system to a previously defined orbit. The performance of the control systems are compared showing that the OLFC presents better results.